LMFDB - Embedded newform 1380.2.t.a.1057.9

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			1057.9
Character	$\chi$	$=$	1380.1057
Dual form			1380.2.t.a.1333.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{3} +(-2.09989 + 0.768407i) q^{5} +(-0.0117285 + 0.0117285i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{3} +(-2.09989 + 0.768407i) q^{5} +(-0.0117285 + 0.0117285i) q^{7} -1.00000i q^{9} +1.72770i q^{11} +(-2.37219 + 2.37219i) q^{13} +(0.941503 - 2.02819i) q^{15} +(1.66583 - 1.66583i) q^{17} -6.73367 q^{19} -0.0165866i q^{21} +(-0.0541507 - 4.79553i) q^{23} +(3.81910 - 3.22714i) q^{25} +(0.707107 + 0.707107i) q^{27} -0.894482i q^{29} +6.90064 q^{31} +(-1.22167 - 1.22167i) q^{33} +(0.0156163 - 0.0336408i) q^{35} +(-0.0575199 + 0.0575199i) q^{37} -3.35478i q^{39} +0.278794 q^{41} +(4.31887 + 4.31887i) q^{43} +(0.768407 + 2.09989i) q^{45} +(-7.61450 - 7.61450i) q^{47} +6.99972i q^{49} +2.35584i q^{51} +(-9.64615 - 9.64615i) q^{53} +(-1.32757 - 3.62798i) q^{55} +(4.76142 - 4.76142i) q^{57} -15.1371i q^{59} -5.91692i q^{61} +(0.0117285 + 0.0117285i) q^{63} +(3.15853 - 6.80414i) q^{65} +(-1.99060 + 1.99060i) q^{67} +(3.42924 + 3.35266i) q^{69} +12.6488 q^{71} +(7.55474 - 7.55474i) q^{73} +(-0.418577 + 4.98245i) q^{75} +(-0.0202632 - 0.0202632i) q^{77} +3.91526 q^{79} -1.00000 q^{81} +(-12.2961 - 12.2961i) q^{83} +(-2.21803 + 4.77810i) q^{85} +(0.632494 + 0.632494i) q^{87} -6.61134 q^{89} -0.0556442i q^{91} +(-4.87949 + 4.87949i) q^{93} +(14.1400 - 5.17420i) q^{95} +(9.80227 - 9.80227i) q^{97} +1.72770 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−2.09989	+	0.768407i	−0.939101	+	0.343642i
$5$	−2.09989	+	0.768407i	−0.939101	+	0.343642i
$6$		0			0
$7$	−0.0117285	+	0.0117285i	−0.00443294	+	0.00443294i	−0.709320	−	0.704887i	$-0.750998\pi$
$7$	−0.0117285	+	0.0117285i	−0.00443294	+	0.00443294i	0.704887	+	0.709320i	$0.250998\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$			1.72770i			0.520920i	0.965485	+	0.260460i	$0.0838742\pi$
$11$			1.72770i			0.520920i	−0.965485	+	0.260460i	$0.916126\pi$
$12$		0			0
$13$	−2.37219	+	2.37219i	−0.657926	+	0.657926i	−0.954889	−	0.296963i	$-0.904026\pi$
$13$	−2.37219	+	2.37219i	−0.657926	+	0.657926i	0.296963	+	0.954889i	$0.404026\pi$
$14$		0			0
$15$	0.941503	−	2.02819i	0.243095	−	0.523678i
$16$		0			0
$17$	1.66583	−	1.66583i	0.404023	−	0.404023i	−0.475625	−	0.879648i	$-0.657778\pi$
$17$	1.66583	−	1.66583i	0.404023	−	0.404023i	0.879648	+	0.475625i	$0.157778\pi$
$18$		0			0
$19$	−6.73367			−1.54481			−0.772405	−	0.635131i	$-0.780946\pi$
$19$	−6.73367			−1.54481			−0.772405	+	0.635131i	$0.780946\pi$
$20$		0			0
$21$		−	0.0165866i		−	0.00361948i
$22$		0			0
$23$	−0.0541507	−	4.79553i	−0.0112912	−	0.999936i
$23$	−0.0541507	−	4.79553i	−0.0112912	−	0.999936i
$24$		0			0
$25$	3.81910	−	3.22714i	0.763820	−	0.645429i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$		−	0.894482i		−	0.166101i	−0.996545	−	0.0830506i	$-0.973534\pi$
$29$		−	0.894482i		−	0.166101i	0.996545	−	0.0830506i	$-0.0264663\pi$
$30$		0			0
$31$	6.90064			1.23939			0.619696	−	0.784842i	$-0.287256\pi$
$31$	6.90064			1.23939			0.619696	+	0.784842i	$0.287256\pi$
$32$		0			0
$33$	−1.22167	−	1.22167i	−0.212665	−	0.212665i
$34$		0			0
$35$	0.0156163	−	0.0336408i	0.00263963	−	0.00568633i
$36$		0			0
$37$	−0.0575199	+	0.0575199i	−0.00945621	+	0.00945621i	−0.711819	−	0.702363i	$-0.752128\pi$
$37$	−0.0575199	+	0.0575199i	−0.00945621	+	0.00945621i	0.702363	+	0.711819i	$0.252128\pi$
$38$		0			0
$39$		−	3.35478i		−	0.537194i
$40$		0			0
$41$	0.278794			0.0435403			0.0217702	−	0.999763i	$-0.493070\pi$
$41$	0.278794			0.0435403			0.0217702	+	0.999763i	$0.493070\pi$
$42$		0			0
$43$	4.31887	+	4.31887i	0.658622	+	0.658622i	0.955054	−	0.296432i	$-0.0957969\pi$
$43$	4.31887	+	4.31887i	0.658622	+	0.658622i	−0.296432	+	0.955054i	$0.595797\pi$
$44$		0			0
$45$	0.768407	+	2.09989i	0.114547	+	0.313034i
$46$		0			0
$47$	−7.61450	−	7.61450i	−1.11069	−	1.11069i	−0.993057	−	0.117632i	$-0.962470\pi$
$47$	−7.61450	−	7.61450i	−1.11069	−	1.11069i	−0.117632	−	0.993057i	$-0.537530\pi$
$48$		0			0
$49$			6.99972i			0.999961i
$50$		0			0
$51$			2.35584i			0.329883i
$52$		0			0
$53$	−9.64615	−	9.64615i	−1.32500	−	1.32500i	−0.909671	−	0.415329i	$-0.863666\pi$
$53$	−9.64615	−	9.64615i	−1.32500	−	1.32500i	−0.415329	−	0.909671i	$-0.636334\pi$
$54$		0			0
$55$	−1.32757	−	3.62798i	−0.179010	−	0.489196i
$56$		0			0
$57$	4.76142	−	4.76142i	0.630666	−	0.630666i
$58$		0			0
$59$		−	15.1371i		−	1.97068i	−0.170607	−	0.985339i	$-0.554573\pi$
$59$		−	15.1371i		−	1.97068i	0.170607	−	0.985339i	$-0.445427\pi$
$60$		0			0
$61$		−	5.91692i		−	0.757584i	−0.925482	−	0.378792i	$-0.876340\pi$
$61$		−	5.91692i		−	0.757584i	0.925482	−	0.378792i	$-0.123660\pi$
$62$		0			0
$63$	0.0117285	+	0.0117285i	0.00147765	+	0.00147765i
$64$		0			0
$65$	3.15853	−	6.80414i	0.391768	−	0.843950i
$66$		0			0
$67$	−1.99060	+	1.99060i	−0.243191	+	0.243191i	−0.818169	−	0.574978i	$-0.805011\pi$
$67$	−1.99060	+	1.99060i	−0.243191	+	0.243191i	0.574978	+	0.818169i	$0.305011\pi$
$68$		0			0
$69$	3.42924	+	3.35266i	0.412832	+	0.403613i
$70$		0			0
$71$	12.6488			1.50113			0.750567	−	0.660795i	$-0.229781\pi$
$71$	12.6488			1.50113			0.750567	+	0.660795i	$0.229781\pi$
$72$		0			0
$73$	7.55474	−	7.55474i	0.884215	−	0.884215i	−0.109745	−	0.993960i	$-0.535003\pi$
$73$	7.55474	−	7.55474i	0.884215	−	0.884215i	0.993960	+	0.109745i	$0.0350034\pi$
$74$		0			0
$75$	−0.418577	+	4.98245i	−0.0483331	+	0.575324i
$76$		0			0
$77$	−0.0202632	−	0.0202632i	−0.00230921	−	0.00230921i
$78$		0			0
$79$	3.91526			0.440502			0.220251	−	0.975443i	$-0.429312\pi$
$79$	3.91526			0.440502			0.220251	+	0.975443i	$0.429312\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−12.2961	−	12.2961i	−1.34967	−	1.34967i	−0.886014	−	0.463659i	$-0.846536\pi$
$83$	−12.2961	−	12.2961i	−1.34967	−	1.34967i	−0.463659	−	0.886014i	$-0.653464\pi$
$84$		0			0
$85$	−2.21803	+	4.77810i	−0.240579	+	0.518257i
$86$		0			0
$87$	0.632494	+	0.632494i	0.0678105	+	0.0678105i
$88$		0			0
$89$	−6.61134			−0.700800			−0.350400	−	0.936600i	$-0.613954\pi$
$89$	−6.61134			−0.700800			−0.350400	+	0.936600i	$0.613954\pi$
$90$		0			0
$91$		−	0.0556442i		−	0.00583310i
$92$		0			0
$93$	−4.87949	+	4.87949i	−0.505979	+	0.505979i
$94$		0			0
$95$	14.1400	−	5.17420i	1.45073	−	0.530861i
$96$		0			0
$97$	9.80227	−	9.80227i	0.995269	−	0.995269i	−0.00471962	−	0.999989i	$-0.501502\pi$
$97$	9.80227	−	9.80227i	0.995269	−	0.995269i	0.999989	+	0.00471962i	$0.00150231\pi$
$98$		0			0
$99$	1.72770			0.173640
$100$		0			0
$101$	8.42053			0.837874			0.418937	−	0.908015i	$-0.362403\pi$
$101$	8.42053			0.837874			0.418937	+	0.908015i	$0.362403\pi$
$102$		0			0
$103$	−11.3577	−	11.3577i	−1.11910	−	1.11910i	−0.991873	−	0.127232i	$-0.959391\pi$
$103$	−11.3577	−	11.3577i	−1.11910	−	1.11910i	−0.127232	−	0.991873i	$-0.540609\pi$
$104$		0			0
$105$	0.0127452	+	0.0348300i	0.00124381	+	0.00339906i
$106$		0			0
$107$	−7.94663	+	7.94663i	−0.768230	+	0.768230i	−0.977795	−	0.209565i	$-0.932795\pi$
$107$	−7.94663	+	7.94663i	−0.768230	+	0.768230i	0.209565	+	0.977795i	$0.432795\pi$
$108$		0			0
$109$	10.3003			0.986589			0.493295	−	0.869862i	$-0.335792\pi$
$109$	10.3003			0.986589			0.493295	+	0.869862i	$0.335792\pi$
$110$		0			0
$111$		−	0.0813454i		−	0.00772096i
$112$		0			0
$113$	6.53608	+	6.53608i	0.614863	+	0.614863i	0.944209	−	0.329346i	$-0.106828\pi$
$113$	6.53608	+	6.53608i	0.614863	+	0.614863i	−0.329346	+	0.944209i	$0.606828\pi$
$114$		0			0
$115$	3.79863	+	10.0285i	0.354224	+	0.935161i
$116$		0			0
$117$	2.37219	+	2.37219i	0.219309	+	0.219309i
$118$		0			0
$119$			0.0390752i			0.00358202i
$120$		0			0
$121$	8.01507			0.728642
$122$		0			0
$123$	−0.197137	+	0.197137i	−0.0177753	+	0.0177753i
$124$		0			0
$125$	−5.53995	+	9.71128i	−0.495508	+	0.868603i
$126$		0			0
$127$	−2.73971	−	2.73971i	−0.243110	−	0.243110i	0.575026	−	0.818135i	$-0.304992\pi$
$127$	−2.73971	−	2.73971i	−0.243110	−	0.243110i	−0.818135	+	0.575026i	$0.804992\pi$
$128$		0			0
$129$	−6.10781			−0.537762
$130$		0			0
$131$	−11.6163			−1.01492			−0.507458	−	0.861676i	$-0.669415\pi$
$131$	−11.6163			−1.01492			−0.507458	+	0.861676i	$0.669415\pi$
$132$		0			0
$133$	0.0789756	−	0.0789756i	0.00684805	−	0.00684805i
$134$		0			0
$135$	−2.02819	−	0.941503i	−0.174559	−	0.0810317i
$136$		0			0
$137$	1.80967	−	1.80967i	0.154611	−	0.154611i	−0.625563	−	0.780174i	$-0.715131\pi$
$137$	1.80967	−	1.80967i	0.154611	−	0.154611i	0.780174	+	0.625563i	$0.215131\pi$
$138$		0			0
$139$		−	5.50003i		−	0.466507i	−0.972416	−	0.233253i	$-0.925063\pi$
$139$		−	5.50003i		−	0.466507i	0.972416	−	0.233253i	$-0.0749371\pi$
$140$		0			0
$141$	10.7685			0.906874
$142$		0			0
$143$	−4.09842	−	4.09842i	−0.342727	−	0.342727i
$144$		0			0
$145$	0.687326	+	1.87832i	0.0570793	+	0.155986i
$146$		0			0
$147$	−4.94955	−	4.94955i	−0.408232	−	0.408232i
$148$		0			0
$149$	1.57524			0.129049			0.0645243	−	0.997916i	$-0.479447\pi$
$149$	1.57524			0.129049			0.0645243	+	0.997916i	$0.479447\pi$
$150$		0			0
$151$	−17.0184			−1.38494			−0.692469	−	0.721448i	$-0.743477\pi$
$151$	−17.0184			−1.38494			−0.692469	+	0.721448i	$0.743477\pi$
$152$		0			0
$153$	−1.66583	−	1.66583i	−0.134674	−	0.134674i
$154$		0			0
$155$	−14.4906	+	5.30250i	−1.16391	+	0.425907i
$156$		0			0
$157$	8.29982	−	8.29982i	0.662398	−	0.662398i	−0.293547	−	0.955945i	$-0.594836\pi$
$157$	8.29982	−	8.29982i	0.662398	−	0.662398i	0.955945	+	0.293547i	$0.0948357\pi$
$158$		0			0
$159$	13.6417			1.08186
$160$		0			0
$161$	0.0568793	+	0.0556091i	0.00448271	+	0.00438261i
$162$		0			0
$163$	−16.4524	+	16.4524i	−1.28865	+	1.28865i	−0.353044	+	0.935607i	$0.614853\pi$
$163$	−16.4524	+	16.4524i	−1.28865	+	1.28865i	−0.935607	+	0.353044i	$0.885147\pi$
$164$		0			0
$165$	3.50410	+	1.62663i	0.272794	+	0.126633i
$166$		0			0
$167$	−3.26933	−	3.26933i	−0.252989	−	0.252989i	0.569206	−	0.822195i	$-0.307251\pi$
$167$	−3.26933	−	3.26933i	−0.252989	−	0.252989i	−0.822195	+	0.569206i	$0.807251\pi$
$168$		0			0
$169$			1.74546i			0.134266i
$170$		0			0
$171$			6.73367i			0.514936i
$172$		0			0
$173$	3.37850	−	3.37850i	0.256862	−	0.256862i	−0.566914	−	0.823777i	$-0.691863\pi$
$173$	3.37850	−	3.37850i	0.256862	−	0.256862i	0.823777	+	0.566914i	$0.191863\pi$
$174$		0			0
$175$	−0.00694275	+	0.0826417i	−0.000524823	+	0.00624712i
$176$		0			0
$177$	10.7035	+	10.7035i	0.804526	+	0.804526i
$178$		0			0
$179$			2.90634i			0.217230i	0.994084	+	0.108615i	$0.0346416\pi$
$179$			2.90634i			0.217230i	−0.994084	+	0.108615i	$0.965358\pi$
$180$		0			0
$181$			4.39491i			0.326671i	0.986571	+	0.163336i	$0.0522254\pi$
$181$			4.39491i			0.326671i	−0.986571	+	0.163336i	$0.947775\pi$
$182$		0			0
$183$	4.18390	+	4.18390i	0.309283	+	0.309283i
$184$		0			0
$185$	0.0765869	−	0.164984i	0.00563078	−	0.0121299i
$186$		0			0
$187$	2.87805	+	2.87805i	0.210464	+	0.210464i
$188$		0			0
$189$	−0.0165866			−0.00120649
$190$		0			0
$191$			7.01334i			0.507467i	0.967274	+	0.253734i	$0.0816587\pi$
$191$			7.01334i			0.507467i	−0.967274	+	0.253734i	$0.918341\pi$
$192$		0			0
$193$	−10.7410	+	10.7410i	−0.773151	+	0.773151i	−0.978656	−	0.205505i	$-0.934116\pi$
$193$	−10.7410	+	10.7410i	−0.773151	+	0.773151i	0.205505	+	0.978656i	$0.434116\pi$
$194$		0			0
$195$	2.57783	+	7.04468i	0.184603	+	0.504480i
$196$		0			0
$197$	−1.15071	−	1.15071i	−0.0819848	−	0.0819848i	0.664925	−	0.746910i	$-0.268463\pi$
$197$	−1.15071	−	1.15071i	−0.0819848	−	0.0819848i	−0.746910	+	0.664925i	$0.768463\pi$
$198$		0			0
$199$	−17.6728			−1.25279			−0.626397	−	0.779504i	$-0.715471\pi$
$199$	−17.6728			−1.25279			−0.626397	+	0.779504i	$0.715471\pi$
$200$		0			0
$201$		−	2.81513i		−	0.198564i
$202$		0			0
$203$	0.0104909	+	0.0104909i	0.000736317	+	0.000736317i
$204$		0			0
$205$	−0.585438	+	0.214227i	−0.0408888	+	0.0149623i
$206$		0			0
$207$	−4.79553	+	0.0541507i	−0.333312	+	0.00376374i
$208$		0			0
$209$		−	11.6337i		−	0.804722i
$210$		0			0
$211$	6.29187			0.433150			0.216575	−	0.976266i	$-0.430511\pi$
$211$	6.29187			0.433150			0.216575	+	0.976266i	$0.430511\pi$
$212$		0			0
$213$	−8.94403	+	8.94403i	−0.612835	+	0.612835i
$214$		0			0
$215$	−12.3878	−	5.75052i	−0.844842	−	0.392182i
$216$		0			0
$217$	−0.0809339	+	0.0809339i	−0.00549415	+	0.00549415i
$218$		0			0
$219$			10.6840i			0.721958i
$220$		0			0
$221$			7.90331i			0.531634i
$222$		0			0
$223$	−6.61400	+	6.61400i	−0.442906	+	0.442906i	−0.892988	−	0.450081i	$-0.851395\pi$
$223$	−6.61400	+	6.61400i	−0.442906	+	0.442906i	0.450081	+	0.892988i	$0.351395\pi$
$224$		0			0
$225$	−3.22714	−	3.81910i	−0.215143	−	0.254607i
$226$		0			0
$227$	−0.842807	+	0.842807i	−0.0559391	+	0.0559391i	−0.734523	−	0.678584i	$-0.762594\pi$
$227$	−0.842807	+	0.842807i	−0.0559391	+	0.0559391i	0.678584	+	0.734523i	$0.262594\pi$
$228$		0			0
$229$	20.3773			1.34657			0.673285	−	0.739383i	$-0.264883\pi$
$229$	20.3773			1.34657			0.673285	+	0.739383i	$0.264883\pi$
$230$		0			0
$231$	0.0286565			0.00188546
$232$		0			0
$233$	−15.0006	+	15.0006i	−0.982722	+	0.982722i	−0.999853	−	0.0171312i	$-0.994547\pi$
$233$	−15.0006	+	15.0006i	−0.982722	+	0.982722i	0.0171312	+	0.999853i	$0.494547\pi$
$234$		0			0
$235$	21.8407	+	10.1386i	1.42473	+	0.661370i
$236$		0			0
$237$	−2.76851	+	2.76851i	−0.179834	+	0.179834i
$238$		0			0
$239$		−	17.0614i		−	1.10361i	−0.833974	−	0.551804i	$-0.813940\pi$
$239$		−	17.0614i		−	1.10361i	0.833974	−	0.551804i	$-0.186060\pi$
$240$		0			0
$241$			23.3681i			1.50527i	0.658438	+	0.752635i	$0.271217\pi$
$241$			23.3681i			1.50527i	−0.658438	+	0.752635i	$0.728783\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	−5.37864	−	14.6987i	−0.343628	−	0.939064i
$246$		0			0
$247$	15.9735	−	15.9735i	1.01637	−	1.01637i
$248$		0			0
$249$	17.3893			1.10200
$250$		0			0
$251$		−	11.0277i		−	0.696063i	−0.937483	−	0.348032i	$-0.886850\pi$
$251$		−	11.0277i		−	0.696063i	0.937483	−	0.348032i	$-0.113150\pi$
$252$		0			0
$253$	8.28521	−	0.0935560i	0.520887	−	0.00588181i
$254$		0			0
$255$	−1.81024	−	4.94701i	−0.113362	−	0.309794i
$256$		0			0
$257$	−1.64897	−	1.64897i	−0.102860	−	0.102860i	0.653804	−	0.756664i	$-0.273172\pi$
$257$	−1.64897	−	1.64897i	−0.102860	−	0.102860i	−0.756664	+	0.653804i	$0.773172\pi$
$258$		0			0
$259$		−	0.00134924i		−	8.38377e-5i
$260$		0			0
$261$	−0.894482			−0.0553670
$262$		0			0
$263$	1.85419	+	1.85419i	0.114334	+	0.114334i	0.761959	−	0.647625i	$-0.224238\pi$
$263$	1.85419	+	1.85419i	0.114334	+	0.114334i	−0.647625	+	0.761959i	$0.724238\pi$
$264$		0			0
$265$	27.6680	+	12.8437i	1.69963	+	0.788983i
$266$		0			0
$267$	4.67492	−	4.67492i	0.286101	−	0.286101i
$268$		0			0
$269$		−	18.0253i		−	1.09902i	−0.835486	−	0.549511i	$-0.814814\pi$
$269$		−	18.0253i		−	1.09902i	0.835486	−	0.549511i	$-0.185186\pi$
$270$		0			0
$271$	−31.0616			−1.88686			−0.943429	−	0.331574i	$-0.892420\pi$
$271$	−31.0616			−1.88686			−0.943429	+	0.331574i	$0.892420\pi$
$272$		0			0
$273$	0.0393464	+	0.0393464i	0.00238135	+	0.00238135i
$274$		0			0
$275$	5.57552	+	6.59825i	0.336217	+	0.397889i
$276$		0			0
$277$	−17.2388	−	17.2388i	−1.03578	−	1.03578i	−0.999336	−	0.0364415i	$-0.988398\pi$
$277$	−17.2388	−	17.2388i	−1.03578	−	1.03578i	−0.0364415	−	0.999336i	$-0.511602\pi$
$278$		0			0
$279$		−	6.90064i		−	0.413130i
$280$		0			0
$281$			28.7503i			1.71510i	0.514401	+	0.857550i	$0.328014\pi$
$281$			28.7503i			1.71510i	−0.514401	+	0.857550i	$0.671986\pi$
$282$		0			0
$283$	−1.63943	−	1.63943i	−0.0974541	−	0.0974541i	0.656699	−	0.754153i	$-0.271952\pi$
$283$	−1.63943	−	1.63943i	−0.0974541	−	0.0974541i	−0.754153	+	0.656699i	$0.771952\pi$
$284$		0			0
$285$	−6.33977	+	13.6572i	−0.375535	+	0.808982i
$286$		0			0
$287$	−0.00326983	+	0.00326983i	−0.000193012	+	0.000193012i
$288$		0			0
$289$			11.4500i			0.673531i
$290$		0			0
$291$			13.8625i			0.812634i
$292$		0			0
$293$	−2.90209	−	2.90209i	−0.169542	−	0.169542i	0.617236	−	0.786778i	$-0.288252\pi$
$293$	−2.90209	−	2.90209i	−0.169542	−	0.169542i	−0.786778	+	0.617236i	$0.788252\pi$
$294$		0			0
$295$	11.6314	+	31.7862i	0.677208	+	1.85067i
$296$		0			0
$297$	−1.22167	+	1.22167i	−0.0708882	+	0.0708882i
$298$		0			0
$299$	11.5043	+	11.2474i	0.665313	+	0.650455i
$300$		0			0
$301$	−0.101307			−0.00583926
$302$		0			0
$303$	−5.95421	+	5.95421i	−0.342060	+	0.342060i
$304$		0			0
$305$	4.54660	+	12.4249i	0.260338	+	0.711448i
$306$		0			0
$307$	−20.9933	−	20.9933i	−1.19815	−	1.19815i	−0.974719	−	0.223434i	$-0.928273\pi$
$307$	−20.9933	−	20.9933i	−1.19815	−	1.19815i	−0.223434	−	0.974719i	$-0.571727\pi$
$308$		0			0
$309$	16.0622			0.913745
$310$		0			0
$311$	26.0182			1.47536			0.737678	−	0.675153i	$-0.235922\pi$
$311$	26.0182			1.47536			0.737678	+	0.675153i	$0.235922\pi$
$312$		0			0
$313$	−13.7233	−	13.7233i	−0.775690	−	0.775690i	0.203405	−	0.979095i	$-0.434799\pi$
$313$	−13.7233	−	13.7233i	−0.775690	−	0.775690i	−0.979095	+	0.203405i	$0.934799\pi$
$314$		0			0
$315$	−0.0336408	−	0.0156163i	−0.00189544	−	0.000879878i
$316$		0			0
$317$	−18.5746	−	18.5746i	−1.04325	−	1.04325i	−0.999021	−	0.0442316i	$-0.985916\pi$
$317$	−18.5746	−	18.5746i	−1.04325	−	1.04325i	−0.0442316	−	0.999021i	$-0.514084\pi$
$318$		0			0
$319$	1.54539			0.0865254
$320$		0			0
$321$		−	11.2382i		−	0.627257i
$322$		0			0
$323$	−11.2171	+	11.2171i	−0.624138	+	0.624138i
$324$		0			0
$325$	−1.40423	+	16.7150i	−0.0778929	+	0.927182i
$326$		0			0
$327$	−7.28341	+	7.28341i	−0.402773	+	0.402773i
$328$		0			0
$329$	0.178613			0.00984725
$330$		0			0
$331$	−8.54938			−0.469916			−0.234958	−	0.972006i	$-0.575495\pi$
$331$	−8.54938			−0.469916			−0.234958	+	0.972006i	$0.575495\pi$
$332$		0			0
$333$	0.0575199	+	0.0575199i	0.00315207	+	0.00315207i
$334$		0			0
$335$	2.65046	−	5.70964i	0.144810	−	0.311951i
$336$		0			0
$337$	13.7074	−	13.7074i	0.746687	−	0.746687i	−0.227168	−	0.973855i	$-0.572947\pi$
$337$	13.7074	−	13.7074i	0.746687	−	0.746687i	0.973855	+	0.227168i	$0.0729468\pi$
$338$		0			0
$339$	−9.24341			−0.502033
$340$		0			0
$341$			11.9222i			0.645624i
$342$		0			0
$343$	−0.164195	−	0.164195i	−0.00886571	−	0.00886571i
$344$		0			0
$345$	−9.77724	−	4.40517i	−0.526389	−	0.237167i
$346$		0			0
$347$	7.02177	+	7.02177i	0.376949	+	0.376949i	0.870000	−	0.493052i	$-0.164119\pi$
$347$	7.02177	+	7.02177i	0.376949	+	0.376949i	−0.493052	+	0.870000i	$0.664119\pi$
$348$		0			0
$349$			21.7920i			1.16650i	0.812294	+	0.583249i	$0.198219\pi$
$349$			21.7920i			1.16650i	−0.812294	+	0.583249i	$0.801781\pi$
$350$		0			0
$351$	−3.35478			−0.179065
$352$		0			0
$353$	−14.0973	+	14.0973i	−0.750326	+	0.750326i	−0.974540	−	0.224214i	$-0.928019\pi$
$353$	−14.0973	+	14.0973i	−0.750326	+	0.750326i	0.224214	+	0.974540i	$0.428019\pi$
$354$		0			0
$355$	−26.5611	+	9.71940i	−1.40972	+	0.515852i
$356$		0			0
$357$	−0.0276304	−	0.0276304i	−0.00146235	−	0.00146235i
$358$		0			0
$359$	−21.4103			−1.12999			−0.564997	−	0.825093i	$-0.691123\pi$
$359$	−21.4103			−1.12999			−0.564997	+	0.825093i	$0.691123\pi$
$360$		0			0
$361$	26.3423			1.38644
$362$		0			0
$363$	−5.66751	+	5.66751i	−0.297467	+	0.297467i
$364$		0			0
$365$	−10.0590	+	21.6692i	−0.526514	+	1.13422i
$366$		0			0
$367$	−13.3282	+	13.3282i	−0.695726	+	0.695726i	−0.963486	−	0.267760i	$-0.913717\pi$
$367$	−13.3282	+	13.3282i	−0.695726	+	0.695726i	0.267760	+	0.963486i	$0.413717\pi$
$368$		0			0
$369$		−	0.278794i		−	0.0145134i
$370$		0			0
$371$	0.226269			0.0117473
$372$		0			0
$373$	24.6632	+	24.6632i	1.27701	+	1.27701i	0.942331	+	0.334681i	$0.108629\pi$
$373$	24.6632	+	24.6632i	1.27701	+	1.27701i	0.334681	+	0.942331i	$0.391371\pi$
$374$		0			0
$375$	−2.94958	−	10.7842i	−0.152316	−	0.556896i
$376$		0			0
$377$	2.12188	+	2.12188i	0.109282	+	0.109282i
$378$		0			0
$379$	11.8558			0.608994			0.304497	−	0.952513i	$-0.401512\pi$
$379$	11.8558			0.608994			0.304497	+	0.952513i	$0.401512\pi$
$380$		0			0
$381$	3.87453			0.198498
$382$		0			0
$383$	−11.5598	−	11.5598i	−0.590679	−	0.590679i	0.347136	−	0.937815i	$-0.387154\pi$
$383$	−11.5598	−	11.5598i	−0.590679	−	0.590679i	−0.937815	+	0.347136i	$0.887154\pi$
$384$		0			0
$385$	0.0581210	+	0.0269802i	0.00296212	+	0.00137504i
$386$		0			0
$387$	4.31887	−	4.31887i	0.219541	−	0.219541i
$388$		0			0
$389$	11.8359			0.600106			0.300053	−	0.953923i	$-0.402996\pi$
$389$	11.8359			0.600106			0.300053	+	0.953923i	$0.402996\pi$
$390$		0			0
$391$	−8.07873	−	7.89832i	−0.408559	−	0.399435i
$392$		0			0
$393$	8.21393	−	8.21393i	0.414338	−	0.414338i
$394$		0			0
$395$	−8.22164	+	3.00852i	−0.413675	+	0.151375i
$396$		0			0
$397$	3.53582	+	3.53582i	0.177458	+	0.177458i	0.790247	−	0.612789i	$-0.209952\pi$
$397$	3.53582	+	3.53582i	0.177458	+	0.177458i	−0.612789	+	0.790247i	$0.709952\pi$
$398$		0			0
$399$			0.111688i			0.00559141i
$400$		0			0
$401$		−	22.6536i		−	1.13127i	−0.824657	−	0.565633i	$-0.808632\pi$
$401$		−	22.6536i		−	1.13127i	0.824657	−	0.565633i	$-0.191368\pi$
$402$		0			0
$403$	−16.3696	+	16.3696i	−0.815428	+	0.815428i
$404$		0			0
$405$	2.09989	−	0.768407i	0.104345	−	0.0381824i
$406$		0			0
$407$	−0.0993769	−	0.0993769i	−0.00492593	−	0.00492593i
$408$		0			0
$409$		−	2.72111i		−	0.134550i	−0.997734	−	0.0672750i	$-0.978570\pi$
$409$		−	2.72111i		−	0.134550i	0.997734	−	0.0672750i	$-0.0214305\pi$
$410$		0			0
$411$			2.55927i			0.126239i
$412$		0			0
$413$	0.177535	+	0.177535i	0.00873590	+	0.00873590i
$414$		0			0
$415$	35.2689	+	16.3721i	1.73128	+	0.803675i
$416$		0			0
$417$	3.88911	+	3.88911i	0.190451	+	0.190451i
$418$		0			0
$419$	29.6820			1.45006			0.725030	−	0.688717i	$-0.241826\pi$
$419$	29.6820			1.45006			0.725030	+	0.688717i	$0.241826\pi$
$420$		0			0
$421$		−	12.9116i		−	0.629271i	−0.949213	−	0.314636i	$-0.898118\pi$
$421$		−	12.9116i		−	0.629271i	0.949213	−	0.314636i	$-0.101882\pi$
$422$		0			0
$423$	−7.61450	+	7.61450i	−0.370230	+	0.370230i
$424$		0			0
$425$	0.986100	−	11.7378i	0.0478329	−	0.569369i
$426$		0			0
$427$	0.0693964	+	0.0693964i	0.00335833	+	0.00335833i
$428$		0			0
$429$	5.79604			0.279835
$430$		0			0
$431$		−	17.6210i		−	0.848772i	−0.905481	−	0.424386i	$-0.860490\pi$
$431$		−	17.6210i		−	0.848772i	0.905481	−	0.424386i	$-0.139510\pi$
$432$		0			0
$433$	−9.30573	−	9.30573i	−0.447205	−	0.447205i	0.447220	−	0.894424i	$-0.352414\pi$
$433$	−9.30573	−	9.30573i	−0.447205	−	0.447205i	−0.894424	+	0.447220i	$0.852414\pi$
$434$		0			0
$435$	−1.81418	−	0.842157i	−0.0869834	−	0.0403784i
$436$		0			0
$437$	0.364633	+	32.2915i	0.0174428	+	1.54471i
$438$		0			0
$439$		−	2.67753i		−	0.127791i	−0.997957	−	0.0638957i	$-0.979648\pi$
$439$		−	2.67753i		−	0.127791i	0.997957	−	0.0638957i	$-0.0203525\pi$
$440$		0			0
$441$	6.99972			0.333320
$442$		0			0
$443$	14.8957	−	14.8957i	0.707717	−	0.707717i	−0.258338	−	0.966055i	$-0.583175\pi$
$443$	14.8957	−	14.8957i	0.707717	−	0.707717i	0.966055	+	0.258338i	$0.0831748\pi$
$444$		0			0
$445$	13.8831	−	5.08020i	0.658122	−	0.240824i
$446$		0			0
$447$	−1.11386	+	1.11386i	−0.0526839	+	0.0526839i
$448$		0			0
$449$		−	24.4085i		−	1.15191i	−0.817482	−	0.575954i	$-0.804631\pi$
$449$		−	24.4085i		−	1.15191i	0.817482	−	0.575954i	$-0.195369\pi$
$450$		0			0
$451$			0.481672i			0.0226810i
$452$		0			0
$453$	12.0338	−	12.0338i	0.565398	−	0.565398i
$454$		0			0
$455$	0.0427574	+	0.116847i	0.00200450	+	0.00547787i
$456$		0			0
$457$	3.49970	−	3.49970i	0.163709	−	0.163709i	−0.620498	−	0.784208i	$-0.713070\pi$
$457$	3.49970	−	3.49970i	0.163709	−	0.163709i	0.784208	+	0.620498i	$0.213070\pi$
$458$		0			0
$459$	2.35584			0.109961
$460$		0			0
$461$	−15.6454			−0.728680			−0.364340	−	0.931266i	$-0.618705\pi$
$461$	−15.6454			−0.728680			−0.364340	+	0.931266i	$0.618705\pi$
$462$		0			0
$463$	19.9374	−	19.9374i	0.926569	−	0.926569i	−0.0709131	−	0.997482i	$-0.522591\pi$
$463$	19.9374	−	19.9374i	0.926569	−	0.926569i	0.997482	+	0.0709131i	$0.0225913\pi$
$464$		0			0
$465$	6.49697	−	13.9958i	0.301290	−	0.649041i
$466$		0			0
$467$	4.29888	−	4.29888i	0.198929	−	0.198929i	−0.600612	−	0.799541i	$-0.705076\pi$
$467$	4.29888	−	4.29888i	0.198929	−	0.198929i	0.799541	+	0.600612i	$0.205076\pi$
$468$		0			0
$469$		−	0.0466934i		−	0.00215610i
$470$		0			0
$471$			11.7377i			0.540845i
$472$		0			0
$473$	−7.46169	+	7.46169i	−0.343089	+	0.343089i
$474$		0			0
$475$	−25.7166	+	21.7305i	−1.17996	+	0.997065i
$476$		0			0
$477$	−9.64615	+	9.64615i	−0.441667	+	0.441667i
$478$		0			0
$479$	25.9392			1.18519			0.592596	−	0.805500i	$-0.298103\pi$
$479$	25.9392			1.18519			0.592596	+	0.805500i	$0.298103\pi$
$480$		0			0
$481$		−	0.272896i		−	0.0124430i
$482$		0			0
$483$	−0.0795412		0.000898174i	−0.00361925		4.08683e-5i
$484$		0			0
$485$	−13.0516	+	28.1158i	−0.592642	+	1.27667i
$486$		0			0
$487$	11.3525	+	11.3525i	0.514430	+	0.514430i	0.915881	−	0.401451i	$-0.131494\pi$
$487$	11.3525	+	11.3525i	0.514430	+	0.514430i	−0.401451	+	0.915881i	$0.631494\pi$
$488$		0			0
$489$		−	23.2672i		−	1.05218i
$490$		0			0
$491$	−33.9816			−1.53357			−0.766784	−	0.641906i	$-0.778144\pi$
$491$	−33.9816			−1.53357			−0.766784	+	0.641906i	$0.778144\pi$
$492$		0			0
$493$	−1.49005	−	1.49005i	−0.0671086	−	0.0671086i
$494$		0			0
$495$	−3.62798	+	1.32757i	−0.163065	+	0.0596700i
$496$		0			0
$497$	−0.148351	+	0.148351i	−0.00665444	+	0.00665444i
$498$		0			0
$499$			7.63815i			0.341930i	0.985277	+	0.170965i	$0.0546886\pi$
$499$			7.63815i			0.341930i	−0.985277	+	0.170965i	$0.945311\pi$
$500$		0			0
$501$	4.62353			0.206564
$502$		0			0
$503$	−10.4184	−	10.4184i	−0.464535	−	0.464535i	0.435603	−	0.900139i	$-0.356535\pi$
$503$	−10.4184	−	10.4184i	−0.464535	−	0.464535i	−0.900139	+	0.435603i	$0.856535\pi$
$504$		0			0
$505$	−17.6822	+	6.47039i	−0.786848	+	0.287929i
$506$		0			0
$507$	−1.23423	−	1.23423i	−0.0548140	−	0.0548140i
$508$		0			0
$509$		−	13.7018i		−	0.607320i	−0.952780	−	0.303660i	$-0.901791\pi$
$509$		−	13.7018i		−	0.607320i	0.952780	−	0.303660i	$-0.0982088\pi$
$510$		0			0
$511$			0.177211i			0.00783935i
$512$		0			0
$513$	−4.76142	−	4.76142i	−0.210222	−	0.210222i
$514$		0			0
$515$	32.5772	+	15.1226i	1.43552	+	0.666381i
$516$		0			0
$517$	13.1555	−	13.1555i	0.578580	−	0.578580i
$518$		0			0
$519$			4.77792i			0.209727i
$520$		0			0
$521$			10.4040i			0.455806i	0.973684	+	0.227903i	$0.0731870\pi$
$521$			10.4040i			0.455806i	−0.973684	+	0.227903i	$0.926813\pi$
$522$		0			0
$523$	19.8761	+	19.8761i	0.869120	+	0.869120i	0.992375	−	0.123255i	$-0.0393333\pi$
$523$	19.8761	+	19.8761i	0.869120	+	0.869120i	−0.123255	+	0.992375i	$0.539333\pi$
$524$		0			0
$525$	−0.0535272	−	0.0633457i	−0.00233612	−	0.00276463i
$526$		0			0
$527$	11.4953	−	11.4953i	0.500742	−	0.500742i
$528$		0			0
$529$	−22.9941	+	0.519362i	−0.999745	+	0.0225810i
$530$		0			0
$531$	−15.1371			−0.656893
$532$		0			0
$533$	−0.661352	+	0.661352i	−0.0286463	+	0.0286463i
$534$		0			0
$535$	10.5808	−	22.7933i	0.457449	−	0.985441i
$536$		0			0
$537$	−2.05510	−	2.05510i	−0.0886839	−	0.0886839i
$538$		0			0
$539$	−12.0934			−0.520899
$540$		0			0
$541$	3.70430			0.159260			0.0796302	−	0.996824i	$-0.474626\pi$
$541$	3.70430			0.159260			0.0796302	+	0.996824i	$0.474626\pi$
$542$		0			0
$543$	−3.10767	−	3.10767i	−0.133363	−	0.133363i
$544$		0			0
$545$	−21.6295	+	7.91481i	−0.926506	+	0.339033i
$546$		0			0
$547$	2.28076	+	2.28076i	0.0975182	+	0.0975182i	0.754183	−	0.656665i	$-0.228033\pi$
$547$	2.28076	+	2.28076i	0.0975182	+	0.0975182i	−0.656665	+	0.754183i	$0.728033\pi$
$548$		0			0
$549$	−5.91692			−0.252528
$550$		0			0
$551$			6.02314i			0.256595i
$552$		0			0
$553$	−0.0459200	+	0.0459200i	−0.00195272	+	0.00195272i
$554$		0			0
$555$	0.0625064	+	0.170817i	0.00265325	+	0.00725076i
$556$		0			0
$557$	26.0661	−	26.0661i	1.10445	−	1.10445i	0.110588	−	0.993866i	$-0.464727\pi$
$557$	26.0661	−	26.0661i	1.10445	−	1.10445i	0.993866	−	0.110588i	$-0.0352734\pi$
$558$		0			0
$559$	−20.4903			−0.866649
$560$		0			0
$561$	−4.07017			−0.171843
$562$		0			0
$563$	13.3486	+	13.3486i	0.562578	+	0.562578i	0.930039	−	0.367461i	$-0.119773\pi$
$563$	13.3486	+	13.3486i	0.562578	+	0.562578i	−0.367461	+	0.930039i	$0.619773\pi$
$564$		0			0
$565$	−18.7474	−	8.70270i	−0.788711	−	0.366125i
$566$		0			0
$567$	0.0117285	−	0.0117285i	0.000492549	−	0.000492549i
$568$		0			0
$569$	24.4230			1.02386			0.511932	−	0.859026i	$-0.328930\pi$
$569$	24.4230			1.02386			0.511932	+	0.859026i	$0.328930\pi$
$570$		0			0
$571$		−	6.36696i		−	0.266449i	−0.991086	−	0.133225i	$-0.957467\pi$
$571$		−	6.36696i		−	0.266449i	0.991086	−	0.133225i	$-0.0425332\pi$
$572$		0			0
$573$	−4.95918	−	4.95918i	−0.207173	−	0.207173i
$574$		0			0
$575$	−15.6827	−	18.1398i	−0.654012	−	0.756484i
$576$		0			0
$577$	−5.01040	−	5.01040i	−0.208586	−	0.208586i	0.595081	−	0.803666i	$-0.297120\pi$
$577$	−5.01040	−	5.01040i	−0.208586	−	0.208586i	−0.803666	+	0.595081i	$0.797120\pi$
$578$		0			0
$579$		−	15.1900i		−	0.631275i
$580$		0			0
$581$	0.288429			0.0119660
$582$		0			0
$583$	16.6656	−	16.6656i	0.690219	−	0.690219i
$584$		0			0
$585$	−6.80414	−	3.15853i	−0.281317	−	0.130589i
$586$		0			0
$587$	11.4787	+	11.4787i	0.473776	+	0.473776i	0.903134	−	0.429358i	$-0.141260\pi$
$587$	11.4787	+	11.4787i	0.473776	+	0.473776i	−0.429358	+	0.903134i	$0.641260\pi$
$588$		0			0
$589$	−46.4666			−1.91462
$590$		0			0
$591$	1.62735			0.0669403
$592$		0			0
$593$	10.5347	−	10.5347i	0.432610	−	0.432610i	−0.456905	−	0.889515i	$-0.651042\pi$
$593$	10.5347	−	10.5347i	0.432610	−	0.432610i	0.889515	+	0.456905i	$0.151042\pi$
$594$		0			0
$595$	−0.0300257	−	0.0820538i	−0.00123093	−	0.00336388i
$596$		0			0
$597$	12.4966	−	12.4966i	0.511451	−	0.511451i
$598$		0			0
$599$		−	13.4401i		−	0.549146i	−0.961566	−	0.274573i	$-0.911463\pi$
$599$		−	13.4401i		−	0.549146i	0.961566	−	0.274573i	$-0.0885365\pi$
$600$		0			0
$601$	8.20348			0.334627			0.167313	−	0.985904i	$-0.446491\pi$
$601$	8.20348			0.334627			0.167313	+	0.985904i	$0.446491\pi$
$602$		0			0
$603$	1.99060	+	1.99060i	0.0810635	+	0.0810635i
$604$		0			0
$605$	−16.8308	+	6.15883i	−0.684269	+	0.250392i
$606$		0			0
$607$	−11.5736	−	11.5736i	−0.469756	−	0.469756i	0.432080	−	0.901835i	$-0.357780\pi$
$607$	−11.5736	−	11.5736i	−0.469756	−	0.469756i	−0.901835	+	0.432080i	$0.857780\pi$
$608$		0			0
$609$	−0.0148364			−0.000601200
$610$		0			0
$611$	36.1260			1.46150
$612$		0			0
$613$	−27.9916	−	27.9916i	−1.13057	−	1.13057i	−0.990083	−	0.140486i	$-0.955134\pi$
$613$	−27.9916	−	27.9916i	−1.13057	−	1.13057i	−0.140486	−	0.990083i	$-0.544866\pi$
$614$		0			0
$615$	0.262486	−	0.565449i	0.0105844	−	0.0228011i
$616$		0			0
$617$	6.87175	−	6.87175i	0.276646	−	0.276646i	−0.555122	−	0.831769i	$-0.687329\pi$
$617$	6.87175	−	6.87175i	0.276646	−	0.276646i	0.831769	+	0.555122i	$0.187329\pi$
$618$		0			0
$619$	43.3388			1.74193			0.870967	−	0.491342i	$-0.163494\pi$
$619$	43.3388			1.74193			0.870967	+	0.491342i	$0.163494\pi$
$620$		0			0
$621$	3.35266	−	3.42924i	0.134538	−	0.137611i
$622$		0			0
$623$	0.0775408	−	0.0775408i	0.00310661	−	0.00310661i
$624$		0			0
$625$	4.17108	−	24.6496i	0.166843	−	0.985983i
$626$		0			0
$627$	8.22629	+	8.22629i	0.328526	+	0.328526i
$628$		0			0
$629$			0.191637i			0.00764105i
$630$		0			0
$631$		−	29.6526i		−	1.18045i	−0.807238	−	0.590225i	$-0.799039\pi$
$631$		−	29.6526i		−	1.18045i	0.807238	−	0.590225i	$-0.200961\pi$
$632$		0			0
$633$	−4.44902	+	4.44902i	−0.176833	+	0.176833i
$634$		0			0
$635$	7.85830	+	3.64788i	0.311847	+	0.144762i
$636$		0			0
$637$	−16.6047	−	16.6047i	−0.657900	−	0.657900i
$638$		0			0
$639$		−	12.6488i		−	0.500378i
$640$		0			0
$641$		−	7.85702i		−	0.310333i	−0.987888	−	0.155167i	$-0.950409\pi$
$641$		−	7.85702i		−	0.310333i	0.987888	−	0.155167i	$-0.0495915\pi$
$642$		0			0
$643$	8.26989	+	8.26989i	0.326133	+	0.326133i	0.851114	−	0.524981i	$-0.175928\pi$
$643$	8.26989	+	8.26989i	0.326133	+	0.326133i	−0.524981	+	0.851114i	$0.675928\pi$
$644$		0			0
$645$	12.8257	−	4.69328i	0.505013	−	0.184798i
$646$		0			0
$647$	−2.77391	−	2.77391i	−0.109054	−	0.109054i	0.650475	−	0.759528i	$-0.274570\pi$
$647$	−2.77391	−	2.77391i	−0.109054	−	0.109054i	−0.759528	+	0.650475i	$0.774570\pi$
$648$		0			0
$649$	26.1522			1.02657
$650$		0			0
$651$		−	0.114458i		−	0.00448596i
$652$		0			0
$653$	7.86077	−	7.86077i	0.307616	−	0.307616i	−0.536368	−	0.843984i	$-0.680204\pi$
$653$	7.86077	−	7.86077i	0.307616	−	0.307616i	0.843984	+	0.536368i	$0.180204\pi$
$654$		0			0
$655$	24.3929	−	8.92601i	0.953109	−	0.348768i
$656$		0			0
$657$	−7.55474	−	7.55474i	−0.294738	−	0.294738i
$658$		0			0
$659$	−26.7922			−1.04368			−0.521839	−	0.853044i	$-0.674754\pi$
$659$	−26.7922			−1.04368			−0.521839	+	0.853044i	$0.674754\pi$
$660$		0			0
$661$		−	42.4339i		−	1.65049i	−0.564777	−	0.825244i	$-0.691038\pi$
$661$		−	42.4339i		−	1.65049i	0.564777	−	0.825244i	$-0.308962\pi$
$662$		0			0
$663$	−5.58849	−	5.58849i	−0.217039	−	0.217039i
$664$		0			0
$665$	−0.105155	+	0.226526i	−0.00407773	+	0.00878429i
$666$		0			0
$667$	−4.28951	+	0.0484368i	−0.166091	+	0.00187548i
$668$		0			0
$669$		−	9.35361i		−	0.361631i
$670$		0			0
$671$	10.2226			0.394641
$672$		0			0
$673$	−11.5454	+	11.5454i	−0.445043	+	0.445043i	−0.893703	−	0.448659i	$-0.851902\pi$
$673$	−11.5454	+	11.5454i	−0.445043	+	0.445043i	0.448659	+	0.893703i	$0.351902\pi$
$674$		0			0
$675$	4.98245	+	0.418577i	0.191775	+	0.0161110i
$676$		0			0
$677$	−19.8948	+	19.8948i	−0.764619	+	0.764619i	−0.977153	−	0.212535i	$-0.931828\pi$
$677$	−19.8948	+	19.8948i	−0.764619	+	0.764619i	0.212535	+	0.977153i	$0.431828\pi$
$678$		0			0
$679$			0.229931i			0.00882394i
$680$		0			0
$681$		−	1.19191i		−	0.0456741i
$682$		0			0
$683$	−19.3260	+	19.3260i	−0.739487	+	0.739487i	−0.972479	−	0.232991i	$-0.925149\pi$
$683$	−19.3260	+	19.3260i	−0.739487	+	0.739487i	0.232991	+	0.972479i	$0.425149\pi$
$684$		0			0
$685$	−2.40956	+	5.19069i	−0.0920644	+	0.198326i
$686$		0			0
$687$	−14.4089	+	14.4089i	−0.549735	+	0.549735i
$688$		0			0
$689$	45.7649			1.74350
$690$		0			0
$691$	−22.0154			−0.837505			−0.418752	−	0.908100i	$-0.637532\pi$
$691$	−22.0154			−0.837505			−0.418752	+	0.908100i	$0.637532\pi$
$692$		0			0
$693$	−0.0202632	+	0.0202632i	−0.000769736	+	0.000769736i
$694$		0			0
$695$	4.22626	+	11.5495i	0.160311	+	0.438097i
$696$		0			0
$697$	0.464424	−	0.464424i	0.0175913	−	0.0175913i
$698$		0			0
$699$		−	21.2141i		−	0.802389i
$700$		0			0
$701$			33.7843i			1.27602i	0.770030	+	0.638008i	$0.220241\pi$
$701$			33.7843i			1.27602i	−0.770030	+	0.638008i	$0.779759\pi$
$702$		0			0
$703$	0.387320	−	0.387320i	0.0146080	−	0.0146080i
$704$		0			0
$705$	−22.6128	+	8.27462i	−0.851646	+	0.311640i
$706$		0			0
$707$	−0.0987598	+	0.0987598i	−0.00371425	+	0.00371425i
$708$		0			0
$709$	−21.5113			−0.807876			−0.403938	−	0.914786i	$-0.632359\pi$
$709$	−21.5113			−0.807876			−0.403938	+	0.914786i	$0.632359\pi$
$710$		0			0
$711$		−	3.91526i		−	0.146834i
$712$		0			0
$713$	−0.373675	−	33.0922i	−0.0139942	−	1.23931i
$714$		0			0
$715$	11.7555	+	5.45699i	0.439630	+	0.204080i
$716$		0			0
$717$	12.0642	+	12.0642i	0.450546	+	0.450546i
$718$		0			0
$719$			14.6800i			0.547472i	0.961805	+	0.273736i	$0.0882594\pi$
$719$			14.6800i			0.547472i	−0.961805	+	0.273736i	$0.911741\pi$
$720$		0			0
$721$	0.266416			0.00992186
$722$		0			0
$723$	−16.5237	−	16.5237i	−0.614524	−	0.614524i
$724$		0			0
$725$	−2.88662	−	3.41612i	−0.107206	−	0.126871i
$726$		0			0
$727$	−31.3379	+	31.3379i	−1.16226	+	1.16226i	−0.178277	+	0.983980i	$0.557052\pi$
$727$	−31.3379	+	31.3379i	−1.16226	+	1.16226i	−0.983980	+	0.178277i	$0.942948\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	14.3890			0.532196
$732$		0			0
$733$	−13.5985	−	13.5985i	−0.502273	−	0.502273i	0.409870	−	0.912144i	$-0.365574\pi$
$733$	−13.5985	−	13.5985i	−0.502273	−	0.502273i	−0.912144	+	0.409870i	$0.865574\pi$
$734$		0			0
$735$	14.1968	+	6.59026i	0.523657	+	0.243085i
$736$		0			0
$737$	−3.43915	−	3.43915i	−0.126683	−	0.126683i
$738$		0			0
$739$		−	31.5137i		−	1.15925i	−0.814883	−	0.579625i	$-0.803199\pi$
$739$		−	31.5137i		−	1.15925i	0.814883	−	0.579625i	$-0.196801\pi$
$740$		0			0
$741$			22.5900i			0.829863i
$742$		0			0
$743$	−33.9355	−	33.9355i	−1.24497	−	1.24497i	−0.957912	−	0.287061i	$-0.907322\pi$
$743$	−33.9355	−	33.9355i	−1.24497	−	1.24497i	−0.287061	−	0.957912i	$-0.592678\pi$
$744$		0			0
$745$	−3.30783	+	1.21042i	−0.121190	+	0.0443465i
$746$		0			0
$747$	−12.2961	+	12.2961i	−0.449891	+	0.449891i
$748$		0			0
$749$		−	0.186404i		−	0.00681104i
$750$		0			0
$751$		−	13.9950i		−	0.510686i	−0.966851	−	0.255343i	$-0.917812\pi$
$751$		−	13.9950i		−	0.510686i	0.966851	−	0.255343i	$-0.0821883\pi$
$752$		0			0
$753$	7.79778	+	7.79778i	0.284167	+	0.284167i
$754$		0			0
$755$	35.7368	−	13.0771i	1.30060	−	0.475923i
$756$		0			0
$757$	23.8848	−	23.8848i	0.868109	−	0.868109i	−0.124154	−	0.992263i	$-0.539622\pi$
$757$	23.8848	−	23.8848i	0.868109	−	0.868109i	0.992263	+	0.124154i	$0.0396216\pi$
$758$		0			0
$759$	−5.79237	+	5.92468i	−0.210250	+	0.215052i
$760$		0			0
$761$	27.0267			0.979718			0.489859	−	0.871802i	$-0.337048\pi$
$761$	27.0267			0.979718			0.489859	+	0.871802i	$0.337048\pi$
$762$		0			0
$763$	−0.120807	+	0.120807i	−0.00437349	+	0.00437349i
$764$		0			0
$765$	4.77810	+	2.21803i	0.172752	+	0.0801930i
$766$		0			0
$767$	35.9079	+	35.9079i	1.29656	+	1.29656i
$768$		0			0
$769$	−52.5610			−1.89540			−0.947699	−	0.319165i	$-0.896598\pi$
$769$	−52.5610			−1.89540			−0.947699	+	0.319165i	$0.896598\pi$
$770$		0			0
$771$	2.33200			0.0839849
$772$		0			0
$773$	−11.7819	−	11.7819i	−0.423764	−	0.423764i	0.462734	−	0.886497i	$-0.346869\pi$
$773$	−11.7819	−	11.7819i	−0.423764	−	0.423764i	−0.886497	+	0.462734i	$0.846869\pi$
$774$		0			0
$775$	26.3542	−	22.2694i	0.946672	−	0.799939i
$776$		0			0
$777$	0.000954057	0	0.000954057i	3.42266e−5	0	3.42266e-5i
$778$		0			0
$779$	−1.87731			−0.0672615
$780$		0			0
$781$			21.8532i			0.781970i
$782$		0			0
$783$	0.632494	−	0.632494i	0.0226035	−	0.0226035i
$784$		0			0
$785$	−11.0511	+	23.8064i	−0.394430	+	0.849686i
$786$		0			0
$787$	9.86015	−	9.86015i	0.351476	−	0.351476i	−0.509182	−	0.860659i	$-0.670052\pi$
$787$	9.86015	−	9.86015i	0.351476	−	0.351476i	0.860659	+	0.509182i	$0.170052\pi$
$788$		0			0
$789$	−2.62222			−0.0933535
$790$		0			0
$791$	−0.153316			−0.00545130
$792$		0			0
$793$	14.0360	+	14.0360i	0.498435	+	0.498435i
$794$		0			0
$795$	−28.6461	+	10.4824i	−1.01597	+	0.371772i
$796$		0			0
$797$	−23.1046	+	23.1046i	−0.818406	+	0.818406i	−0.985877	−	0.167471i	$-0.946440\pi$
$797$	−23.1046	+	23.1046i	−0.818406	+	0.818406i	0.167471	+	0.985877i	$0.446440\pi$
$798$		0			0
$799$	−25.3689			−0.897488
$800$		0			0
$801$			6.61134i			0.233600i
$802$		0			0
$803$	13.0523	+	13.0523i	0.460605	+	0.460605i
$804$		0			0
$805$	−0.162171	−	0.0730666i	−0.00571577	−	0.00257526i
$806$		0			0
$807$	12.7458	+	12.7458i	0.448674	+	0.448674i
$808$		0			0
$809$			54.7553i			1.92509i	0.271116	+	0.962547i	$0.412607\pi$
$809$			54.7553i			1.92509i	−0.271116	+	0.962547i	$0.587393\pi$
$810$		0			0
$811$	−38.5346			−1.35313			−0.676567	−	0.736381i	$-0.736533\pi$
$811$	−38.5346			−1.35313			−0.676567	+	0.736381i	$0.736533\pi$
$812$		0			0
$813$	21.9639	−	21.9639i	0.770307	−	0.770307i
$814$		0			0
$815$	21.9061	−	47.1904i	0.767338	−	1.65301i
$816$		0			0
$817$	−29.0818	−	29.0818i	−1.01744	−	1.01744i
$818$		0			0
$819$	−0.0556442			−0.00194437
$820$		0			0
$821$	1.82678			0.0637551			0.0318776	−	0.999492i	$-0.489851\pi$
$821$	1.82678			0.0637551			0.0318776	+	0.999492i	$0.489851\pi$
$822$		0			0
$823$	30.5211	−	30.5211i	1.06390	−	1.06390i	0.0660840	−	0.997814i	$-0.478949\pi$
$823$	30.5211	−	30.5211i	1.06390	−	1.06390i	0.997814	−	0.0660840i	$-0.0210505\pi$
$824$		0			0
$825$	−8.60816	−	0.723174i	−0.299698	−	0.0251777i
$826$		0			0
$827$	3.34366	−	3.34366i	0.116270	−	0.116270i	−0.646578	−	0.762848i	$-0.723800\pi$
$827$	3.34366	−	3.34366i	0.116270	−	0.116270i	0.762848	+	0.646578i	$0.223800\pi$
$828$		0			0
$829$			4.28008i			0.148653i	0.997234	+	0.0743266i	$0.0236807\pi$
$829$			4.28008i			0.148653i	−0.997234	+	0.0743266i	$0.976319\pi$
$830$		0			0
$831$	24.3793			0.845709
$832$		0			0
$833$	11.6603	+	11.6603i	0.404007	+	0.404007i
$834$		0			0
$835$	9.37743	+	4.35307i	0.324519	+	0.150644i
$836$		0			0
$837$	4.87949	+	4.87949i	0.168660	+	0.168660i
$838$		0			0
$839$	−16.0883			−0.555429			−0.277714	−	0.960664i	$-0.589577\pi$
$839$	−16.0883			−0.555429			−0.277714	+	0.960664i	$0.589577\pi$
$840$		0			0
$841$	28.1999			0.972410
$842$		0			0
$843$	−20.3295	−	20.3295i	−0.700187	−	0.700187i
$844$		0			0
$845$	−1.34122	−	3.66528i	−0.0461395	−	0.126090i
$846$		0			0
$847$	−0.0940044	+	0.0940044i	−0.00323003	+	0.00323003i
$848$		0			0
$849$	2.31851			0.0795709
$850$		0			0
$851$	0.278953	+	0.272723i	0.00956238	+	0.00934884i
$852$		0			0
$853$	29.6273	−	29.6273i	1.01442	−	1.01442i	0.0145238	−	0.999895i	$-0.495377\pi$
$853$	29.6273	−	29.6273i	1.01442	−	1.01442i	0.999895	−	0.0145238i	$-0.00462323\pi$
$854$		0			0
$855$	−5.17420	−	14.1400i	−0.176954	−	0.483577i
$856$		0			0
$857$	−22.9180	−	22.9180i	−0.782865	−	0.782865i	0.197449	−	0.980313i	$-0.436734\pi$
$857$	−22.9180	−	22.9180i	−0.782865	−	0.782865i	−0.980313	+	0.197449i	$0.936734\pi$
$858$		0			0
$859$			44.9995i			1.53536i	0.640831	+	0.767682i	$0.278590\pi$
$859$			44.9995i			1.53536i	−0.640831	+	0.767682i	$0.721410\pi$
$860$		0			0
$861$		−	0.00462424i		−	0.000157594i
$862$		0			0
$863$	−22.5165	+	22.5165i	−0.766469	+	0.766469i	−0.977483	−	0.211014i	$-0.932324\pi$
$863$	−22.5165	+	22.5165i	−0.766469	+	0.766469i	0.211014	+	0.977483i	$0.432324\pi$
$864$		0			0
$865$	−4.49842	+	9.69054i	−0.152951	+	0.329488i
$866$		0			0
$867$	−8.09639	−	8.09639i	−0.274968	−	0.274968i
$868$		0			0
$869$			6.76439i			0.229466i
$870$		0			0
$871$		−	9.44415i		−	0.320003i
$872$		0			0
$873$	−9.80227	−	9.80227i	−0.331756	−	0.331756i
$874$		0			0
$875$	−0.0489234	−	0.178873i	−0.00165391	−	0.00604703i
$876$		0			0
$877$	−0.130809	−	0.130809i	−0.00441710	−	0.00441710i	0.704895	−	0.709312i	$-0.250994\pi$
$877$	−0.130809	−	0.130809i	−0.00441710	−	0.00441710i	−0.709312	+	0.704895i	$0.750994\pi$
$878$		0			0
$879$	4.10417			0.138430
$880$		0			0
$881$		−	8.93033i		−	0.300871i	−0.988620	−	0.150435i	$-0.951932\pi$
$881$		−	8.93033i		−	0.300871i	0.988620	−	0.150435i	$-0.0480675\pi$
$882$		0			0
$883$	15.0677	−	15.0677i	0.507070	−	0.507070i	−0.406556	−	0.913626i	$-0.633270\pi$
$883$	15.0677	−	15.0677i	0.507070	−	0.507070i	0.913626	+	0.406556i	$0.133270\pi$
$884$		0			0
$885$	−30.7009	−	14.2516i	−1.03200	−	0.479062i
$886$		0			0
$887$	4.25851	+	4.25851i	0.142987	+	0.142987i	0.774977	−	0.631990i	$-0.217762\pi$
$887$	4.25851	+	4.25851i	0.142987	+	0.142987i	−0.631990	+	0.774977i	$0.717762\pi$
$888$		0			0
$889$	0.0642651			0.00215538
$890$		0			0
$891$		−	1.72770i		−	0.0578800i
$892$		0			0
$893$	51.2735	+	51.2735i	1.71580	+	1.71580i
$894$		0			0
$895$	−2.23325	−	6.10301i	−0.0746495	−	0.204001i
$896$		0			0
$897$	−16.0879	+	0.181664i	−0.537160	+	0.00606557i
$898$		0			0
$899$		−	6.17250i		−	0.205864i
$900$		0			0
$901$	−32.1377			−1.07066
$902$		0			0
$903$	0.0716352	−	0.0716352i	0.00238387	−	0.00238387i
$904$		0			0
$905$	−3.37708	−	9.22885i	−0.112258	−	0.306777i
$906$		0			0
$907$	6.23724	−	6.23724i	0.207104	−	0.207104i	−0.595931	−	0.803035i	$-0.703217\pi$
$907$	6.23724	−	6.23724i	0.207104	−	0.207104i	0.803035	+	0.595931i	$0.203217\pi$
$908$		0			0
$909$		−	8.42053i		−	0.279291i
$910$		0			0
$911$		−	46.8771i		−	1.55311i	−0.630050	−	0.776554i	$-0.716966\pi$
$911$		−	46.8771i		−	1.55311i	0.630050	−	0.776554i	$-0.283034\pi$
$912$		0			0
$913$	21.2439	−	21.2439i	0.703071	−	0.703071i
$914$		0			0
$915$	−12.0007	−	5.57080i	−0.396730	−	0.184165i
$916$		0			0
$917$	0.136241	−	0.136241i	0.00449907	−	0.00449907i
$918$		0			0
$919$	−35.5200			−1.17170			−0.585848	−	0.810421i	$-0.699238\pi$
$919$	−35.5200			−1.17170			−0.585848	+	0.810421i	$0.699238\pi$
$920$		0			0
$921$	29.6891			0.978288
$922$		0			0
$923$	−30.0053	+	30.0053i	−0.987635	+	0.987635i
$924$		0			0
$925$	−0.0340493	+	0.405299i	−0.00111954	+	0.0133262i
$926$		0			0
$927$	−11.3577	+	11.3577i	−0.373035	+	0.373035i
$928$		0			0
$929$			15.2702i			0.501000i	0.968117	+	0.250500i	$0.0805949\pi$
$929$			15.2702i			0.501000i	−0.968117	+	0.250500i	$0.919405\pi$
$930$		0			0
$931$		−	47.1338i		−	1.54475i
$932$		0			0
$933$	−18.3976	+	18.3976i	−0.602311	+	0.602311i
$934$		0			0
$935$	−8.25510	−	3.83208i	−0.269971	−	0.125322i
$936$		0			0
$937$	26.0645	−	26.0645i	0.851491	−	0.851491i	−0.138826	−	0.990317i	$-0.544333\pi$
$937$	26.0645	−	26.0645i	0.851491	−	0.851491i	0.990317	+	0.138826i	$0.0443329\pi$
$938$		0			0
$939$	19.4077			0.633348
$940$		0			0
$941$			7.43783i			0.242466i	0.992624	+	0.121233i	$0.0386849\pi$
$941$			7.43783i			0.242466i	−0.992624	+	0.121233i	$0.961315\pi$
$942$		0			0
$943$	−0.0150969	−	1.33697i	−0.000491623	−	0.0435376i
$944$		0			0
$945$	0.0348300	−	0.0127452i	0.00113302	−	0.000414602i
$946$		0			0
$947$	−19.8343	−	19.8343i	−0.644528	−	0.644528i	0.307137	−	0.951665i	$-0.400629\pi$
$947$	−19.8343	−	19.8343i	−0.644528	−	0.644528i	−0.951665	+	0.307137i	$0.900629\pi$
$948$		0			0
$949$			35.8425i			1.16350i
$950$		0			0
$951$	26.2684			0.851812
$952$		0			0
$953$	31.6040	+	31.6040i	1.02375	+	1.02375i	0.999711	+	0.0240441i	$0.00765421\pi$
$953$	31.6040	+	31.6040i	1.02375	+	1.02375i	0.0240441	+	0.999711i	$0.492346\pi$
$954$		0			0
$955$	−5.38910	−	14.7273i	−0.174387	−	0.476563i
$956$		0			0
$957$	−1.09276	+	1.09276i	−0.0353238	+	0.0353238i
$958$		0			0
$959$			0.0424494i			0.00137076i
$960$		0			0
$961$	16.6188			0.536091
$962$		0			0
$963$	7.94663	+	7.94663i	0.256077	+	0.256077i
$964$		0			0
$965$	14.3014	−	30.8083i	0.460379	−	0.991753i
$966$		0			0
$967$	11.9956	+	11.9956i	0.385754	+	0.385754i	0.873170	−	0.487416i	$-0.162060\pi$
$967$	11.9956	+	11.9956i	0.385754	+	0.385754i	−0.487416	+	0.873170i	$0.662060\pi$
$968$		0			0
$969$		−	15.8634i		−	0.509607i
$970$		0			0
$971$			20.2973i			0.651373i	0.945478	+	0.325686i	$0.105595\pi$
$971$			20.2973i			0.651373i	−0.945478	+	0.325686i	$0.894405\pi$
$972$		0			0
$973$	0.0645069	+	0.0645069i	0.00206800	+	0.00206800i
$974$		0			0
$975$	−10.8264	−	12.8122i	−0.346721	−	0.410320i
$976$		0			0
$977$	−23.2680	+	23.2680i	−0.744411	+	0.744411i	−0.973423	−	0.229013i	$-0.926450\pi$
$977$	−23.2680	+	23.2680i	−0.744411	+	0.744411i	0.229013	+	0.973423i	$0.426450\pi$
$978$		0			0
$979$		−	11.4224i		−	0.365061i
$980$		0			0
$981$		−	10.3003i		−	0.328863i
$982$		0			0
$983$	−7.96631	−	7.96631i	−0.254086	−	0.254086i	0.568558	−	0.822643i	$-0.307502\pi$
$983$	−7.96631	−	7.96631i	−0.254086	−	0.254086i	−0.822643	+	0.568558i	$0.807502\pi$
$984$		0			0
$985$	3.30059	+	1.53216i	0.105165	+	0.0488186i
$986$		0			0
$987$	−0.126298	+	0.126298i	−0.00402012	+	0.00402012i
$988$		0			0
$989$	20.4774	−	20.9451i	0.651143	−	0.666016i
$990$		0			0
$991$	12.4553			0.395655			0.197827	−	0.980237i	$-0.436611\pi$
$991$	12.4553			0.395655			0.197827	+	0.980237i	$0.436611\pi$
$992$		0			0
$993$	6.04532	−	6.04532i	0.191842	−	0.191842i
$994$		0			0
$995$	37.1111	−	13.5799i	1.17650	−	0.430513i
$996$		0			0
$997$	21.3456	+	21.3456i	0.676021	+	0.676021i	0.959097	−	0.283077i	$-0.0913551\pi$
$997$	21.3456	+	21.3456i	0.676021	+	0.676021i	−0.283077	+	0.959097i	$0.591355\pi$
$998$		0			0
$999$	−0.0813454			−0.00257365

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.t.a.1057.9	✓	48
5.3	odd	4	inner	1380.2.t.a.1333.10	yes	48
23.22	odd	2	inner	1380.2.t.a.1057.10	yes	48
115.68	even	4	inner	1380.2.t.a.1333.9	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.t.a.1057.9	✓	48	1.1	even	1	trivial
1380.2.t.a.1057.10	yes	48	23.22	odd	2	inner
1380.2.t.a.1333.9	yes	48	115.68	even	4	inner
1380.2.t.a.1333.10	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(-2.09989 + 0.768407i) q^{5} +(-0.0117285 + 0.0117285i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{3} +(-2.09989 + 0.768407i) q^{5} +(-0.0117285 + 0.0117285i) q^{7} -1.00000i q^{9} +1.72770i q^{11} +(-2.37219 + 2.37219i) q^{13} +(0.941503 - 2.02819i) q^{15} +(1.66583 - 1.66583i) q^{17} -6.73367 q^{19} -0.0165866i q^{21} +(-0.0541507 - 4.79553i) q^{23} +(3.81910 - 3.22714i) q^{25} +(0.707107 + 0.707107i) q^{27} -0.894482i q^{29} +6.90064 q^{31} +(-1.22167 - 1.22167i) q^{33} +(0.0156163 - 0.0336408i) q^{35} +(-0.0575199 + 0.0575199i) q^{37} -3.35478i q^{39} +0.278794 q^{41} +(4.31887 + 4.31887i) q^{43} +(0.768407 + 2.09989i) q^{45} +(-7.61450 - 7.61450i) q^{47} +6.99972i q^{49} +2.35584i q^{51} +(-9.64615 - 9.64615i) q^{53} +(-1.32757 - 3.62798i) q^{55} +(4.76142 - 4.76142i) q^{57} -15.1371i q^{59} -5.91692i q^{61} +(0.0117285 + 0.0117285i) q^{63} +(3.15853 - 6.80414i) q^{65} +(-1.99060 + 1.99060i) q^{67} +(3.42924 + 3.35266i) q^{69} +12.6488 q^{71} +(7.55474 - 7.55474i) q^{73} +(-0.418577 + 4.98245i) q^{75} +(-0.0202632 - 0.0202632i) q^{77} +3.91526 q^{79} -1.00000 q^{81} +(-12.2961 - 12.2961i) q^{83} +(-2.21803 + 4.77810i) q^{85} +(0.632494 + 0.632494i) q^{87} -6.61134 q^{89} -0.0556442i q^{91} +(-4.87949 + 4.87949i) q^{93} +(14.1400 - 5.17420i) q^{95} +(9.80227 - 9.80227i) q^{97} +1.72770 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 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

Properties

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