LMFDB - Embedded newform 1920.2.bl.a.289.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1920,2,Mod(289,1920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1920, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1920.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.bl (of order $4$, degree $2$, not 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:	$15.3312771881$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			289.15
Character	$\chi$	$=$	1920.289
Dual form			1920.2.bl.a.1249.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{3} +(-0.770325 - 2.09919i) q^{5} -3.05002 q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{3} +(-0.770325 - 2.09919i) q^{5} -3.05002 q^{7} -1.00000i q^{9} +(1.80989 - 1.80989i) q^{11} +(2.47057 - 2.47057i) q^{13} +(-2.02905 - 0.939649i) q^{15} -3.66653i q^{17} +(2.31596 + 2.31596i) q^{19} +(-2.15669 + 2.15669i) q^{21} -4.86336 q^{23} +(-3.81320 + 3.23412i) q^{25} +(-0.707107 - 0.707107i) q^{27} +(-4.74672 - 4.74672i) q^{29} +1.86172 q^{31} -2.55957i q^{33} +(2.34951 + 6.40257i) q^{35} +(5.40092 + 5.40092i) q^{37} -3.49392i q^{39} +6.47424i q^{41} +(-4.19382 - 4.19382i) q^{43} +(-2.09919 + 0.770325i) q^{45} +8.24387i q^{47} +2.30263 q^{49} +(-2.59263 - 2.59263i) q^{51} +(-9.99761 - 9.99761i) q^{53} +(-5.19350 - 2.40510i) q^{55} +3.27526 q^{57} +(2.47155 - 2.47155i) q^{59} +(-8.01822 - 8.01822i) q^{61} +3.05002i q^{63} +(-7.08935 - 3.28306i) q^{65} +(-8.60064 + 8.60064i) q^{67} +(-3.43891 + 3.43891i) q^{69} +6.63653i q^{71} -2.70041 q^{73} +(-0.409472 + 4.98321i) q^{75} +(-5.52020 + 5.52020i) q^{77} -10.9690 q^{79} -1.00000 q^{81} +(3.65688 - 3.65688i) q^{83} +(-7.69675 + 2.82442i) q^{85} -6.71288 q^{87} -13.1530i q^{89} +(-7.53530 + 7.53530i) q^{91} +(1.31644 - 1.31644i) q^{93} +(3.07760 - 6.64569i) q^{95} -12.4932i q^{97} +(-1.80989 - 1.80989i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 8 q^{19} - 48 q^{31} - 24 q^{35} + 48 q^{49} - 8 q^{51} + 32 q^{59} - 16 q^{61} + 16 q^{65} + 16 q^{69} + 16 q^{75} - 96 q^{79} - 48 q^{81} + 32 q^{91} - 48 q^{95}+O(q^{100}) $ 48 * q - 8 * q^19 - 48 * q^31 - 24 * q^35 + 48 * q^49 - 8 * q^51 + 32 * q^59 - 16 * q^61 + 16 * q^65 + 16 * q^69 + 16 * q^75 - 96 * q^79 - 48 * q^81 + 32 * q^91 - 48 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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
$5$	−0.770325	−	2.09919i	−0.344500	−	0.938786i
$5$	−0.770325	−	2.09919i	−0.344500	−	0.938786i
$6$		0			0
$7$	−3.05002			−1.15280			−0.576400	−	0.817168i	$-0.695543\pi$
$7$	−3.05002			−1.15280			−0.576400	+	0.817168i	$0.695543\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	1.80989	−	1.80989i	0.545702	−	0.545702i	−0.379493	−	0.925195i	$-0.623901\pi$
$11$	1.80989	−	1.80989i	0.545702	−	0.545702i	0.925195	+	0.379493i	$0.123901\pi$
$12$		0			0
$13$	2.47057	−	2.47057i	0.685214	−	0.685214i	−0.275956	−	0.961170i	$-0.588995\pi$
$13$	2.47057	−	2.47057i	0.685214	−	0.685214i	0.961170	+	0.275956i	$0.0889946\pi$
$14$		0			0
$15$	−2.02905	−	0.939649i	−0.523899	−	0.242616i
$16$		0			0
$17$		−	3.66653i		−	0.889265i	−0.895713	−	0.444632i	$-0.853334\pi$
$17$		−	3.66653i		−	0.889265i	0.895713	−	0.444632i	$-0.146666\pi$
$18$		0			0
$19$	2.31596	+	2.31596i	0.531318	+	0.531318i	0.920964	−	0.389647i	$-0.127403\pi$
$19$	2.31596	+	2.31596i	0.531318	+	0.531318i	−0.389647	+	0.920964i	$0.627403\pi$
$20$		0			0
$21$	−2.15669	+	2.15669i	−0.470629	+	0.470629i
$22$		0			0
$23$	−4.86336			−1.01408			−0.507040	−	0.861922i	$-0.669260\pi$
$23$	−4.86336			−1.01408			−0.507040	+	0.861922i	$0.669260\pi$
$24$		0			0
$25$	−3.81320	+	3.23412i	−0.762640	+	0.646824i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$	−4.74672	−	4.74672i	−0.881444	−	0.881444i	0.112237	−	0.993681i	$-0.464198\pi$
$29$	−4.74672	−	4.74672i	−0.881444	−	0.881444i	−0.993681	+	0.112237i	$0.964198\pi$
$30$		0			0
$31$	1.86172			0.334375			0.167188	−	0.985925i	$-0.446531\pi$
$31$	1.86172			0.334375			0.167188	+	0.985925i	$0.446531\pi$
$32$		0			0
$33$		−	2.55957i		−	0.445564i
$34$		0			0
$35$	2.34951	+	6.40257i	0.397139	+	1.08223i
$36$		0			0
$37$	5.40092	+	5.40092i	0.887905	+	0.887905i	0.994322	−	0.106416i	$-0.0339376\pi$
$37$	5.40092	+	5.40092i	0.887905	+	0.887905i	−0.106416	+	0.994322i	$0.533938\pi$
$38$		0			0
$39$		−	3.49392i		−	0.559475i
$40$		0			0
$41$			6.47424i			1.01111i	0.862796	+	0.505553i	$0.168712\pi$
$41$			6.47424i			1.01111i	−0.862796	+	0.505553i	$0.831288\pi$
$42$		0			0
$43$	−4.19382	−	4.19382i	−0.639551	−	0.639551i	0.310893	−	0.950445i	$-0.399372\pi$
$43$	−4.19382	−	4.19382i	−0.639551	−	0.639551i	−0.950445	+	0.310893i	$0.899372\pi$
$44$		0			0
$45$	−2.09919	+	0.770325i	−0.312929	+	0.114833i
$46$		0			0
$47$			8.24387i			1.20249i	0.799064	+	0.601246i	$0.205329\pi$
$47$			8.24387i			1.20249i	−0.799064	+	0.601246i	$0.794671\pi$
$48$		0			0
$49$	2.30263			0.328947
$50$		0			0
$51$	−2.59263	−	2.59263i	−0.363041	−	0.363041i
$52$		0			0
$53$	−9.99761	−	9.99761i	−1.37328	−	1.37328i	−0.855539	−	0.517739i	$-0.826774\pi$
$53$	−9.99761	−	9.99761i	−1.37328	−	1.37328i	−0.517739	−	0.855539i	$-0.673226\pi$
$54$		0			0
$55$	−5.19350	−	2.40510i	−0.700292	−	0.324303i
$56$		0			0
$57$	3.27526			0.433819
$58$		0			0
$59$	2.47155	−	2.47155i	0.321769	−	0.321769i	−0.527676	−	0.849445i	$-0.676937\pi$
$59$	2.47155	−	2.47155i	0.321769	−	0.321769i	0.849445	+	0.527676i	$0.176937\pi$
$60$		0			0
$61$	−8.01822	−	8.01822i	−1.02663	−	1.02663i	−0.999636	−	0.0269927i	$-0.991407\pi$
$61$	−8.01822	−	8.01822i	−1.02663	−	1.02663i	−0.0269927	−	0.999636i	$-0.508593\pi$
$62$		0			0
$63$			3.05002i			0.384267i
$64$		0			0
$65$	−7.08935	−	3.28306i	−0.879325	−	0.407213i
$66$		0			0
$67$	−8.60064	+	8.60064i	−1.05074	+	1.05074i	−0.0520936	+	0.998642i	$0.516589\pi$
$67$	−8.60064	+	8.60064i	−1.05074	+	1.05074i	−0.998642	+	0.0520936i	$0.983411\pi$
$68$		0			0
$69$	−3.43891	+	3.43891i	−0.413997	+	0.413997i
$70$		0			0
$71$			6.63653i			0.787611i	0.919194	+	0.393806i	$0.128842\pi$
$71$			6.63653i			0.787611i	−0.919194	+	0.393806i	$0.871158\pi$
$72$		0			0
$73$	−2.70041			−0.316059			−0.158030	−	0.987434i	$-0.550514\pi$
$73$	−2.70041			−0.316059			−0.158030	+	0.987434i	$0.550514\pi$
$74$		0			0
$75$	−0.409472	+	4.98321i	−0.0472817	+	0.575411i
$76$		0			0
$77$	−5.52020	+	5.52020i	−0.629085	+	0.629085i
$78$		0			0
$79$	−10.9690			−1.23411			−0.617054	−	0.786921i	$-0.711674\pi$
$79$	−10.9690			−1.23411			−0.617054	+	0.786921i	$0.711674\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	3.65688	−	3.65688i	0.401395	−	0.401395i	−0.477330	−	0.878724i	$-0.658395\pi$
$83$	3.65688	−	3.65688i	0.401395	−	0.401395i	0.878724	+	0.477330i	$0.158395\pi$
$84$		0			0
$85$	−7.69675	+	2.82442i	−0.834830	+	0.306352i
$86$		0			0
$87$	−6.71288			−0.719696
$88$		0			0
$89$		−	13.1530i		−	1.39421i	−0.716968	−	0.697106i	$-0.754471\pi$
$89$		−	13.1530i		−	1.39421i	0.716968	−	0.697106i	$-0.245529\pi$
$90$		0			0
$91$	−7.53530	+	7.53530i	−0.789914	+	0.789914i
$92$		0			0
$93$	1.31644	−	1.31644i	0.136508	−	0.136508i
$94$		0			0
$95$	3.07760	−	6.64569i	0.315755	−	0.681833i
$96$		0			0
$97$		−	12.4932i		−	1.26849i	−0.773131	−	0.634247i	$-0.781310\pi$
$97$		−	12.4932i		−	1.26849i	0.773131	−	0.634247i	$-0.218690\pi$
$98$		0			0
$99$	−1.80989	−	1.80989i	−0.181901	−	0.181901i
$100$		0			0
$101$	−0.569518	+	0.569518i	−0.0566692	+	0.0566692i	−0.734873	−	0.678204i	$-0.762758\pi$
$101$	−0.569518	+	0.569518i	−0.0566692	+	0.0566692i	0.678204	+	0.734873i	$0.262758\pi$
$102$		0			0
$103$	12.2060			1.20269			0.601345	−	0.798989i	$-0.294632\pi$
$103$	12.2060			1.20269			0.601345	+	0.798989i	$0.294632\pi$
$104$		0			0
$105$	6.18866	+	2.86595i	0.603951	+	0.279688i
$106$		0			0
$107$	−7.99550	−	7.99550i	−0.772955	−	0.772955i	0.205667	−	0.978622i	$-0.434063\pi$
$107$	−7.99550	−	7.99550i	−0.772955	−	0.772955i	−0.978622	+	0.205667i	$0.934063\pi$
$108$		0			0
$109$	7.07511	+	7.07511i	0.677672	+	0.677672i	0.959473	−	0.281801i	$-0.0909317\pi$
$109$	7.07511	+	7.07511i	0.677672	+	0.677672i	−0.281801	+	0.959473i	$0.590932\pi$
$110$		0			0
$111$	7.63805			0.724972
$112$		0			0
$113$		−	6.25105i		−	0.588050i	−0.955798	−	0.294025i	$-0.905005\pi$
$113$		−	6.25105i		−	0.588050i	0.955798	−	0.294025i	$-0.0949948\pi$
$114$		0			0
$115$	3.74637	+	10.2091i	0.349351	+	0.952005i
$116$		0			0
$117$	−2.47057	−	2.47057i	−0.228405	−	0.228405i
$118$		0			0
$119$			11.1830i			1.02514i
$120$		0			0
$121$			4.44861i			0.404419i
$122$		0			0
$123$	4.57798	+	4.57798i	0.412782	+	0.412782i
$124$		0			0
$125$	9.72643	+	5.51331i	0.869958	+	0.493125i
$126$		0			0
$127$			14.1884i			1.25902i	0.776993	+	0.629509i	$0.216744\pi$
$127$			14.1884i			1.25902i	−0.776993	+	0.629509i	$0.783256\pi$
$128$		0			0
$129$	−5.93095			−0.522191
$130$		0			0
$131$	12.5522	+	12.5522i	1.09669	+	1.09669i	0.994795	+	0.101896i	$0.0324909\pi$
$131$	12.5522	+	12.5522i	1.09669	+	1.09669i	0.101896	+	0.994795i	$0.467509\pi$
$132$		0			0
$133$	−7.06373	−	7.06373i	−0.612503	−	0.612503i
$134$		0			0
$135$	−0.939649	+	2.02905i	−0.0808721	+	0.174633i
$136$		0			0
$137$	−4.88336			−0.417214			−0.208607	−	0.978000i	$-0.566893\pi$
$137$	−4.88336			−0.417214			−0.208607	+	0.978000i	$0.566893\pi$
$138$		0			0
$139$	−5.84556	+	5.84556i	−0.495814	+	0.495814i	−0.910132	−	0.414318i	$-0.864020\pi$
$139$	−5.84556	+	5.84556i	−0.495814	+	0.495814i	0.414318	+	0.910132i	$0.364020\pi$
$140$		0			0
$141$	5.82930	+	5.82930i	0.490915	+	0.490915i
$142$		0			0
$143$		−	8.94292i		−	0.747845i
$144$		0			0
$145$	−6.30775	+	13.6208i	−0.523830	+	1.13115i
$146$		0			0
$147$	1.62821	−	1.62821i	0.134292	−	0.134292i
$148$		0			0
$149$	15.1483	−	15.1483i	1.24100	−	1.24100i	0.281412	−	0.959587i	$-0.409197\pi$
$149$	15.1483	−	15.1483i	1.24100	−	1.24100i	0.959587	−	0.281412i	$-0.0908029\pi$
$150$		0			0
$151$			4.02031i			0.327168i	0.986529	+	0.163584i	$0.0523056\pi$
$151$			4.02031i			0.327168i	−0.986529	+	0.163584i	$0.947694\pi$
$152$		0			0
$153$	−3.66653			−0.296422
$154$		0			0
$155$	−1.43413	−	3.90811i	−0.115192	−	0.313907i
$156$		0			0
$157$	9.86041	−	9.86041i	0.786946	−	0.786946i	−0.194046	−	0.980992i	$-0.562161\pi$
$157$	9.86041	−	9.86041i	0.786946	−	0.786946i	0.980992	+	0.194046i	$0.0621612\pi$
$158$		0			0
$159$	−14.1388			−1.12128
$160$		0			0
$161$	14.8333			1.16903
$162$		0			0
$163$	−13.1713	+	13.1713i	−1.03165	+	1.03165i	−0.0321718	+	0.999482i	$0.510242\pi$
$163$	−13.1713	+	13.1713i	−1.03165	+	1.03165i	−0.999482	+	0.0321718i	$0.989758\pi$
$164$		0			0
$165$	−5.37302	+	1.97170i	−0.418289	+	0.153497i
$166$		0			0
$167$	−0.0610761			−0.00472621			−0.00236311	−	0.999997i	$-0.500752\pi$
$167$	−0.0610761			−0.00472621			−0.00236311	+	0.999997i	$0.500752\pi$
$168$		0			0
$169$			0.792537i			0.0609644i
$170$		0			0
$171$	2.31596	−	2.31596i	0.177106	−	0.177106i
$172$		0			0
$173$	8.01622	−	8.01622i	0.609462	−	0.609462i	−0.333343	−	0.942805i	$-0.608177\pi$
$173$	8.01622	−	8.01622i	0.609462	−	0.609462i	0.942805	+	0.333343i	$0.108177\pi$
$174$		0			0
$175$	11.6303	−	9.86413i	0.879171	−	0.745658i
$176$		0			0
$177$		−	3.49531i		−	0.262723i
$178$		0			0
$179$	−11.8352	−	11.8352i	−0.884607	−	0.884607i	0.109392	−	0.993999i	$-0.465110\pi$
$179$	−11.8352	−	11.8352i	−0.884607	−	0.884607i	−0.993999	+	0.109392i	$0.965110\pi$
$180$		0			0
$181$	−3.63391	+	3.63391i	−0.270106	+	0.270106i	−0.829143	−	0.559037i	$-0.811171\pi$
$181$	−3.63391	+	3.63391i	−0.270106	+	0.270106i	0.559037	+	0.829143i	$0.311171\pi$
$182$		0			0
$183$	−11.3395			−0.838239
$184$		0			0
$185$	7.17709	−	15.4980i	0.527670	−	1.13944i
$186$		0			0
$187$	−6.63602	−	6.63602i	−0.485274	−	0.485274i
$188$		0			0
$189$	2.15669	+	2.15669i	0.156876	+	0.156876i
$190$		0			0
$191$	19.0823			1.38074			0.690372	−	0.723455i	$-0.257447\pi$
$191$	19.0823			1.38074			0.690372	+	0.723455i	$0.257447\pi$
$192$		0			0
$193$		−	2.99015i		−	0.215236i	−0.994192	−	0.107618i	$-0.965678\pi$
$193$		−	2.99015i		−	0.215236i	0.994192	−	0.107618i	$-0.0343223\pi$
$194$		0			0
$195$	−7.33440	+	2.69145i	−0.525227	+	0.192739i
$196$		0			0
$197$	1.37271	+	1.37271i	0.0978016	+	0.0978016i	0.754315	−	0.656513i	$-0.227969\pi$
$197$	1.37271	+	1.37271i	0.0978016	+	0.0978016i	−0.656513	+	0.754315i	$0.727969\pi$
$198$		0			0
$199$		−	15.7129i		−	1.11386i	−0.830560	−	0.556930i	$-0.811979\pi$
$199$		−	15.7129i		−	1.11386i	0.830560	−	0.556930i	$-0.188021\pi$
$200$		0			0
$201$			12.1631i			0.857922i
$202$		0			0
$203$	14.4776	+	14.4776i	1.01613	+	1.01613i
$204$		0			0
$205$	13.5907	−	4.98727i	0.949213	−	0.348326i
$206$		0			0
$207$			4.86336i			0.338027i
$208$		0			0
$209$	8.38326			0.579882
$210$		0			0
$211$	−16.8391	−	16.8391i	−1.15925	−	1.15925i	−0.984637	−	0.174614i	$-0.944132\pi$
$211$	−16.8391	−	16.8391i	−1.15925	−	1.15925i	−0.174614	−	0.984637i	$-0.555868\pi$
$212$		0			0
$213$	4.69274	+	4.69274i	0.321541	+	0.321541i
$214$		0			0
$215$	−5.57302	+	12.0342i	−0.380077	+	0.820727i
$216$		0			0
$217$	−5.67830			−0.385468
$218$		0			0
$219$	−1.90948	+	1.90948i	−0.129031	+	0.129031i
$220$		0			0
$221$	−9.05844	−	9.05844i	−0.609336	−	0.609336i
$222$		0			0
$223$		−	10.6893i		−	0.715809i	−0.933758	−	0.357905i	$-0.883491\pi$
$223$		−	10.6893i		−	0.715809i	0.933758	−	0.357905i	$-0.116509\pi$
$224$		0			0
$225$	3.23412	+	3.81320i	0.215608	+	0.254213i
$226$		0			0
$227$	15.0722	−	15.0722i	1.00037	−	1.00037i	0.000374434	−	1.00000i	$-0.499881\pi$
$227$	15.0722	−	15.0722i	1.00037	−	1.00037i	1.00000		0.000374434i	$-0.000119186\pi$
$228$		0			0
$229$	3.23629	−	3.23629i	0.213860	−	0.213860i	−0.592045	−	0.805905i	$-0.701679\pi$
$229$	3.23629	−	3.23629i	0.213860	−	0.213860i	0.805905	+	0.592045i	$0.201679\pi$
$230$		0			0
$231$			7.80674i			0.513646i
$232$		0			0
$233$	−4.75428			−0.311463			−0.155732	−	0.987799i	$-0.549773\pi$
$233$	−4.75428			−0.311463			−0.155732	+	0.987799i	$0.549773\pi$
$234$		0			0
$235$	17.3054	−	6.35046i	1.12888	−	0.414258i
$236$		0			0
$237$	−7.75625	+	7.75625i	−0.503823	+	0.503823i
$238$		0			0
$239$	11.9224			0.771196			0.385598	−	0.922667i	$-0.373995\pi$
$239$	11.9224			0.771196			0.385598	+	0.922667i	$0.373995\pi$
$240$		0			0
$241$	−28.2991			−1.82291			−0.911453	−	0.411403i	$-0.865039\pi$
$241$	−28.2991			−1.82291			−0.911453	+	0.411403i	$0.865039\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	−1.77377	−	4.83366i	−0.113322	−	0.308811i
$246$		0			0
$247$	11.4435			0.728133
$248$		0			0
$249$		−	5.17161i		−	0.327737i
$250$		0			0
$251$	4.39215	−	4.39215i	0.277230	−	0.277230i	−0.554772	−	0.832002i	$-0.687195\pi$
$251$	4.39215	−	4.39215i	0.277230	−	0.277230i	0.832002	+	0.554772i	$0.187195\pi$
$252$		0			0
$253$	−8.80214	+	8.80214i	−0.553386	+	0.553386i
$254$		0			0
$255$	−3.44526	+	7.43959i	−0.215750	+	0.465885i
$256$		0			0
$257$		−	2.53050i		−	0.157849i	−0.996881	−	0.0789243i	$-0.974851\pi$
$257$		−	2.53050i		−	0.157849i	0.996881	−	0.0789243i	$-0.0251485\pi$
$258$		0			0
$259$	−16.4729	−	16.4729i	−1.02358	−	1.02358i
$260$		0			0
$261$	−4.74672	+	4.74672i	−0.293815	+	0.293815i
$262$		0			0
$263$	0.540983			0.0333584			0.0166792	−	0.999861i	$-0.494691\pi$
$263$	0.540983			0.0333584			0.0166792	+	0.999861i	$0.494691\pi$
$264$		0			0
$265$	−13.2855	+	28.6883i	−0.816120	+	1.76231i
$266$		0			0
$267$	−9.30055	−	9.30055i	−0.569184	−	0.569184i
$268$		0			0
$269$	3.00188	+	3.00188i	0.183028	+	0.183028i	0.792674	−	0.609646i	$-0.208688\pi$
$269$	3.00188	+	3.00188i	0.183028	+	0.183028i	−0.609646	+	0.792674i	$0.708688\pi$
$270$		0			0
$271$	−8.44312			−0.512883			−0.256442	−	0.966560i	$-0.582550\pi$
$271$	−8.44312			−0.512883			−0.256442	+	0.966560i	$0.582550\pi$
$272$		0			0
$273$			10.6565i			0.644962i
$274$		0			0
$275$	−1.04807	+	12.7549i	−0.0632011	+	0.769147i
$276$		0			0
$277$	12.2494	+	12.2494i	0.735992	+	0.735992i	0.971800	−	0.235807i	$-0.0757735\pi$
$277$	12.2494	+	12.2494i	0.735992	+	0.735992i	−0.235807	+	0.971800i	$0.575773\pi$
$278$		0			0
$279$		−	1.86172i		−	0.111458i
$280$		0			0
$281$		−	16.6912i		−	0.995715i	−0.867259	−	0.497857i	$-0.834120\pi$
$281$		−	16.6912i		−	0.995715i	0.867259	−	0.497857i	$-0.165880\pi$
$282$		0			0
$283$	1.25800	+	1.25800i	0.0747802	+	0.0747802i	0.743508	−	0.668727i	$-0.233161\pi$
$283$	1.25800	+	1.25800i	0.0747802	+	0.0747802i	−0.668727	+	0.743508i	$0.733161\pi$
$284$		0			0
$285$	−2.52302	−	6.87540i	−0.149451	−	0.407264i
$286$		0			0
$287$		−	19.7466i		−	1.16560i
$288$		0			0
$289$	3.55654			0.209208
$290$		0			0
$291$	−8.83403	−	8.83403i	−0.517860	−	0.517860i
$292$		0			0
$293$	12.4197	+	12.4197i	0.725564	+	0.725564i	0.969733	−	0.244169i	$-0.0785151\pi$
$293$	12.4197	+	12.4197i	0.725564	+	0.725564i	−0.244169	+	0.969733i	$0.578515\pi$
$294$		0			0
$295$	−7.09216	−	3.28436i	−0.412922	−	0.191223i
$296$		0			0
$297$	−2.55957			−0.148521
$298$		0			0
$299$	−12.0153	+	12.0153i	−0.694862	+	0.694862i
$300$		0			0
$301$	12.7912	+	12.7912i	0.737275	+	0.737275i
$302$		0			0
$303$			0.805420i			0.0462702i
$304$		0			0
$305$	−10.6551	+	23.0084i	−0.610111	+	1.31746i
$306$		0			0
$307$	21.6994	−	21.6994i	1.23845	−	1.23845i	0.277816	−	0.960634i	$-0.410389\pi$
$307$	21.6994	−	21.6994i	1.23845	−	1.23845i	0.960634	−	0.277816i	$-0.0896107\pi$
$308$		0			0
$309$	8.63093	−	8.63093i	0.490996	−	0.490996i
$310$		0			0
$311$		−	13.6575i		−	0.774447i	−0.921986	−	0.387224i	$-0.873434\pi$
$311$		−	13.6575i		−	0.774447i	0.921986	−	0.387224i	$-0.126566\pi$
$312$		0			0
$313$	13.7537			0.777403			0.388701	−	0.921364i	$-0.372924\pi$
$313$	13.7537			0.777403			0.388701	+	0.921364i	$0.372924\pi$
$314$		0			0
$315$	6.40257	−	2.34951i	0.360744	−	0.132380i
$316$		0			0
$317$	−16.5311	+	16.5311i	−0.928477	+	0.928477i	−0.997608	−	0.0691306i	$-0.977977\pi$
$317$	−16.5311	+	16.5311i	−0.928477	+	0.928477i	0.0691306	+	0.997608i	$0.477977\pi$
$318$		0			0
$319$	−17.1821			−0.962012
$320$		0			0
$321$	−11.3073			−0.631115
$322$		0			0
$323$	8.49155	−	8.49155i	0.472482	−	0.472482i
$324$		0			0
$325$	−1.43066	+	17.4109i	−0.0793588	+	0.965784i
$326$		0			0
$327$	10.0057			0.553317
$328$		0			0
$329$		−	25.1440i		−	1.38623i
$330$		0			0
$331$	8.05179	−	8.05179i	0.442566	−	0.442566i	−0.450307	−	0.892874i	$-0.648686\pi$
$331$	8.05179	−	8.05179i	0.442566	−	0.442566i	0.892874	+	0.450307i	$0.148686\pi$
$332$		0			0
$333$	5.40092	−	5.40092i	0.295968	−	0.295968i
$334$		0			0
$335$	24.6797	+	11.4291i	1.34839	+	0.624438i
$336$		0			0
$337$			4.77730i			0.260236i	0.991499	+	0.130118i	$0.0415356\pi$
$337$			4.77730i			0.260236i	−0.991499	+	0.130118i	$0.958464\pi$
$338$		0			0
$339$	−4.42016	−	4.42016i	−0.240070	−	0.240070i
$340$		0			0
$341$	3.36951	−	3.36951i	0.182469	−	0.182469i
$342$		0			0
$343$	14.3271			0.773589
$344$		0			0
$345$	9.86802	+	4.56985i	0.531276	+	0.246033i
$346$		0			0
$347$	−3.32673	−	3.32673i	−0.178588	−	0.178588i	0.612152	−	0.790740i	$-0.290304\pi$
$347$	−3.32673	−	3.32673i	−0.178588	−	0.178588i	−0.790740	+	0.612152i	$0.790304\pi$
$348$		0			0
$349$	−21.8586	−	21.8586i	−1.17007	−	1.17007i	−0.982194	−	0.187872i	$-0.939841\pi$
$349$	−21.8586	−	21.8586i	−1.17007	−	1.17007i	−0.187872	−	0.982194i	$-0.560159\pi$
$350$		0			0
$351$	−3.49392			−0.186492
$352$		0			0
$353$			5.19436i			0.276468i	0.990400	+	0.138234i	$0.0441426\pi$
$353$			5.19436i			0.276468i	−0.990400	+	0.138234i	$0.955857\pi$
$354$		0			0
$355$	13.9313	−	5.11229i	0.739399	−	0.271332i
$356$		0			0
$357$	7.90758	+	7.90758i	0.418513	+	0.418513i
$358$		0			0
$359$		−	21.0115i		−	1.10894i	−0.832203	−	0.554472i	$-0.812920\pi$
$359$		−	21.0115i		−	1.10894i	0.832203	−	0.554472i	$-0.187080\pi$
$360$		0			0
$361$		−	8.27265i		−	0.435403i
$362$		0			0
$363$	3.14564	+	3.14564i	0.165103	+	0.165103i
$364$		0			0
$365$	2.08020	+	5.66868i	0.108882	+	0.296712i
$366$		0			0
$367$			24.5855i			1.28335i	0.766976	+	0.641676i	$0.221760\pi$
$367$			24.5855i			1.28335i	−0.766976	+	0.641676i	$0.778240\pi$
$368$		0			0
$369$	6.47424			0.337035
$370$		0			0
$371$	30.4929	+	30.4929i	1.58311	+	1.58311i
$372$		0			0
$373$	−1.00389	−	1.00389i	−0.0519795	−	0.0519795i	0.680639	−	0.732619i	$-0.261702\pi$
$373$	−1.00389	−	1.00389i	−0.0519795	−	0.0519795i	−0.732619	+	0.680639i	$0.761702\pi$
$374$		0			0
$375$	10.7761	−	2.97913i	0.556477	−	0.153842i
$376$		0			0
$377$	−23.4542			−1.20796
$378$		0			0
$379$	4.93721	−	4.93721i	0.253607	−	0.253607i	−0.568841	−	0.822448i	$-0.692608\pi$
$379$	4.93721	−	4.93721i	0.253607	−	0.253607i	0.822448	+	0.568841i	$0.192608\pi$
$380$		0			0
$381$	10.0327	+	10.0327i	0.513992	+	0.513992i
$382$		0			0
$383$		−	4.25312i		−	0.217324i	−0.994079	−	0.108662i	$-0.965343\pi$
$383$		−	4.25312i		−	0.217324i	0.994079	−	0.108662i	$-0.0346566\pi$
$384$		0			0
$385$	15.8403	+	7.33560i	0.807296	+	0.373857i
$386$		0			0
$387$	−4.19382	+	4.19382i	−0.213184	+	0.213184i
$388$		0			0
$389$	15.1555	−	15.1555i	0.768414	−	0.768414i	−0.209413	−	0.977827i	$-0.567155\pi$
$389$	15.1555	−	15.1555i	0.768414	−	0.768414i	0.977827	+	0.209413i	$0.0671553\pi$
$390$		0			0
$391$			17.8317i			0.901786i
$392$		0			0
$393$	17.7515			0.895445
$394$		0			0
$395$	8.44969	+	23.0260i	0.425150	+	1.15856i
$396$		0			0
$397$	2.06126	−	2.06126i	0.103451	−	0.103451i	−0.653487	−	0.756938i	$-0.726694\pi$
$397$	2.06126	−	2.06126i	0.103451	−	0.103451i	0.756938	+	0.653487i	$0.226694\pi$
$398$		0			0
$399$	−9.98962			−0.500107
$400$		0			0
$401$	10.1012			0.504431			0.252215	−	0.967671i	$-0.418841\pi$
$401$	10.1012			0.504431			0.252215	+	0.967671i	$0.418841\pi$
$402$		0			0
$403$	4.59952	−	4.59952i	0.229119	−	0.229119i
$404$		0			0
$405$	0.770325	+	2.09919i	0.0382778	+	0.104310i
$406$		0			0
$407$	19.5501			0.969063
$408$		0			0
$409$		−	15.5464i		−	0.768720i	−0.923183	−	0.384360i	$-0.874422\pi$
$409$		−	15.5464i		−	0.768720i	0.923183	−	0.384360i	$-0.125578\pi$
$410$		0			0
$411$	−3.45306	+	3.45306i	−0.170327	+	0.170327i
$412$		0			0
$413$	−7.53829	+	7.53829i	−0.370935	+	0.370935i
$414$		0			0
$415$	−10.4935	−	4.85950i	−0.515104	−	0.238543i
$416$		0			0
$417$			8.26686i			0.404830i
$418$		0			0
$419$	−0.811206	−	0.811206i	−0.0396300	−	0.0396300i	0.687014	−	0.726644i	$-0.258921\pi$
$419$	−0.811206	−	0.811206i	−0.0396300	−	0.0396300i	−0.726644	+	0.687014i	$0.758921\pi$
$420$		0			0
$421$	−6.67755	+	6.67755i	−0.325444	+	0.325444i	−0.850851	−	0.525407i	$-0.823913\pi$
$421$	−6.67755	+	6.67755i	−0.325444	+	0.325444i	0.525407	+	0.850851i	$0.323913\pi$
$422$		0			0
$423$	8.24387			0.400831
$424$		0			0
$425$	11.8580	+	13.9812i	0.575197	+	0.678189i
$426$		0			0
$427$	24.4558	+	24.4558i	1.18350	+	1.18350i
$428$		0			0
$429$	−6.32360	−	6.32360i	−0.305306	−	0.305306i
$430$		0			0
$431$	−20.8900			−1.00623			−0.503117	−	0.864218i	$-0.667814\pi$
$431$	−20.8900			−1.00623			−0.503117	+	0.864218i	$0.667814\pi$
$432$		0			0
$433$			21.0344i			1.01085i	0.862870	+	0.505426i	$0.168664\pi$
$433$			21.0344i			1.01085i	−0.862870	+	0.505426i	$0.831336\pi$
$434$		0			0
$435$	5.17110	+	14.0916i	0.247935	+	0.675641i
$436$		0			0
$437$	−11.2633	−	11.2633i	−0.538799	−	0.538799i
$438$		0			0
$439$		−	27.5268i		−	1.31378i	−0.753986	−	0.656891i	$-0.771871\pi$
$439$		−	27.5268i		−	1.31378i	0.753986	−	0.656891i	$-0.228129\pi$
$440$		0			0
$441$		−	2.30263i		−	0.109649i
$442$		0			0
$443$	−15.3577	−	15.3577i	−0.729667	−	0.729667i	0.240886	−	0.970553i	$-0.422562\pi$
$443$	−15.3577	−	15.3577i	−0.729667	−	0.729667i	−0.970553	+	0.240886i	$0.922562\pi$
$444$		0			0
$445$	−27.6106	+	10.1321i	−1.30887	+	0.480306i
$446$		0			0
$447$		−	21.4230i		−	1.01327i
$448$		0			0
$449$	34.2343			1.61562			0.807808	−	0.589445i	$-0.200654\pi$
$449$	34.2343			1.61562			0.807808	+	0.589445i	$0.200654\pi$
$450$		0			0
$451$	11.7177	+	11.7177i	0.551763	+	0.551763i
$452$		0			0
$453$	2.84279	+	2.84279i	0.133566	+	0.133566i
$454$		0			0
$455$	21.6227	+	10.0134i	1.01369	+	0.469435i
$456$		0			0
$457$	37.3287			1.74616			0.873081	−	0.487575i	$-0.162119\pi$
$457$	37.3287			1.74616			0.873081	+	0.487575i	$0.162119\pi$
$458$		0			0
$459$	−2.59263	+	2.59263i	−0.121014	+	0.121014i
$460$		0			0
$461$	−4.31480	−	4.31480i	−0.200960	−	0.200960i	0.599451	−	0.800411i	$-0.295386\pi$
$461$	−4.31480	−	4.31480i	−0.200960	−	0.200960i	−0.800411	+	0.599451i	$0.795386\pi$
$462$		0			0
$463$		−	12.6151i		−	0.586272i	−0.956071	−	0.293136i	$-0.905301\pi$
$463$		−	12.6151i		−	0.586272i	0.956071	−	0.293136i	$-0.0946988\pi$
$464$		0			0
$465$	−3.77754	−	1.74937i	−0.175179	−	0.0811250i
$466$		0			0
$467$	−3.20222	+	3.20222i	−0.148181	+	0.148181i	−0.777305	−	0.629124i	$-0.783414\pi$
$467$	−3.20222	+	3.20222i	−0.148181	+	0.148181i	0.629124	+	0.777305i	$0.283414\pi$
$468$		0			0
$469$	26.2321	−	26.2321i	1.21129	−	1.21129i
$470$		0			0
$471$		−	13.9447i		−	0.642539i
$472$		0			0
$473$	−15.1807			−0.698009
$474$		0			0
$475$	−16.3213	−	1.34113i	−0.748873	−	0.0615352i
$476$		0			0
$477$	−9.99761	+	9.99761i	−0.457759	+	0.457759i
$478$		0			0
$479$	−9.07562			−0.414676			−0.207338	−	0.978269i	$-0.566480\pi$
$479$	−9.07562			−0.414676			−0.207338	+	0.978269i	$0.566480\pi$
$480$		0			0
$481$	26.6867			1.21681
$482$		0			0
$483$	10.4888	−	10.4888i	0.477255	−	0.477255i
$484$		0			0
$485$	−26.2256	+	9.62383i	−1.19084	+	0.436996i
$486$		0			0
$487$	1.02703			0.0465390			0.0232695	−	0.999729i	$-0.492592\pi$
$487$	1.02703			0.0465390			0.0232695	+	0.999729i	$0.492592\pi$
$488$		0			0
$489$			18.6270i			0.842342i
$490$		0			0
$491$	20.0654	−	20.0654i	0.905539	−	0.905539i	−0.0903689	−	0.995908i	$-0.528805\pi$
$491$	20.0654	−	20.0654i	0.905539	−	0.905539i	0.995908	+	0.0903689i	$0.0288046\pi$
$492$		0			0
$493$	−17.4040	+	17.4040i	−0.783837	+	0.783837i
$494$		0			0
$495$	−2.40510	+	5.19350i	−0.108101	+	0.233431i
$496$		0			0
$497$		−	20.2416i		−	0.907958i
$498$		0			0
$499$	−15.1622	−	15.1622i	−0.678752	−	0.678752i	0.280966	−	0.959718i	$-0.409345\pi$
$499$	−15.1622	−	15.1622i	−0.678752	−	0.678752i	−0.959718	+	0.280966i	$0.909345\pi$
$500$		0			0
$501$	−0.0431873	+	0.0431873i	−0.00192947	+	0.00192947i
$502$		0			0
$503$	15.6071			0.695885			0.347942	−	0.937516i	$-0.386880\pi$
$503$	15.6071			0.695885			0.347942	+	0.937516i	$0.386880\pi$
$504$		0			0
$505$	1.63424	+	0.756813i	0.0727228	+	0.0336777i
$506$		0			0
$507$	0.560408	+	0.560408i	0.0248886	+	0.0248886i
$508$		0			0
$509$	−10.8076	−	10.8076i	−0.479040	−	0.479040i	0.425785	−	0.904824i	$-0.359998\pi$
$509$	−10.8076	−	10.8076i	−0.479040	−	0.479040i	−0.904824	+	0.425785i	$0.859998\pi$
$510$		0			0
$511$	8.23632			0.364353
$512$		0			0
$513$		−	3.27526i		−	0.144606i
$514$		0			0
$515$	−9.40257	−	25.6227i	−0.414327	−	1.12907i
$516$		0			0
$517$	14.9205	+	14.9205i	0.656202	+	0.656202i
$518$		0			0
$519$		−	11.3367i		−	0.497624i
$520$		0			0
$521$			32.1238i			1.40737i	0.710513	+	0.703684i	$0.248463\pi$
$521$			32.1238i			1.40737i	−0.710513	+	0.703684i	$0.751537\pi$
$522$		0			0
$523$	−3.26553	−	3.26553i	−0.142792	−	0.142792i	0.632097	−	0.774889i	$-0.282194\pi$
$523$	−3.26553	−	3.26553i	−0.142792	−	0.142792i	−0.774889	+	0.632097i	$0.782194\pi$
$524$		0			0
$525$	1.24890	−	15.1989i	0.0545064	−	0.663334i
$526$		0			0
$527$		−	6.82607i		−	0.297348i
$528$		0			0
$529$	0.652259			0.0283591
$530$		0			0
$531$	−2.47155	−	2.47155i	−0.107256	−	0.107256i
$532$		0			0
$533$	15.9951	+	15.9951i	0.692824	+	0.692824i
$534$		0			0
$535$	−10.6249	+	22.9432i	−0.459356	+	0.991922i
$536$		0			0
$537$	−16.7375			−0.722278
$538$		0			0
$539$	4.16751	−	4.16751i	0.179507	−	0.179507i
$540$		0			0
$541$	25.5767	+	25.5767i	1.09963	+	1.09963i	0.994454	+	0.105176i	$0.0335405\pi$
$541$	25.5767	+	25.5767i	1.09963	+	1.09963i	0.105176	+	0.994454i	$0.466459\pi$
$542$		0			0
$543$			5.13913i			0.220541i
$544$		0			0
$545$	9.40186	−	20.3021i	0.402731	−	0.869647i
$546$		0			0
$547$	−6.44163	+	6.44163i	−0.275424	+	0.275424i	−0.831279	−	0.555855i	$-0.812391\pi$
$547$	−6.44163	+	6.44163i	−0.275424	+	0.275424i	0.555855	+	0.831279i	$0.312391\pi$
$548$		0			0
$549$	−8.01822	+	8.01822i	−0.342209	+	0.342209i
$550$		0			0
$551$		−	21.9864i		−	0.936654i
$552$		0			0
$553$	33.4557			1.42268
$554$		0			0
$555$	−5.88378	−	16.0337i	−0.249753	−	0.680594i
$556$		0			0
$557$	1.38276	−	1.38276i	0.0585893	−	0.0585893i	−0.677205	−	0.735794i	$-0.736809\pi$
$557$	1.38276	−	1.38276i	0.0585893	−	0.0585893i	0.735794	+	0.677205i	$0.236809\pi$
$558$		0			0
$559$	−20.7223			−0.876459
$560$		0			0
$561$	−9.38474			−0.396224
$562$		0			0
$563$	−4.13198	+	4.13198i	−0.174142	+	0.174142i	−0.788797	−	0.614654i	$-0.789296\pi$
$563$	−4.13198	+	4.13198i	−0.174142	+	0.174142i	0.614654	+	0.788797i	$0.289296\pi$
$564$		0			0
$565$	−13.1221	+	4.81534i	−0.552053	+	0.202583i
$566$		0			0
$567$	3.05002			0.128089
$568$		0			0
$569$		−	14.2348i		−	0.596755i	−0.954448	−	0.298378i	$-0.903554\pi$
$569$		−	14.2348i		−	0.596755i	0.954448	−	0.298378i	$-0.0964455\pi$
$570$		0			0
$571$	−14.6986	+	14.6986i	−0.615116	+	0.615116i	−0.944275	−	0.329158i	$-0.893235\pi$
$571$	−14.6986	+	14.6986i	−0.615116	+	0.615116i	0.329158	+	0.944275i	$0.393235\pi$
$572$		0			0
$573$	13.4932	−	13.4932i	0.563686	−	0.563686i
$574$		0			0
$575$	18.5450	−	15.7287i	0.773378	−	0.655931i
$576$		0			0
$577$			8.52221i			0.354784i	0.984140	+	0.177392i	$0.0567661\pi$
$577$			8.52221i			0.354784i	−0.984140	+	0.177392i	$0.943234\pi$
$578$		0			0
$579$	−2.11436	−	2.11436i	−0.0878696	−	0.0878696i
$580$		0			0
$581$	−11.1536	+	11.1536i	−0.462728	+	0.462728i
$582$		0			0
$583$	−36.1891			−1.49880
$584$		0			0
$585$	−3.28306	+	7.08935i	−0.135738	+	0.293108i
$586$		0			0
$587$	−13.9568	−	13.9568i	−0.576057	−	0.576057i	0.357757	−	0.933815i	$-0.383541\pi$
$587$	−13.9568	−	13.9568i	−0.576057	−	0.576057i	−0.933815	+	0.357757i	$0.883541\pi$
$588$		0			0
$589$	4.31168	+	4.31168i	0.177660	+	0.177660i
$590$		0			0
$591$	1.94131			0.0798547
$592$		0			0
$593$			22.9285i			0.941561i	0.882250	+	0.470781i	$0.156028\pi$
$593$			22.9285i			0.941561i	−0.882250	+	0.470781i	$0.843972\pi$
$594$		0			0
$595$	23.4752	−	8.61455i	0.962391	−	0.353162i
$596$		0			0
$597$	−11.1107	−	11.1107i	−0.454731	−	0.454731i
$598$		0			0
$599$			15.8822i			0.648928i	0.945898	+	0.324464i	$0.105184\pi$
$599$			15.8822i			0.648928i	−0.945898	+	0.324464i	$0.894816\pi$
$600$		0			0
$601$			4.12190i			0.168136i	0.996460	+	0.0840680i	$0.0267913\pi$
$601$			4.12190i			0.168136i	−0.996460	+	0.0840680i	$0.973209\pi$
$602$		0			0
$603$	8.60064	+	8.60064i	0.350245	+	0.350245i
$604$		0			0
$605$	9.33847	−	3.42687i	0.379663	−	0.139322i
$606$		0			0
$607$			26.7142i			1.08429i	0.840283	+	0.542147i	$0.182389\pi$
$607$			26.7142i			1.08429i	−0.840283	+	0.542147i	$0.817611\pi$
$608$		0			0
$609$	20.4744			0.829666
$610$		0			0
$611$	20.3671	+	20.3671i	0.823964	+	0.823964i
$612$		0			0
$613$	−10.0253	−	10.0253i	−0.404918	−	0.404918i	0.475044	−	0.879962i	$-0.342432\pi$
$613$	−10.0253	−	10.0253i	−0.404918	−	0.404918i	−0.879962	+	0.475044i	$0.842432\pi$
$614$		0			0
$615$	6.08351	−	13.1366i	0.245311	−	0.529718i
$616$		0			0
$617$	26.3757			1.06185			0.530923	−	0.847420i	$-0.321845\pi$
$617$	26.3757			1.06185			0.530923	+	0.847420i	$0.321845\pi$
$618$		0			0
$619$	7.39439	−	7.39439i	0.297206	−	0.297206i	−0.542713	−	0.839918i	$-0.682603\pi$
$619$	7.39439	−	7.39439i	0.297206	−	0.297206i	0.839918	+	0.542713i	$0.182603\pi$
$620$		0			0
$621$	3.43891	+	3.43891i	0.137999	+	0.137999i
$622$		0			0
$623$			40.1168i			1.60725i
$624$		0			0
$625$	4.08096	−	24.6647i	0.163239	−	0.986587i
$626$		0			0
$627$	5.92786	−	5.92786i	0.236736	−	0.236736i
$628$		0			0
$629$	19.8026	−	19.8026i	0.789583	−	0.789583i
$630$		0			0
$631$		−	34.8730i		−	1.38827i	−0.719844	−	0.694136i	$-0.755787\pi$
$631$		−	34.8730i		−	1.38827i	0.719844	−	0.694136i	$-0.244213\pi$
$632$		0			0
$633$	−23.8141			−0.946525
$634$		0			0
$635$	29.7842	−	10.9297i	1.18195	−	0.433732i
$636$		0			0
$637$	5.68882	−	5.68882i	0.225399	−	0.225399i
$638$		0			0
$639$	6.63653			0.262537
$640$		0			0
$641$	6.05015			0.238966			0.119483	−	0.992836i	$-0.461876\pi$
$641$	6.05015			0.238966			0.119483	+	0.992836i	$0.461876\pi$
$642$		0			0
$643$	7.52447	−	7.52447i	0.296736	−	0.296736i	−0.542998	−	0.839734i	$-0.682711\pi$
$643$	7.52447	−	7.52447i	0.296736	−	0.296736i	0.839734	+	0.542998i	$0.182711\pi$
$644$		0			0
$645$	4.56876	+	12.4502i	0.179895	+	0.490226i
$646$		0			0
$647$	−24.8356			−0.976389			−0.488194	−	0.872735i	$-0.662344\pi$
$647$	−24.8356			−0.976389			−0.488194	+	0.872735i	$0.662344\pi$
$648$		0			0
$649$		−	8.94648i		−	0.351180i
$650$		0			0
$651$	−4.01516	+	4.01516i	−0.157367	+	0.157367i
$652$		0			0
$653$	20.0550	−	20.0550i	0.784813	−	0.784813i	−0.195826	−	0.980639i	$-0.562739\pi$
$653$	20.0550	−	20.0550i	0.784813	−	0.784813i	0.980639	+	0.195826i	$0.0627386\pi$
$654$		0			0
$655$	16.6802	−	36.0187i	0.651749	−	1.40737i
$656$		0			0
$657$			2.70041i			0.105353i
$658$		0			0
$659$	−20.7719	−	20.7719i	−0.809158	−	0.809158i	0.175349	−	0.984506i	$-0.443895\pi$
$659$	−20.7719	−	20.7719i	−0.809158	−	0.809158i	−0.984506	+	0.175349i	$0.943895\pi$
$660$		0			0
$661$	11.2908	−	11.2908i	0.439161	−	0.439161i	−0.452568	−	0.891730i	$-0.649492\pi$
$661$	11.2908	−	11.2908i	0.439161	−	0.439161i	0.891730	+	0.452568i	$0.149492\pi$
$662$		0			0
$663$	−12.8106			−0.497521
$664$		0			0
$665$	−9.38674	+	20.2695i	−0.364002	+	0.786017i
$666$		0			0
$667$	23.0850	+	23.0850i	0.893855	+	0.893855i
$668$		0			0
$669$	−7.55849	−	7.55849i	−0.292228	−	0.292228i
$670$		0			0
$671$	−29.0242			−1.12047
$672$		0			0
$673$			1.03722i			0.0399820i	0.999800	+	0.0199910i	$0.00636376\pi$
$673$			1.03722i			0.0399820i	−0.999800	+	0.0199910i	$0.993636\pi$
$674$		0			0
$675$	4.98321	+	0.409472i	0.191804	+	0.0157606i
$676$		0			0
$677$	18.4431	+	18.4431i	0.708825	+	0.708825i	0.966288	−	0.257463i	$-0.0828867\pi$
$677$	18.4431	+	18.4431i	0.708825	+	0.708825i	−0.257463	+	0.966288i	$0.582887\pi$
$678$		0			0
$679$			38.1046i			1.46232i
$680$		0			0
$681$		−	21.3153i		−	0.816802i
$682$		0			0
$683$	0.922102	+	0.922102i	0.0352833	+	0.0352833i	0.724528	−	0.689245i	$-0.242058\pi$
$683$	0.922102	+	0.922102i	0.0352833	+	0.0352833i	−0.689245	+	0.724528i	$0.742058\pi$
$684$		0			0
$685$	3.76178	+	10.2511i	0.143730	+	0.391675i
$686$		0			0
$687$		−	4.57681i		−	0.174616i
$688$		0			0
$689$	−49.3997			−1.88198
$690$		0			0
$691$	7.34104	+	7.34104i	0.279266	+	0.279266i	0.832816	−	0.553550i	$-0.186727\pi$
$691$	7.34104	+	7.34104i	0.279266	+	0.279266i	−0.553550	+	0.832816i	$0.686727\pi$
$692$		0			0
$693$	5.52020	+	5.52020i	0.209695	+	0.209695i
$694$		0			0
$695$	16.7739	+	7.76795i	0.636271	+	0.294655i
$696$		0			0
$697$	23.7380			0.899141
$698$		0			0
$699$	−3.36178	+	3.36178i	−0.127154	+	0.127154i
$700$		0			0
$701$	−25.7637	−	25.7637i	−0.973080	−	0.973080i	0.0265667	−	0.999647i	$-0.491543\pi$
$701$	−25.7637	−	25.7637i	−0.973080	−	0.973080i	−0.999647	+	0.0265667i	$0.991543\pi$
$702$		0			0
$703$			25.0166i			0.943520i
$704$		0			0
$705$	7.74635	−	16.7273i	0.291744	−	0.629985i
$706$		0			0
$707$	1.73704	−	1.73704i	0.0653282	−	0.0653282i
$708$		0			0
$709$	−18.8691	+	18.8691i	−0.708645	+	0.708645i	−0.966250	−	0.257605i	$-0.917067\pi$
$709$	−18.8691	+	18.8691i	−0.708645	+	0.708645i	0.257605	+	0.966250i	$0.417067\pi$
$710$		0			0
$711$			10.9690i			0.411369i
$712$		0			0
$713$	−9.05423			−0.339084
$714$		0			0
$715$	−18.7729	+	6.88896i	−0.702067	+	0.257632i
$716$		0			0
$717$	8.43041	−	8.43041i	0.314839	−	0.314839i
$718$		0			0
$719$	−48.8119			−1.82038			−0.910189	−	0.414194i	$-0.864063\pi$
$719$	−48.8119			−1.82038			−0.910189	+	0.414194i	$0.864063\pi$
$720$		0			0
$721$	−37.2285			−1.38646
$722$		0			0
$723$	−20.0105	+	20.0105i	−0.744199	+	0.744199i
$724$		0			0
$725$	33.4517	+	2.74873i	1.24236	+	0.102085i
$726$		0			0
$727$	−20.2737			−0.751908			−0.375954	−	0.926638i	$-0.622685\pi$
$727$	−20.2737			−0.751908			−0.375954	+	0.926638i	$0.622685\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−15.3768	+	15.3768i	−0.568730	+	0.568730i
$732$		0			0
$733$	−21.1889	+	21.1889i	−0.782631	+	0.782631i	−0.980274	−	0.197643i	$-0.936671\pi$
$733$	−21.1889	+	21.1889i	−0.782631	+	0.782631i	0.197643	+	0.980274i	$0.436671\pi$
$734$		0			0
$735$	−4.67216	−	2.16367i	−0.172335	−	0.0798080i
$736$		0			0
$737$			31.1324i			1.14678i
$738$		0			0
$739$	3.65840	+	3.65840i	0.134576	+	0.134576i	0.771186	−	0.636610i	$-0.219664\pi$
$739$	3.65840	+	3.65840i	0.134576	+	0.134576i	−0.636610	+	0.771186i	$0.719664\pi$
$740$		0			0
$741$	8.09178	−	8.09178i	0.297259	−	0.297259i
$742$		0			0
$743$	4.42017			0.162160			0.0810802	−	0.996708i	$-0.474163\pi$
$743$	4.42017			0.162160			0.0810802	+	0.996708i	$0.474163\pi$
$744$		0			0
$745$	−43.4684	−	20.1301i	−1.59256	−	0.737509i
$746$		0			0
$747$	−3.65688	−	3.65688i	−0.133798	−	0.133798i
$748$		0			0
$749$	24.3865	+	24.3865i	0.891062	+	0.891062i
$750$		0			0
$751$	30.4414			1.11082			0.555411	−	0.831576i	$-0.312561\pi$
$751$	30.4414			1.11082			0.555411	+	0.831576i	$0.312561\pi$
$752$		0			0
$753$		−	6.21144i		−	0.226358i
$754$		0			0
$755$	8.43940	−	3.09695i	0.307141	−	0.112710i
$756$		0			0
$757$	−18.5016	−	18.5016i	−0.672454	−	0.672454i	0.285828	−	0.958281i	$-0.407732\pi$
$757$	−18.5016	−	18.5016i	−0.672454	−	0.672454i	−0.958281	+	0.285828i	$0.907732\pi$
$758$		0			0
$759$			12.4481i			0.451838i
$760$		0			0
$761$			11.9248i			0.432273i	0.976363	+	0.216137i	$0.0693456\pi$
$761$			11.9248i			0.432273i	−0.976363	+	0.216137i	$0.930654\pi$
$762$		0			0
$763$	−21.5792	−	21.5792i	−0.781220	−	0.781220i
$764$		0			0
$765$	2.82442	+	7.69675i	0.102117	+	0.278277i
$766$		0			0
$767$		−	12.2123i		−	0.440961i
$768$		0			0
$769$	51.5679			1.85958			0.929792	−	0.368085i	$-0.119986\pi$
$769$	51.5679			1.85958			0.929792	+	0.368085i	$0.119986\pi$
$770$		0			0
$771$	−1.78934	−	1.78934i	−0.0644414	−	0.0644414i
$772$		0			0
$773$	−13.7126	−	13.7126i	−0.493209	−	0.493209i	0.416107	−	0.909316i	$-0.363394\pi$
$773$	−13.7126	−	13.7126i	−0.493209	−	0.493209i	−0.909316	+	0.416107i	$0.863394\pi$
$774$		0			0
$775$	−7.09912	+	6.02103i	−0.255008	+	0.216282i
$776$		0			0
$777$	−23.2962			−0.835747
$778$		0			0
$779$	−14.9941	+	14.9941i	−0.537219	+	0.537219i
$780$		0			0
$781$	12.0114	+	12.0114i	0.429801	+	0.429801i
$782$		0			0
$783$			6.71288i			0.239899i
$784$		0			0
$785$	−28.2946	−	13.1031i	−1.00988	−	0.467671i
$786$		0			0
$787$	−31.1247	+	31.1247i	−1.10948	+	1.10948i	−0.116257	+	0.993219i	$0.537090\pi$
$787$	−31.1247	+	31.1247i	−1.10948	+	1.10948i	−0.993219	+	0.116257i	$0.962910\pi$
$788$		0			0
$789$	0.382533	−	0.382533i	0.0136185	−	0.0136185i
$790$		0			0
$791$			19.0658i			0.677903i
$792$		0			0
$793$	−39.6192			−1.40692
$794$		0			0
$795$	10.8914	+	29.6799i	0.386280	+	1.05264i
$796$		0			0
$797$	33.0578	−	33.0578i	1.17097	−	1.17097i	0.188987	−	0.981980i	$-0.439479\pi$
$797$	33.0578	−	33.0578i	1.17097	−	1.17097i	0.981980	−	0.188987i	$-0.0605205\pi$
$798$		0			0
$799$	30.2264			1.06933
$800$		0			0
$801$	−13.1530			−0.464737
$802$		0			0
$803$	−4.88745	+	4.88745i	−0.172474	+	0.172474i
$804$		0			0
$805$	−11.4265	−	31.1380i	−0.402731	−	1.09747i
$806$		0			0
$807$	4.24531			0.149442
$808$		0			0
$809$			2.77525i			0.0975726i	0.998809	+	0.0487863i	$0.0155353\pi$
$809$			2.77525i			0.0975726i	−0.998809	+	0.0487863i	$0.984465\pi$
$810$		0			0
$811$	21.8766	−	21.8766i	0.768192	−	0.768192i	−0.209596	−	0.977788i	$-0.567215\pi$
$811$	21.8766	−	21.8766i	0.768192	−	0.768192i	0.977788	+	0.209596i	$0.0672149\pi$
$812$		0			0
$813$	−5.97019	+	5.97019i	−0.209384	+	0.209384i
$814$		0			0
$815$	37.7952	+	17.5029i	1.32391	+	0.613098i
$816$		0			0
$817$		−	19.4254i		−	0.679610i
$818$		0			0
$819$	7.53530	+	7.53530i	0.263305	+	0.263305i
$820$		0			0
$821$	15.1782	−	15.1782i	0.529722	−	0.529722i	−0.390767	−	0.920490i	$-0.627790\pi$
$821$	15.1782	−	15.1782i	0.529722	−	0.529722i	0.920490	+	0.390767i	$0.127790\pi$
$822$		0			0
$823$	5.51325			0.192180			0.0960900	−	0.995373i	$-0.469366\pi$
$823$	5.51325			0.192180			0.0960900	+	0.995373i	$0.469366\pi$
$824$		0			0
$825$	8.27795	+	9.76014i	0.288201	+	0.339805i
$826$		0			0
$827$	6.06405	+	6.06405i	0.210868	+	0.210868i	0.804636	−	0.593768i	$-0.202360\pi$
$827$	6.06405	+	6.06405i	0.210868	+	0.210868i	−0.593768	+	0.804636i	$0.702360\pi$
$828$		0			0
$829$	−6.12109	−	6.12109i	−0.212594	−	0.212594i	0.592774	−	0.805369i	$-0.298033\pi$
$829$	−6.12109	−	6.12109i	−0.212594	−	0.212594i	−0.805369	+	0.592774i	$0.798033\pi$
$830$		0			0
$831$	17.3232			0.600935
$832$		0			0
$833$		−	8.44267i		−	0.292521i
$834$		0			0
$835$	0.0470485	+	0.128210i	0.00162818	+	0.00443690i
$836$		0			0
$837$	−1.31644	−	1.31644i	−0.0455027	−	0.0455027i
$838$		0			0
$839$		−	17.2421i		−	0.595265i	−0.954681	−	0.297632i	$-0.903803\pi$
$839$		−	17.2421i		−	0.595265i	0.954681	−	0.297632i	$-0.0961970\pi$
$840$		0			0
$841$			16.0627i			0.553888i
$842$		0			0
$843$	−11.8025	−	11.8025i	−0.406499	−	0.406499i
$844$		0			0
$845$	1.66369	−	0.610511i	0.0572325	−	0.0210022i
$846$		0			0
$847$		−	13.5683i		−	0.466214i
$848$		0			0
$849$	1.77908			0.0610578
$850$		0			0
$851$	−26.2666	−	26.2666i	−0.900407	−	0.900407i
$852$		0			0
$853$	3.60897	+	3.60897i	0.123569	+	0.123569i	0.766187	−	0.642618i	$-0.222152\pi$
$853$	3.60897	+	3.60897i	0.123569	+	0.123569i	−0.642618	+	0.766187i	$0.722152\pi$
$854$		0			0
$855$	−6.64569	−	3.07760i	−0.227278	−	0.105252i
$856$		0			0
$857$	−31.6802			−1.08217			−0.541087	−	0.840966i	$-0.681987\pi$
$857$	−31.6802			−1.08217			−0.541087	+	0.840966i	$0.681987\pi$
$858$		0			0
$859$	−14.9872	+	14.9872i	−0.511358	+	0.511358i	−0.914942	−	0.403585i	$-0.867764\pi$
$859$	−14.9872	+	14.9872i	−0.511358	+	0.511358i	0.403585	+	0.914942i	$0.367764\pi$
$860$		0			0
$861$	−13.9629	−	13.9629i	−0.475855	−	0.475855i
$862$		0			0
$863$		−	17.4922i		−	0.595440i	−0.954653	−	0.297720i	$-0.903774\pi$
$863$		−	17.4922i		−	0.595440i	0.954653	−	0.297720i	$-0.0962262\pi$
$864$		0			0
$865$	−23.0027	−	10.6525i	−0.782114	−	0.362195i
$866$		0			0
$867$	2.51485	−	2.51485i	0.0854089	−	0.0854089i
$868$		0			0
$869$	−19.8527	+	19.8527i	−0.673455	+	0.673455i
$870$		0			0
$871$			42.4970i			1.43996i
$872$		0			0
$873$	−12.4932			−0.422831
$874$		0			0
$875$	−29.6658	−	16.8157i	−1.00289	−	0.568475i
$876$		0			0
$877$	30.4741	−	30.4741i	1.02904	−	1.02904i	0.0294719	−	0.999566i	$-0.490617\pi$
$877$	30.4741	−	30.4741i	1.02904	−	1.02904i	0.999566	−	0.0294719i	$-0.00938257\pi$
$878$		0			0
$879$	17.5640			0.592420
$880$		0			0
$881$	−3.45819			−0.116509			−0.0582547	−	0.998302i	$-0.518554\pi$
$881$	−3.45819			−0.116509			−0.0582547	+	0.998302i	$0.518554\pi$
$882$		0			0
$883$	16.7282	−	16.7282i	0.562949	−	0.562949i	−0.367195	−	0.930144i	$-0.619682\pi$
$883$	16.7282	−	16.7282i	0.562949	−	0.562949i	0.930144	+	0.367195i	$0.119682\pi$
$884$		0			0
$885$	−7.33731	+	2.69252i	−0.246641	+	0.0905081i
$886$		0			0
$887$	−2.56980			−0.0862855			−0.0431428	−	0.999069i	$-0.513737\pi$
$887$	−2.56980			−0.0862855			−0.0431428	+	0.999069i	$0.513737\pi$
$888$		0			0
$889$		−	43.2750i		−	1.45140i
$890$		0			0
$891$	−1.80989	+	1.80989i	−0.0606336	+	0.0606336i
$892$		0			0
$893$	−19.0925	+	19.0925i	−0.638905	+	0.638905i
$894$		0			0
$895$	−15.7274	+	33.9614i	−0.525710	+	1.13520i
$896$		0			0
$897$			16.9922i			0.567352i
$898$		0			0
$899$	−8.83708	−	8.83708i	−0.294733	−	0.294733i
$900$		0			0
$901$	−36.6566	+	36.6566i	−1.22121	+	1.22121i
$902$		0			0
$903$	18.0895			0.601982
$904$		0			0
$905$	10.4276	+	4.82898i	0.346624	+	0.160521i
$906$		0			0
$907$	35.2994	+	35.2994i	1.17210	+	1.17210i	0.981709	+	0.190388i	$0.0609745\pi$
$907$	35.2994	+	35.2994i	1.17210	+	1.17210i	0.190388	+	0.981709i	$0.439026\pi$
$908$		0			0
$909$	0.569518	+	0.569518i	0.0188897	+	0.0188897i
$910$		0			0
$911$	−17.3104			−0.573518			−0.286759	−	0.958003i	$-0.592578\pi$
$911$	−17.3104			−0.573518			−0.286759	+	0.958003i	$0.592578\pi$
$912$		0			0
$913$		−	13.2371i		−	0.438084i
$914$		0			0
$915$	8.73509	+	23.8037i	0.288773	+	0.786927i
$916$		0			0
$917$	−38.2845	−	38.2845i	−1.26427	−	1.26427i
$918$		0			0
$919$			16.7668i			0.553085i	0.961002	+	0.276543i	$0.0891887\pi$
$919$			16.7668i			0.553085i	−0.961002	+	0.276543i	$0.910811\pi$
$920$		0			0
$921$		−	30.6876i		−	1.01119i
$922$		0			0
$923$	16.3960	+	16.3960i	0.539682	+	0.539682i
$924$		0			0
$925$	−38.0620	−	3.12757i	−1.25147	−	0.102834i
$926$		0			0
$927$		−	12.2060i		−	0.400897i
$928$		0			0
$929$	−29.1505			−0.956396			−0.478198	−	0.878252i	$-0.658710\pi$
$929$	−29.1505			−0.956396			−0.478198	+	0.878252i	$0.658710\pi$
$930$		0			0
$931$	5.33280	+	5.33280i	0.174776	+	0.174776i
$932$		0			0
$933$	−9.65733	−	9.65733i	−0.316167	−	0.316167i
$934$		0			0
$935$	−8.81837	+	19.0421i	−0.288391	+	0.622745i
$936$		0			0
$937$	44.3671			1.44941			0.724705	−	0.689059i	$-0.241976\pi$
$937$	44.3671			1.44941			0.724705	+	0.689059i	$0.241976\pi$
$938$		0			0
$939$	9.72531	−	9.72531i	0.317373	−	0.317373i
$940$		0			0
$941$	0.969738	+	0.969738i	0.0316125	+	0.0316125i	0.722736	−	0.691124i	$-0.242884\pi$
$941$	0.969738	+	0.969738i	0.0316125	+	0.0316125i	−0.691124	+	0.722736i	$0.742884\pi$
$942$		0			0
$943$		−	31.4865i		−	1.02534i
$944$		0			0
$945$	2.86595	−	6.18866i	0.0932294	−	0.201317i
$946$		0			0
$947$	−29.4598	+	29.4598i	−0.957316	+	0.957316i	−0.999126	−	0.0418099i	$-0.986688\pi$
$947$	−29.4598	+	29.4598i	−0.957316	+	0.957316i	0.0418099	+	0.999126i	$0.486688\pi$
$948$		0			0
$949$	−6.67157	+	6.67157i	−0.216568	+	0.216568i
$950$		0			0
$951$			23.3785i			0.758098i
$952$		0			0
$953$	57.8116			1.87270			0.936351	−	0.351065i	$-0.114180\pi$
$953$	57.8116			1.87270			0.936351	+	0.351065i	$0.114180\pi$
$954$		0			0
$955$	−14.6995	−	40.0573i	−0.475666	−	1.29622i
$956$		0			0
$957$	−12.1496	+	12.1496i	−0.392740	+	0.392740i
$958$		0			0
$959$	14.8944			0.480964
$960$		0			0
$961$	−27.5340			−0.888193
$962$		0			0
$963$	−7.99550	+	7.99550i	−0.257652	+	0.257652i
$964$		0			0
$965$	−6.27689	+	2.30339i	−0.202060	+	0.0741487i
$966$		0			0
$967$	8.69630			0.279654			0.139827	−	0.990176i	$-0.455345\pi$
$967$	8.69630			0.279654			0.139827	+	0.990176i	$0.455345\pi$
$968$		0			0
$969$		−	12.0089i		−	0.385780i
$970$		0			0
$971$	−15.8418	+	15.8418i	−0.508388	+	0.508388i	−0.914031	−	0.405643i	$-0.867048\pi$
$971$	−15.8418	+	15.8418i	−0.508388	+	0.508388i	0.405643	+	0.914031i	$0.367048\pi$
$972$		0			0
$973$	17.8291	−	17.8291i	0.571574	−	0.571574i
$974$		0			0
$975$	11.2997	+	13.3230i	0.361881	+	0.426678i
$976$		0			0
$977$			59.1087i			1.89106i	0.325541	+	0.945528i	$0.394454\pi$
$977$			59.1087i			1.89106i	−0.325541	+	0.945528i	$0.605546\pi$
$978$		0			0
$979$	−23.8054	−	23.8054i	−0.760824	−	0.760824i
$980$		0			0
$981$	7.07511	−	7.07511i	0.225891	−	0.225891i
$982$		0			0
$983$	−49.7311			−1.58618			−0.793088	−	0.609107i	$-0.791528\pi$
$983$	−49.7311			−1.58618			−0.793088	+	0.609107i	$0.791528\pi$
$984$		0			0
$985$	1.82415	−	3.93901i	0.0581222	−	0.125507i
$986$		0			0
$987$	−17.7795	−	17.7795i	−0.565927	−	0.565927i
$988$		0			0
$989$	20.3960	+	20.3960i	0.648556	+	0.648556i
$990$		0			0
$991$	54.8832			1.74342			0.871710	−	0.490021i	$-0.163011\pi$
$991$	54.8832			1.74342			0.871710	+	0.490021i	$0.163011\pi$
$992$		0			0
$993$		−	11.3869i		−	0.361354i
$994$		0			0
$995$	−32.9844	+	12.1041i	−1.04568	+	0.383724i
$996$		0			0
$997$	−2.92958	−	2.92958i	−0.0927806	−	0.0927806i	0.659193	−	0.751974i	$-0.270898\pi$
$997$	−2.92958	−	2.92958i	−0.0927806	−	0.0927806i	−0.751974	+	0.659193i	$0.770898\pi$
$998$		0			0
$999$		−	7.63805i		−	0.241657i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.bl.a.289.15		48
4.3	odd	2		1920.2.bl.b.289.10		48
5.4	even	2	inner	1920.2.bl.a.289.10		48
8.3	odd	2		960.2.bl.a.529.19		48
8.5	even	2		240.2.bl.a.109.7	✓	48
16.3	odd	4		960.2.bl.a.49.1		48
16.5	even	4	inner	1920.2.bl.a.1249.10		48
16.11	odd	4		1920.2.bl.b.1249.15		48
16.13	even	4		240.2.bl.a.229.18	yes	48
20.19	odd	2		1920.2.bl.b.289.15		48
24.5	odd	2		720.2.bm.h.109.18		48
40.19	odd	2		960.2.bl.a.529.1		48
40.29	even	2		240.2.bl.a.109.18	yes	48
48.29	odd	4		720.2.bm.h.469.7		48
80.19	odd	4		960.2.bl.a.49.19		48
80.29	even	4		240.2.bl.a.229.7	yes	48
80.59	odd	4		1920.2.bl.b.1249.10		48
80.69	even	4	inner	1920.2.bl.a.1249.15		48
120.29	odd	2		720.2.bm.h.109.7		48
240.29	odd	4		720.2.bm.h.469.18		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.7	✓	48	8.5	even	2
240.2.bl.a.109.18	yes	48	40.29	even	2
240.2.bl.a.229.7	yes	48	80.29	even	4
240.2.bl.a.229.18	yes	48	16.13	even	4
720.2.bm.h.109.7		48	120.29	odd	2
720.2.bm.h.109.18		48	24.5	odd	2
720.2.bm.h.469.7		48	48.29	odd	4
720.2.bm.h.469.18		48	240.29	odd	4
960.2.bl.a.49.1		48	16.3	odd	4
960.2.bl.a.49.19		48	80.19	odd	4
960.2.bl.a.529.1		48	40.19	odd	2
960.2.bl.a.529.19		48	8.3	odd	2
1920.2.bl.a.289.10		48	5.4	even	2	inner
1920.2.bl.a.289.15		48	1.1	even	1	trivial
1920.2.bl.a.1249.10		48	16.5	even	4	inner
1920.2.bl.a.1249.15		48	80.69	even	4	inner
1920.2.bl.b.289.10		48	4.3	odd	2
1920.2.bl.b.289.15		48	20.19	odd	2
1920.2.bl.b.1249.10		48	80.59	odd	4
1920.2.bl.b.1249.15		48	16.11	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.bl (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(-0.770325 - 2.09919i) q^{5} -3.05002 q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{3} +(-0.770325 - 2.09919i) q^{5} -3.05002 q^{7} -1.00000i q^{9} +(1.80989 - 1.80989i) q^{11} +(2.47057 - 2.47057i) q^{13} +(-2.02905 - 0.939649i) q^{15} -3.66653i q^{17} +(2.31596 + 2.31596i) q^{19} +(-2.15669 + 2.15669i) q^{21} -4.86336 q^{23} +(-3.81320 + 3.23412i) q^{25} +(-0.707107 - 0.707107i) q^{27} +(-4.74672 - 4.74672i) q^{29} +1.86172 q^{31} -2.55957i q^{33} +(2.34951 + 6.40257i) q^{35} +(5.40092 + 5.40092i) q^{37} -3.49392i q^{39} +6.47424i q^{41} +(-4.19382 - 4.19382i) q^{43} +(-2.09919 + 0.770325i) q^{45} +8.24387i q^{47} +2.30263 q^{49} +(-2.59263 - 2.59263i) q^{51} +(-9.99761 - 9.99761i) q^{53} +(-5.19350 - 2.40510i) q^{55} +3.27526 q^{57} +(2.47155 - 2.47155i) q^{59} +(-8.01822 - 8.01822i) q^{61} +3.05002i q^{63} +(-7.08935 - 3.28306i) q^{65} +(-8.60064 + 8.60064i) q^{67} +(-3.43891 + 3.43891i) q^{69} +6.63653i q^{71} -2.70041 q^{73} +(-0.409472 + 4.98321i) q^{75} +(-5.52020 + 5.52020i) q^{77} -10.9690 q^{79} -1.00000 q^{81} +(3.65688 - 3.65688i) q^{83} +(-7.69675 + 2.82442i) q^{85} -6.71288 q^{87} -13.1530i q^{89} +(-7.53530 + 7.53530i) q^{91} +(1.31644 - 1.31644i) q^{93} +(3.07760 - 6.64569i) q^{95} -12.4932i q^{97} +(-1.80989 - 1.80989i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 8 q^{19} - 48 q^{31} - 24 q^{35} + 48 q^{49} - 8 q^{51} + 32 q^{59} - 16 q^{61} + 16 q^{65} + 16 q^{69} + 16 q^{75} - 96 q^{79} - 48 q^{81} + 32 q^{91} - 48 q^{95}+O(q^{100}) \) 48 * q - 8 * q^19 - 48 * q^31 - 24 * q^35 + 48 * q^49 - 8 * q^51 + 32 * q^59 - 16 * q^61 + 16 * q^65 + 16 * q^69 + 16 * q^75 - 96 * q^79 - 48 * q^81 + 32 * q^91 - 48 * q^95

Introduction

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