LMFDB - Embedded newform 1920.2.bl.b.289.14

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			289.14
Character	$\chi$	$=$	1920.289
Dual form			1920.2.bl.b.1249.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{3} +(-0.162008 - 2.23019i) q^{5} -2.93661 q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{3} +(-0.162008 - 2.23019i) q^{5} -2.93661 q^{7} -1.00000i q^{9} +(-0.663996 + 0.663996i) q^{11} +(-1.12767 + 1.12767i) q^{13} +(-1.69154 - 1.46243i) q^{15} +7.47528i q^{17} +(0.423555 + 0.423555i) q^{19} +(-2.07650 + 2.07650i) q^{21} -6.17642 q^{23} +(-4.94751 + 0.722620i) q^{25} +(-0.707107 - 0.707107i) q^{27} +(2.95128 + 2.95128i) q^{29} -1.82581 q^{31} +0.939032i q^{33} +(0.475756 + 6.54921i) q^{35} +(5.53509 + 5.53509i) q^{37} +1.59476i q^{39} -12.3694i q^{41} +(0.897614 + 0.897614i) q^{43} +(-2.23019 + 0.162008i) q^{45} +4.12733i q^{47} +1.62370 q^{49} +(5.28582 + 5.28582i) q^{51} +(-0.146479 - 0.146479i) q^{53} +(1.58841 + 1.37327i) q^{55} +0.598997 q^{57} +(-7.72645 + 7.72645i) q^{59} +(7.37519 + 7.37519i) q^{61} +2.93661i q^{63} +(2.69760 + 2.33222i) q^{65} +(8.68265 - 8.68265i) q^{67} +(-4.36739 + 4.36739i) q^{69} +8.95735i q^{71} +0.174246 q^{73} +(-2.98745 + 4.00938i) q^{75} +(1.94990 - 1.94990i) q^{77} -3.06488 q^{79} -1.00000 q^{81} +(-9.18751 + 9.18751i) q^{83} +(16.6713 - 1.21106i) q^{85} +4.17374 q^{87} +8.71473i q^{89} +(3.31152 - 3.31152i) q^{91} +(-1.29104 + 1.29104i) q^{93} +(0.875989 - 1.01323i) q^{95} +10.5481i q^{97} +(0.663996 + 0.663996i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−0.162008	−	2.23019i	−0.0724524	−	0.997372i
$5$	−0.162008	−	2.23019i	−0.0724524	−	0.997372i
$6$		0			0
$7$	−2.93661			−1.10994			−0.554968	−	0.831872i	$-0.687269\pi$
$7$	−2.93661			−1.10994			−0.554968	+	0.831872i	$0.687269\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−0.663996	+	0.663996i	−0.200202	+	0.200202i	−0.800087	−	0.599884i	$-0.795213\pi$
$11$	−0.663996	+	0.663996i	−0.200202	+	0.200202i	0.599884	+	0.800087i	$0.295213\pi$
$12$		0			0
$13$	−1.12767	+	1.12767i	−0.312758	+	0.312758i	−0.845977	−	0.533219i	$-0.820982\pi$
$13$	−1.12767	+	1.12767i	−0.312758	+	0.312758i	0.533219	+	0.845977i	$0.320982\pi$
$14$		0			0
$15$	−1.69154	−	1.46243i	−0.436754	−	0.377597i
$16$		0			0
$17$			7.47528i			1.81302i	0.422182	+	0.906511i	$0.361264\pi$
$17$			7.47528i			1.81302i	−0.422182	+	0.906511i	$0.638736\pi$
$18$		0			0
$19$	0.423555	+	0.423555i	0.0971702	+	0.0971702i	0.754021	−	0.656851i	$-0.228112\pi$
$19$	0.423555	+	0.423555i	0.0971702	+	0.0971702i	−0.656851	+	0.754021i	$0.728112\pi$
$20$		0			0
$21$	−2.07650	+	2.07650i	−0.453129	+	0.453129i
$22$		0			0
$23$	−6.17642			−1.28787			−0.643936	−	0.765079i	$-0.722700\pi$
$23$	−6.17642			−1.28787			−0.643936	+	0.765079i	$0.722700\pi$
$24$		0			0
$25$	−4.94751	+	0.722620i	−0.989501	+	0.144524i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$	2.95128	+	2.95128i	0.548038	+	0.548038i	0.925873	−	0.377835i	$-0.123331\pi$
$29$	2.95128	+	2.95128i	0.548038	+	0.548038i	−0.377835	+	0.925873i	$0.623331\pi$
$30$		0			0
$31$	−1.82581			−0.327924			−0.163962	−	0.986467i	$-0.552428\pi$
$31$	−1.82581			−0.327924			−0.163962	+	0.986467i	$0.552428\pi$
$32$		0			0
$33$			0.939032i			0.163465i
$34$		0			0
$35$	0.475756	+	6.54921i	0.0804175	+	1.10702i
$36$		0			0
$37$	5.53509	+	5.53509i	0.909963	+	0.909963i	0.996269	−	0.0863055i	$-0.0275061\pi$
$37$	5.53509	+	5.53509i	0.909963	+	0.909963i	−0.0863055	+	0.996269i	$0.527506\pi$
$38$		0			0
$39$			1.59476i			0.255366i
$40$		0			0
$41$		−	12.3694i		−	1.93178i	−0.258959	−	0.965888i	$-0.583380\pi$
$41$		−	12.3694i		−	1.93178i	0.258959	−	0.965888i	$-0.416620\pi$
$42$		0			0
$43$	0.897614	+	0.897614i	0.136885	+	0.136885i	0.772229	−	0.635344i	$-0.219142\pi$
$43$	0.897614	+	0.897614i	0.136885	+	0.136885i	−0.635344	+	0.772229i	$0.719142\pi$
$44$		0			0
$45$	−2.23019	+	0.162008i	−0.332457	+	0.0241508i
$46$		0			0
$47$			4.12733i			0.602033i	0.953619	+	0.301017i	$0.0973260\pi$
$47$			4.12733i			0.602033i	−0.953619	+	0.301017i	$0.902674\pi$
$48$		0			0
$49$	1.62370			0.231956
$50$		0			0
$51$	5.28582	+	5.28582i	0.740163	+	0.740163i
$52$		0			0
$53$	−0.146479	−	0.146479i	−0.0201204	−	0.0201204i	0.696975	−	0.717095i	$-0.254529\pi$
$53$	−0.146479	−	0.146479i	−0.0201204	−	0.0201204i	−0.717095	+	0.696975i	$0.754529\pi$
$54$		0			0
$55$	1.58841	+	1.37327i	0.214181	+	0.185171i
$56$		0			0
$57$	0.598997			0.0793391
$58$		0			0
$59$	−7.72645	+	7.72645i	−1.00590	+	1.00590i	−0.00591515	+	0.999983i	$0.501883\pi$
$59$	−7.72645	+	7.72645i	−1.00590	+	1.00590i	−0.999983	+	0.00591515i	$0.998117\pi$
$60$		0			0
$61$	7.37519	+	7.37519i	0.944297	+	0.944297i	0.998528	−	0.0542318i	$-0.0172710\pi$
$61$	7.37519	+	7.37519i	0.944297	+	0.944297i	−0.0542318	+	0.998528i	$0.517271\pi$
$62$		0			0
$63$			2.93661i			0.369978i
$64$		0			0
$65$	2.69760	+	2.33222i	0.334597	+	0.289276i
$66$		0			0
$67$	8.68265	−	8.68265i	1.06075	−	1.06075i	0.0627239	−	0.998031i	$-0.480021\pi$
$67$	8.68265	−	8.68265i	1.06075	−	1.06075i	0.998031	−	0.0627239i	$-0.0199787\pi$
$68$		0			0
$69$	−4.36739	+	4.36739i	−0.525772	+	0.525772i
$70$		0			0
$71$			8.95735i			1.06304i	0.847045	+	0.531521i	$0.178379\pi$
$71$			8.95735i			1.06304i	−0.847045	+	0.531521i	$0.821621\pi$
$72$		0			0
$73$	0.174246			0.0203940			0.0101970	−	0.999948i	$-0.496754\pi$
$73$	0.174246			0.0203940			0.0101970	+	0.999948i	$0.496754\pi$
$74$		0			0
$75$	−2.98745	+	4.00938i	−0.344961	+	0.462964i
$76$		0			0
$77$	1.94990	−	1.94990i	0.222212	−	0.222212i
$78$		0			0
$79$	−3.06488			−0.344826			−0.172413	−	0.985025i	$-0.555156\pi$
$79$	−3.06488			−0.344826			−0.172413	+	0.985025i	$0.555156\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−9.18751	+	9.18751i	−1.00846	+	1.00846i	−0.00849620	+	0.999964i	$0.502704\pi$
$83$	−9.18751	+	9.18751i	−1.00846	+	1.00846i	−0.999964	+	0.00849620i	$0.997296\pi$
$84$		0			0
$85$	16.6713	−	1.21106i	1.80826	−	0.131358i
$86$		0			0
$87$	4.17374			0.447471
$88$		0			0
$89$			8.71473i			0.923760i	0.886942	+	0.461880i	$0.152825\pi$
$89$			8.71473i			0.923760i	−0.886942	+	0.461880i	$0.847175\pi$
$90$		0			0
$91$	3.31152	−	3.31152i	0.347142	−	0.347142i
$92$		0			0
$93$	−1.29104	+	1.29104i	−0.133875	+	0.133875i
$94$		0			0
$95$	0.875989	−	1.01323i	0.0898746	−	0.103955i
$96$		0			0
$97$			10.5481i			1.07100i	0.844535	+	0.535500i	$0.179877\pi$
$97$			10.5481i			1.07100i	−0.844535	+	0.535500i	$0.820123\pi$
$98$		0			0
$99$	0.663996	+	0.663996i	0.0667341	+	0.0667341i
$100$		0			0
$101$	9.65550	−	9.65550i	0.960758	−	0.960758i	−0.0385005	−	0.999259i	$-0.512258\pi$
$101$	9.65550	−	9.65550i	0.960758	−	0.960758i	0.999259	+	0.0385005i	$0.0122581\pi$
$102$		0			0
$103$	−14.5564			−1.43428			−0.717141	−	0.696928i	$-0.754550\pi$
$103$	−14.5564			−1.43428			−0.717141	+	0.696928i	$0.754550\pi$
$104$		0			0
$105$	4.96740	+	4.29458i	0.484769	+	0.419108i
$106$		0			0
$107$	−5.86260	−	5.86260i	−0.566759	−	0.566759i	0.364460	−	0.931219i	$-0.381253\pi$
$107$	−5.86260	−	5.86260i	−0.566759	−	0.566759i	−0.931219	+	0.364460i	$0.881253\pi$
$108$		0			0
$109$	−4.91625	−	4.91625i	−0.470891	−	0.470891i	0.431312	−	0.902203i	$-0.358051\pi$
$109$	−4.91625	−	4.91625i	−0.470891	−	0.470891i	−0.902203	+	0.431312i	$0.858051\pi$
$110$		0			0
$111$	7.82780			0.742982
$112$		0			0
$113$		−	12.8334i		−	1.20726i	−0.797263	−	0.603632i	$-0.793720\pi$
$113$		−	12.8334i		−	1.20726i	0.797263	−	0.603632i	$-0.206280\pi$
$114$		0			0
$115$	1.00063	+	13.7746i	0.0933094	+	1.28449i
$116$		0			0
$117$	1.12767	+	1.12767i	0.104253	+	0.104253i
$118$		0			0
$119$		−	21.9520i		−	2.01234i
$120$		0			0
$121$			10.1182i			0.919838i
$122$		0			0
$123$	−8.74649	−	8.74649i	−0.788644	−	0.788644i
$124$		0			0
$125$	2.41312	+	10.9168i	0.215836	+	0.976430i
$126$		0			0
$127$		−	1.07042i		−	0.0949847i	−0.998872	−	0.0474924i	$-0.984877\pi$
$127$		−	1.07042i		−	0.0949847i	0.998872	−	0.0474924i	$-0.0151230\pi$
$128$		0			0
$129$	1.26942			0.111766
$130$		0			0
$131$	−10.9024	−	10.9024i	−0.952545	−	0.952545i	0.0463789	−	0.998924i	$-0.485232\pi$
$131$	−10.9024	−	10.9024i	−0.952545	−	0.952545i	−0.998924	+	0.0463789i	$0.985232\pi$
$132$		0			0
$133$	−1.24382	−	1.24382i	−0.107853	−	0.107853i
$134$		0			0
$135$	−1.46243	+	1.69154i	−0.125866	+	0.145585i
$136$		0			0
$137$	−10.0549			−0.859046			−0.429523	−	0.903056i	$-0.641318\pi$
$137$	−10.0549			−0.859046			−0.429523	+	0.903056i	$0.641318\pi$
$138$		0			0
$139$	2.90773	−	2.90773i	0.246630	−	0.246630i	−0.572956	−	0.819586i	$-0.694203\pi$
$139$	2.90773	−	2.90773i	0.246630	−	0.246630i	0.819586	+	0.572956i	$0.194203\pi$
$140$		0			0
$141$	2.91847	+	2.91847i	0.245779	+	0.245779i
$142$		0			0
$143$		−	1.49753i		−	0.125230i
$144$		0			0
$145$	6.10378	−	7.06004i	0.506891	−	0.586305i
$146$		0			0
$147$	1.14813	−	1.14813i	0.0946958	−	0.0946958i
$148$		0			0
$149$	1.26131	−	1.26131i	0.103331	−	0.103331i	−0.653551	−	0.756882i	$-0.726722\pi$
$149$	1.26131	−	1.26131i	0.103331	−	0.103331i	0.756882	+	0.653551i	$0.226722\pi$
$150$		0			0
$151$			20.4739i			1.66614i	0.553169	+	0.833069i	$0.313418\pi$
$151$			20.4739i			1.66614i	−0.553169	+	0.833069i	$0.686582\pi$
$152$		0			0
$153$	7.47528			0.604341
$154$		0			0
$155$	0.295796	+	4.07190i	0.0237589	+	0.327063i
$156$		0			0
$157$	8.13344	−	8.13344i	0.649119	−	0.649119i	−0.303661	−	0.952780i	$-0.598209\pi$
$157$	8.13344	−	8.13344i	0.649119	−	0.649119i	0.952780	+	0.303661i	$0.0982091\pi$
$158$		0			0
$159$	−0.207152			−0.0164282
$160$		0			0
$161$	18.1377			1.42945
$162$		0			0
$163$	−4.08947	+	4.08947i	−0.320312	+	0.320312i	−0.848887	−	0.528575i	$-0.822727\pi$
$163$	−4.08947	+	4.08947i	−0.320312	+	0.320312i	0.528575	+	0.848887i	$0.322727\pi$
$164$		0			0
$165$	2.09422	−	0.152131i	0.163035	−	0.0118434i
$166$		0			0
$167$	−9.52867			−0.737350			−0.368675	−	0.929558i	$-0.620189\pi$
$167$	−9.52867			−0.737350			−0.368675	+	0.929558i	$0.620189\pi$
$168$		0			0
$169$			10.4567i			0.804364i
$170$		0			0
$171$	0.423555	−	0.423555i	0.0323901	−	0.0323901i
$172$		0			0
$173$	−6.18234	+	6.18234i	−0.470035	+	0.470035i	−0.901926	−	0.431891i	$-0.857847\pi$
$173$	−6.18234	+	6.18234i	−0.470035	+	0.470035i	0.431891	+	0.901926i	$0.357847\pi$
$174$		0			0
$175$	14.5289	−	2.12205i	1.09828	−	0.160412i
$176$		0			0
$177$			10.9268i			0.821312i
$178$		0			0
$179$	−10.3548	−	10.3548i	−0.773954	−	0.773954i	0.204841	−	0.978795i	$-0.434332\pi$
$179$	−10.3548	−	10.3548i	−0.773954	−	0.773954i	−0.978795	+	0.204841i	$0.934332\pi$
$180$		0			0
$181$	−5.98013	+	5.98013i	−0.444500	+	0.444500i	−0.893521	−	0.449021i	$-0.851773\pi$
$181$	−5.98013	+	5.98013i	−0.444500	+	0.444500i	0.449021	+	0.893521i	$0.351773\pi$
$182$		0			0
$183$	10.4301			0.771015
$184$		0			0
$185$	11.4476	−	13.2410i	0.841643	−	0.973501i
$186$		0			0
$187$	−4.96356	−	4.96356i	−0.362971	−	0.362971i
$188$		0			0
$189$	2.07650	+	2.07650i	0.151043	+	0.151043i
$190$		0			0
$191$	0.404932			0.0292998			0.0146499	−	0.999893i	$-0.495337\pi$
$191$	0.404932			0.0292998			0.0146499	+	0.999893i	$0.495337\pi$
$192$		0			0
$193$			6.48969i			0.467138i	0.972340	+	0.233569i	$0.0750405\pi$
$193$			6.48969i			0.467138i	−0.972340	+	0.233569i	$0.924959\pi$
$194$		0			0
$195$	3.55662	−	0.258365i	0.254695	−	0.0185019i
$196$		0			0
$197$	−18.4425	−	18.4425i	−1.31397	−	1.31397i	−0.918460	−	0.395514i	$-0.870566\pi$
$197$	−18.4425	−	18.4425i	−1.31397	−	1.31397i	−0.395514	−	0.918460i	$-0.629434\pi$
$198$		0			0
$199$			13.4696i			0.954833i	0.878677	+	0.477417i	$0.158427\pi$
$199$			13.4696i			0.954833i	−0.878677	+	0.477417i	$0.841573\pi$
$200$		0			0
$201$		−	12.2791i		−	0.866103i
$202$		0			0
$203$	−8.66676	−	8.66676i	−0.608287	−	0.608287i
$204$		0			0
$205$	−27.5861	+	2.00395i	−1.92670	+	0.139962i
$206$		0			0
$207$			6.17642i			0.429291i
$208$		0			0
$209$	−0.562478			−0.0389074
$210$		0			0
$211$	6.07749	+	6.07749i	0.418392	+	0.418392i	0.884649	−	0.466257i	$-0.154398\pi$
$211$	6.07749	+	6.07749i	0.418392	+	0.418392i	−0.466257	+	0.884649i	$0.654398\pi$
$212$		0			0
$213$	6.33380	+	6.33380i	0.433985	+	0.433985i
$214$		0			0
$215$	1.85643	−	2.14727i	0.126607	−	0.146443i
$216$		0			0
$217$	5.36168			0.363975
$218$		0			0
$219$	0.123211	−	0.123211i	0.00832581	−	0.00832581i
$220$		0			0
$221$	−8.42963	−	8.42963i	−0.567038	−	0.567038i
$222$		0			0
$223$		−	22.0794i		−	1.47855i	−0.673405	−	0.739273i	$-0.735169\pi$
$223$		−	22.0794i		−	1.47855i	0.673405	−	0.739273i	$-0.264831\pi$
$224$		0			0
$225$	0.722620	+	4.94751i	0.0481746	+	0.329834i
$226$		0			0
$227$	−5.55919	+	5.55919i	−0.368977	+	0.368977i	−0.867104	−	0.498127i	$-0.834021\pi$
$227$	−5.55919	+	5.55919i	−0.368977	+	0.368977i	0.498127	+	0.867104i	$0.334021\pi$
$228$		0			0
$229$	−11.8223	+	11.8223i	−0.781242	+	0.781242i	−0.980040	−	0.198798i	$-0.936296\pi$
$229$	−11.8223	+	11.8223i	−0.781242	+	0.781242i	0.198798	+	0.980040i	$0.436296\pi$
$230$		0			0
$231$		−	2.75757i		−	0.181435i
$232$		0			0
$233$	−8.92024			−0.584385			−0.292192	−	0.956360i	$-0.594385\pi$
$233$	−8.92024			−0.584385			−0.292192	+	0.956360i	$0.594385\pi$
$234$		0			0
$235$	9.20474	−	0.668663i	0.600451	−	0.0436188i
$236$		0			0
$237$	−2.16720	+	2.16720i	−0.140775	+	0.140775i
$238$		0			0
$239$	−22.9320			−1.48335			−0.741673	−	0.670762i	$-0.765967\pi$
$239$	−22.9320			−1.48335			−0.741673	+	0.670762i	$0.765967\pi$
$240$		0			0
$241$	−6.48232			−0.417563			−0.208781	−	0.977962i	$-0.566950\pi$
$241$	−6.48232			−0.417563			−0.208781	+	0.977962i	$0.566950\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	−0.263052	−	3.62115i	−0.0168058	−	0.231347i
$246$		0			0
$247$	−0.955258			−0.0607816
$248$		0			0
$249$			12.9931i			0.823404i
$250$		0			0
$251$	14.4218	−	14.4218i	0.910293	−	0.910293i	−0.0860018	−	0.996295i	$-0.527409\pi$
$251$	14.4218	−	14.4218i	0.910293	−	0.910293i	0.996295	+	0.0860018i	$0.0274091\pi$
$252$		0			0
$253$	4.10112	−	4.10112i	0.257835	−	0.257835i
$254$		0			0
$255$	10.9320	−	12.6447i	0.684591	−	0.791844i
$256$		0			0
$257$		−	0.193739i		−	0.0120851i	−0.999982	−	0.00604256i	$-0.998077\pi$
$257$		−	0.193739i		−	0.0120851i	0.999982	−	0.00604256i	$-0.00192342\pi$
$258$		0			0
$259$	−16.2544	−	16.2544i	−1.01000	−	1.01000i
$260$		0			0
$261$	2.95128	−	2.95128i	0.182679	−	0.182679i
$262$		0			0
$263$	16.5708			1.02180			0.510900	−	0.859640i	$-0.329312\pi$
$263$	16.5708			1.02180			0.510900	+	0.859640i	$0.329312\pi$
$264$		0			0
$265$	−0.302944	+	0.350406i	−0.0186097	+	0.0215253i
$266$		0			0
$267$	6.16225	+	6.16225i	0.377123	+	0.377123i
$268$		0			0
$269$	−7.09381	−	7.09381i	−0.432517	−	0.432517i	0.456967	−	0.889484i	$-0.348936\pi$
$269$	−7.09381	−	7.09381i	−0.432517	−	0.432517i	−0.889484	+	0.456967i	$0.848936\pi$
$270$		0			0
$271$	−2.62278			−0.159323			−0.0796613	−	0.996822i	$-0.525384\pi$
$271$	−2.62278			−0.159323			−0.0796613	+	0.996822i	$0.525384\pi$
$272$		0			0
$273$		−	4.68320i		−	0.283440i
$274$		0			0
$275$	2.80531	−	3.76494i	0.169166	−	0.227035i
$276$		0			0
$277$	7.97533	+	7.97533i	0.479191	+	0.479191i	0.904873	−	0.425682i	$-0.139966\pi$
$277$	7.97533	+	7.97533i	0.479191	+	0.479191i	−0.425682	+	0.904873i	$0.639966\pi$
$278$		0			0
$279$			1.82581i			0.109308i
$280$		0			0
$281$			9.97850i			0.595267i	0.954680	+	0.297634i	$0.0961974\pi$
$281$			9.97850i			0.595267i	−0.954680	+	0.297634i	$0.903803\pi$
$282$		0			0
$283$	20.4056	+	20.4056i	1.21299	+	1.21299i	0.970040	+	0.242946i	$0.0781139\pi$
$283$	20.4056	+	20.4056i	1.21299	+	1.21299i	0.242946	+	0.970040i	$0.421886\pi$
$284$		0			0
$285$	−0.0970426	−	1.33588i	−0.00574831	−	0.0791306i
$286$		0			0
$287$			36.3242i			2.14415i
$288$		0			0
$289$	−38.8798			−2.28705
$290$		0			0
$291$	7.45865	+	7.45865i	0.437234	+	0.437234i
$292$		0			0
$293$	−4.65889	−	4.65889i	−0.272175	−	0.272175i	0.557800	−	0.829975i	$-0.311646\pi$
$293$	−4.65889	−	4.65889i	−0.272175	−	0.272175i	−0.829975	+	0.557800i	$0.811646\pi$
$294$		0			0
$295$	18.4832	+	15.9797i	1.07613	+	0.930374i
$296$		0			0
$297$	0.939032			0.0544882
$298$		0			0
$299$	6.96494	−	6.96494i	0.402793	−	0.402793i
$300$		0			0
$301$	−2.63594	−	2.63594i	−0.151933	−	0.151933i
$302$		0			0
$303$		−	13.6549i		−	0.784456i
$304$		0			0
$305$	15.2532	−	17.6429i	0.873398	−	1.01023i
$306$		0			0
$307$	9.05487	−	9.05487i	0.516789	−	0.516789i	−0.399810	−	0.916598i	$-0.630924\pi$
$307$	9.05487	−	9.05487i	0.516789	−	0.516789i	0.916598	+	0.399810i	$0.130924\pi$
$308$		0			0
$309$	−10.2929	+	10.2929i	−0.585543	+	0.585543i
$310$		0			0
$311$			3.39349i			0.192427i	0.995361	+	0.0962137i	$0.0306732\pi$
$311$			3.39349i			0.192427i	−0.995361	+	0.0962137i	$0.969327\pi$
$312$		0			0
$313$	10.8943			0.615784			0.307892	−	0.951421i	$-0.400376\pi$
$313$	10.8943			0.615784			0.307892	+	0.951421i	$0.400376\pi$
$314$		0			0
$315$	6.54921	−	0.475756i	0.369006	−	0.0268058i
$316$		0			0
$317$	−3.45776	+	3.45776i	−0.194207	+	0.194207i	−0.797511	−	0.603304i	$-0.793851\pi$
$317$	−3.45776	+	3.45776i	−0.194207	+	0.194207i	0.603304	+	0.797511i	$0.293851\pi$
$318$		0			0
$319$	−3.91927			−0.219437
$320$		0			0
$321$	−8.29096			−0.462756
$322$		0			0
$323$	−3.16619	+	3.16619i	−0.176172	+	0.176172i
$324$		0			0
$325$	4.76426	−	6.39401i	0.264274	−	0.354676i
$326$		0			0
$327$	−6.95263			−0.384481
$328$		0			0
$329$		−	12.1204i		−	0.668218i
$330$		0			0
$331$	−24.9246	+	24.9246i	−1.36998	+	1.36998i	−0.509526	+	0.860455i	$0.670179\pi$
$331$	−24.9246	+	24.9246i	−1.36998	+	1.36998i	−0.860455	+	0.509526i	$0.829821\pi$
$332$		0			0
$333$	5.53509	−	5.53509i	0.303321	−	0.303321i
$334$		0			0
$335$	−20.7706	−	17.9573i	−1.13482	−	0.981113i
$336$		0			0
$337$		−	9.62502i		−	0.524308i	−0.965026	−	0.262154i	$-0.915567\pi$
$337$		−	9.62502i		−	0.524308i	0.965026	−	0.262154i	$-0.0844329\pi$
$338$		0			0
$339$	−9.07458	−	9.07458i	−0.492863	−	0.492863i
$340$		0			0
$341$	1.21233	−	1.21233i	0.0656512	−	0.0656512i
$342$		0			0
$343$	15.7881			0.852479
$344$		0			0
$345$	10.4477	+	9.03256i	0.562483	+	0.486296i
$346$		0			0
$347$	15.9302	+	15.9302i	0.855178	+	0.855178i	0.990765	−	0.135588i	$-0.0432923\pi$
$347$	15.9302	+	15.9302i	0.855178	+	0.855178i	−0.135588	+	0.990765i	$0.543292\pi$
$348$		0			0
$349$	4.56134	+	4.56134i	0.244163	+	0.244163i	0.818570	−	0.574407i	$-0.194767\pi$
$349$	4.56134	+	4.56134i	0.244163	+	0.244163i	−0.574407	+	0.818570i	$0.694767\pi$
$350$		0			0
$351$	1.59476			0.0851221
$352$		0			0
$353$		−	14.1314i		−	0.752141i	−0.926591	−	0.376070i	$-0.877275\pi$
$353$		−	14.1314i		−	0.752141i	0.926591	−	0.376070i	$-0.122725\pi$
$354$		0			0
$355$	19.9766	−	1.45117i	1.06025	−	0.0770199i
$356$		0			0
$357$	−15.5224	−	15.5224i	−0.821533	−	0.821533i
$358$		0			0
$359$		−	25.2588i		−	1.33311i	−0.745456	−	0.666555i	$-0.767768\pi$
$359$		−	25.2588i		−	1.33311i	0.745456	−	0.666555i	$-0.232232\pi$
$360$		0			0
$361$		−	18.6412i		−	0.981116i
$362$		0			0
$363$	7.15466	+	7.15466i	0.375522	+	0.375522i
$364$		0			0
$365$	−0.0282294	−	0.388602i	−0.00147759	−	0.0203404i
$366$		0			0
$367$			3.01381i			0.157320i	0.996902	+	0.0786598i	$0.0250641\pi$
$367$			3.01381i			0.157320i	−0.996902	+	0.0786598i	$0.974936\pi$
$368$		0			0
$369$	−12.3694			−0.643925
$370$		0			0
$371$	0.430151	+	0.430151i	0.0223323	+	0.0223323i
$372$		0			0
$373$	−13.1060	−	13.1060i	−0.678604	−	0.678604i	0.281080	−	0.959684i	$-0.409307\pi$
$373$	−13.1060	−	13.1060i	−0.678604	−	0.678604i	−0.959684	+	0.281080i	$0.909307\pi$
$374$		0			0
$375$	9.42569	+	6.01302i	0.486740	+	0.310511i
$376$		0			0
$377$	−6.65611			−0.342807
$378$		0			0
$379$	8.34584	−	8.34584i	0.428697	−	0.428697i	−0.459487	−	0.888184i	$-0.651967\pi$
$379$	8.34584	−	8.34584i	0.428697	−	0.428697i	0.888184	+	0.459487i	$0.151967\pi$
$380$		0			0
$381$	−0.756904	−	0.756904i	−0.0387774	−	0.0387774i
$382$		0			0
$383$			25.5695i			1.30654i	0.757124	+	0.653271i	$0.226604\pi$
$383$			25.5695i			1.30654i	−0.757124	+	0.653271i	$0.773396\pi$
$384$		0			0
$385$	−4.66455	−	4.03275i	−0.237727	−	0.205528i
$386$		0			0
$387$	0.897614	−	0.897614i	0.0456283	−	0.0456283i
$388$		0			0
$389$	−4.31954	+	4.31954i	−0.219009	+	0.219009i	−0.808081	−	0.589072i	$-0.799494\pi$
$389$	−4.31954	+	4.31954i	−0.219009	+	0.219009i	0.589072	+	0.808081i	$0.299494\pi$
$390$		0			0
$391$		−	46.1705i		−	2.33494i
$392$		0			0
$393$	−15.4183			−0.777750
$394$		0			0
$395$	0.496537	+	6.83528i	0.0249835	+	0.343920i
$396$		0			0
$397$	23.5750	−	23.5750i	1.18319	−	1.18319i	0.204281	−	0.978912i	$-0.434515\pi$
$397$	23.5750	−	23.5750i	1.18319	−	1.18319i	0.978912	−	0.204281i	$-0.0654855\pi$
$398$		0			0
$399$	−1.75902			−0.0880613
$400$		0			0
$401$	17.1100			0.854430			0.427215	−	0.904150i	$-0.359495\pi$
$401$	17.1100			0.854430			0.427215	+	0.904150i	$0.359495\pi$
$402$		0			0
$403$	2.05890	−	2.05890i	0.102561	−	0.102561i
$404$		0			0
$405$	0.162008	+	2.23019i	0.00805026	+	0.110819i
$406$		0			0
$407$	−7.35056			−0.364354
$408$		0			0
$409$			25.2659i			1.24932i	0.780897	+	0.624659i	$0.214762\pi$
$409$			25.2659i			1.24932i	−0.780897	+	0.624659i	$0.785238\pi$
$410$		0			0
$411$	−7.10987	+	7.10987i	−0.350704	+	0.350704i
$412$		0			0
$413$	22.6896	−	22.6896i	1.11648	−	1.11648i
$414$		0			0
$415$	21.9784	+	19.0014i	1.07888	+	0.932744i
$416$		0			0
$417$		−	4.11215i		−	0.201373i
$418$		0			0
$419$	−15.7885	−	15.7885i	−0.771317	−	0.771317i	0.207020	−	0.978337i	$-0.433624\pi$
$419$	−15.7885	−	15.7885i	−0.771317	−	0.771317i	−0.978337	+	0.207020i	$0.933624\pi$
$420$		0			0
$421$	4.64861	−	4.64861i	0.226559	−	0.226559i	−0.584694	−	0.811254i	$-0.698786\pi$
$421$	4.64861	−	4.64861i	0.226559	−	0.226559i	0.811254	+	0.584694i	$0.198786\pi$
$422$		0			0
$423$	4.12733			0.200678
$424$		0			0
$425$	−5.40179	−	36.9840i	−0.262025	−	1.79399i
$426$		0			0
$427$	−21.6581	−	21.6581i	−1.04811	−	1.04811i
$428$		0			0
$429$	−1.05892	−	1.05892i	−0.0511249	−	0.0511249i
$430$		0			0
$431$	28.6320			1.37915			0.689577	−	0.724213i	$-0.257797\pi$
$431$	28.6320			1.37915			0.689577	+	0.724213i	$0.257797\pi$
$432$		0			0
$433$		−	6.14954i		−	0.295528i	−0.989023	−	0.147764i	$-0.952792\pi$
$433$		−	6.14954i		−	0.295528i	0.989023	−	0.147764i	$-0.0472076\pi$
$434$		0			0
$435$	−0.676180	−	9.30823i	−0.0324204	−	0.446295i
$436$		0			0
$437$	−2.61605	−	2.61605i	−0.125143	−	0.125143i
$438$		0			0
$439$		−	37.8541i		−	1.80668i	−0.428926	−	0.903340i	$-0.641108\pi$
$439$		−	37.8541i		−	1.80668i	0.428926	−	0.903340i	$-0.358892\pi$
$440$		0			0
$441$		−	1.62370i		−	0.0773188i
$442$		0			0
$443$	−3.41746	−	3.41746i	−0.162368	−	0.162368i	0.621247	−	0.783615i	$-0.286627\pi$
$443$	−3.41746	−	3.41746i	−0.162368	−	0.162368i	−0.783615	+	0.621247i	$0.786627\pi$
$444$		0			0
$445$	19.4355	−	1.41186i	0.921332	−	0.0669286i
$446$		0			0
$447$		−	1.78376i		−	0.0843691i
$448$		0			0
$449$	−31.6935			−1.49571			−0.747855	−	0.663862i	$-0.768916\pi$
$449$	−31.6935			−1.49571			−0.747855	+	0.663862i	$0.768916\pi$
$450$		0			0
$451$	8.21324	+	8.21324i	0.386746	+	0.386746i
$452$		0			0
$453$	14.4772	+	14.4772i	0.680198	+	0.680198i
$454$		0			0
$455$	−7.92182	−	6.84883i	−0.371381	−	0.321078i
$456$		0			0
$457$	−7.26208			−0.339706			−0.169853	−	0.985469i	$-0.554329\pi$
$457$	−7.26208			−0.339706			−0.169853	+	0.985469i	$0.554329\pi$
$458$		0			0
$459$	5.28582	−	5.28582i	0.246721	−	0.246721i
$460$		0			0
$461$	−16.1568	−	16.1568i	−0.752499	−	0.752499i	0.222446	−	0.974945i	$-0.428596\pi$
$461$	−16.1568	−	16.1568i	−0.752499	−	0.752499i	−0.974945	+	0.222446i	$0.928596\pi$
$462$		0			0
$463$			13.4637i			0.625710i	0.949801	+	0.312855i	$0.101285\pi$
$463$			13.4637i			0.625710i	−0.949801	+	0.312855i	$0.898715\pi$
$464$		0			0
$465$	3.08842	+	2.67011i	0.143222	+	0.123823i
$466$		0			0
$467$	10.5630	−	10.5630i	0.488795	−	0.488795i	−0.419131	−	0.907926i	$-0.637665\pi$
$467$	10.5630	−	10.5630i	0.488795	−	0.488795i	0.907926	+	0.419131i	$0.137665\pi$
$468$		0			0
$469$	−25.4976	+	25.4976i	−1.17737	+	1.17737i
$470$		0			0
$471$		−	11.5024i		−	0.530003i
$472$		0			0
$473$	−1.19202			−0.0548093
$474$		0			0
$475$	−2.40161	−	1.78947i	−0.110193	−	0.0821066i
$476$		0			0
$477$	−0.146479	+	0.146479i	−0.00670679	+	0.00670679i
$478$		0			0
$479$	−34.2747			−1.56605			−0.783026	−	0.621989i	$-0.786325\pi$
$479$	−34.2747			−1.56605			−0.783026	+	0.621989i	$0.786325\pi$
$480$		0			0
$481$	−12.4835			−0.569197
$482$		0			0
$483$	12.8253	−	12.8253i	0.583573	−	0.583573i
$484$		0			0
$485$	23.5243	−	1.70888i	1.06818	−	0.0775964i
$486$		0			0
$487$	33.4994			1.51800			0.759002	−	0.651088i	$-0.225687\pi$
$487$	33.4994			1.51800			0.759002	+	0.651088i	$0.225687\pi$
$488$		0			0
$489$			5.78338i			0.261533i
$490$		0			0
$491$	0.491541	−	0.491541i	0.0221829	−	0.0221829i	−0.695928	−	0.718111i	$-0.745007\pi$
$491$	0.491541	−	0.491541i	0.0221829	−	0.0221829i	0.718111	+	0.695928i	$0.245007\pi$
$492$		0			0
$493$	−22.0616	+	22.0616i	−0.993606	+	0.993606i
$494$		0			0
$495$	1.37327	−	1.58841i	0.0617237	−	0.0713938i
$496$		0			0
$497$		−	26.3043i		−	1.17991i
$498$		0			0
$499$	−0.863504	−	0.863504i	−0.0386557	−	0.0386557i	0.687515	−	0.726170i	$-0.258702\pi$
$499$	−0.863504	−	0.863504i	−0.0386557	−	0.0386557i	−0.726170	+	0.687515i	$0.758702\pi$
$500$		0			0
$501$	−6.73779	+	6.73779i	−0.301022	+	0.301022i
$502$		0			0
$503$	−12.8335			−0.572218			−0.286109	−	0.958197i	$-0.592362\pi$
$503$	−12.8335			−0.572218			−0.286109	+	0.958197i	$0.592362\pi$
$504$		0			0
$505$	−23.0979	−	19.9693i	−1.02784	−	0.888624i
$506$		0			0
$507$	7.39403	+	7.39403i	0.328380	+	0.328380i
$508$		0			0
$509$	12.6692	+	12.6692i	0.561554	+	0.561554i	0.929749	−	0.368194i	$-0.120024\pi$
$509$	12.6692	+	12.6692i	0.561554	+	0.561554i	−0.368194	+	0.929749i	$0.620024\pi$
$510$		0			0
$511$	−0.511694			−0.0226360
$512$		0			0
$513$		−	0.598997i		−	0.0264464i
$514$		0			0
$515$	2.35825	+	32.4635i	0.103917	+	1.43051i
$516$		0			0
$517$	−2.74053	−	2.74053i	−0.120529	−	0.120529i
$518$		0			0
$519$			8.74315i			0.383782i
$520$		0			0
$521$			30.2561i			1.32554i	0.748821	+	0.662772i	$0.230620\pi$
$521$			30.2561i			1.32554i	−0.748821	+	0.662772i	$0.769380\pi$
$522$		0			0
$523$	4.01063	+	4.01063i	0.175373	+	0.175373i	0.789335	−	0.613962i	$-0.210425\pi$
$523$	4.01063	+	4.01063i	0.175373	+	0.175373i	−0.613962	+	0.789335i	$0.710425\pi$
$524$		0			0
$525$	8.77297	−	11.7740i	0.382884	−	0.513860i
$526$		0			0
$527$		−	13.6484i		−	0.594534i
$528$		0			0
$529$	15.1481			0.658615
$530$		0			0
$531$	7.72645	+	7.72645i	0.335299	+	0.335299i
$532$		0			0
$533$	13.9486	+	13.9486i	0.604179	+	0.604179i
$534$		0			0
$535$	−12.1249	+	14.0245i	−0.524206	+	0.606332i
$536$		0			0
$537$	−14.6439			−0.631931
$538$		0			0
$539$	−1.07813	+	1.07813i	−0.0464382	+	0.0464382i
$540$		0			0
$541$	5.53130	+	5.53130i	0.237809	+	0.237809i	0.815942	−	0.578133i	$-0.196219\pi$
$541$	5.53130	+	5.53130i	0.237809	+	0.237809i	−0.578133	+	0.815942i	$0.696219\pi$
$542$		0			0
$543$			8.45718i			0.362932i
$544$		0			0
$545$	−10.1677	+	11.7607i	−0.435537	+	0.503771i
$546$		0			0
$547$	22.6141	−	22.6141i	0.966908	−	0.966908i	−0.0325622	−	0.999470i	$-0.510367\pi$
$547$	22.6141	−	22.6141i	0.966908	−	0.966908i	0.999470	+	0.0325622i	$0.0103667\pi$
$548$		0			0
$549$	7.37519	−	7.37519i	0.314766	−	0.314766i
$550$		0			0
$551$			2.50006i			0.106506i
$552$		0			0
$553$	9.00038			0.382735
$554$		0			0
$555$	−1.26817	−	17.4575i	−0.0538308	−	0.741029i
$556$		0			0
$557$	6.08239	−	6.08239i	0.257719	−	0.257719i	−0.566407	−	0.824126i	$-0.691667\pi$
$557$	6.08239	−	6.08239i	0.257719	−	0.257719i	0.824126	+	0.566407i	$0.191667\pi$
$558$		0			0
$559$	−2.02442			−0.0856238
$560$		0			0
$561$	−7.01953			−0.296365
$562$		0			0
$563$	23.1946	−	23.1946i	0.977536	−	0.977536i	−0.0222176	−	0.999753i	$-0.507073\pi$
$563$	23.1946	−	23.1946i	0.977536	−	0.977536i	0.999753	+	0.0222176i	$0.00707265\pi$
$564$		0			0
$565$	−28.6209	+	2.07912i	−1.20409	+	0.0874692i
$566$		0			0
$567$	2.93661			0.123326
$568$		0			0
$569$			1.31584i			0.0551629i	0.999620	+	0.0275815i	$0.00878056\pi$
$569$			1.31584i			0.0551629i	−0.999620	+	0.0275815i	$0.991219\pi$
$570$		0			0
$571$	18.2083	−	18.2083i	0.761993	−	0.761993i	−0.214690	−	0.976682i	$-0.568874\pi$
$571$	18.2083	−	18.2083i	0.761993	−	0.761993i	0.976682	+	0.214690i	$0.0688740\pi$
$572$		0			0
$573$	0.286330	−	0.286330i	0.0119616	−	0.0119616i
$574$		0			0
$575$	30.5579	−	4.46320i	1.27435	−	0.186128i
$576$		0			0
$577$			8.13617i			0.338713i	0.985555	+	0.169357i	$0.0541689\pi$
$577$			8.13617i			0.338713i	−0.985555	+	0.169357i	$0.945831\pi$
$578$		0			0
$579$	4.58891	+	4.58891i	0.190708	+	0.190708i
$580$		0			0
$581$	26.9802	−	26.9802i	1.11933	−	1.11933i
$582$		0			0
$583$	0.194522			0.00805629
$584$		0			0
$585$	2.33222	−	2.69760i	0.0964255	−	0.111532i
$586$		0			0
$587$	13.4231	+	13.4231i	0.554030	+	0.554030i	0.927601	−	0.373572i	$-0.121867\pi$
$587$	13.4231	+	13.4231i	0.554030	+	0.554030i	−0.373572	+	0.927601i	$0.621867\pi$
$588$		0			0
$589$	−0.773329	−	0.773329i	−0.0318645	−	0.0318645i
$590$		0			0
$591$	−26.0816			−1.07286
$592$		0			0
$593$			17.9386i			0.736649i	0.929697	+	0.368324i	$0.120068\pi$
$593$			17.9386i			0.736649i	−0.929697	+	0.368324i	$0.879932\pi$
$594$		0			0
$595$	−48.9572	+	3.55641i	−2.00705	+	0.145799i
$596$		0			0
$597$	9.52443	+	9.52443i	0.389809	+	0.389809i
$598$		0			0
$599$			3.98863i			0.162971i	0.996675	+	0.0814855i	$0.0259664\pi$
$599$			3.98863i			0.162971i	−0.996675	+	0.0814855i	$0.974034\pi$
$600$		0			0
$601$		−	20.7775i		−	0.847532i	−0.905772	−	0.423766i	$-0.860708\pi$
$601$		−	20.7775i		−	0.847532i	0.905772	−	0.423766i	$-0.139292\pi$
$602$		0			0
$603$	−8.68265	−	8.68265i	−0.353585	−	0.353585i
$604$		0			0
$605$	22.5656	−	1.63924i	0.917421	−	0.0666445i
$606$		0			0
$607$		−	46.0393i		−	1.86868i	−0.356384	−	0.934340i	$-0.615990\pi$
$607$		−	46.0393i		−	1.86868i	0.356384	−	0.934340i	$-0.384010\pi$
$608$		0			0
$609$	−12.2566			−0.496664
$610$		0			0
$611$	−4.65426	−	4.65426i	−0.188291	−	0.188291i
$612$		0			0
$613$	−13.9783	−	13.9783i	−0.564580	−	0.564580i	0.366025	−	0.930605i	$-0.380718\pi$
$613$	−13.9783	−	13.9783i	−0.564580	−	0.564580i	−0.930605	+	0.366025i	$0.880718\pi$
$614$		0			0
$615$	−18.0893	+	20.9234i	−0.729433	+	0.843711i
$616$		0			0
$617$	−33.5135			−1.34920			−0.674601	−	0.738182i	$-0.735684\pi$
$617$	−33.5135			−1.34920			−0.674601	+	0.738182i	$0.735684\pi$
$618$		0			0
$619$	−4.64277	+	4.64277i	−0.186609	+	0.186609i	−0.794228	−	0.607620i	$-0.792125\pi$
$619$	−4.64277	+	4.64277i	−0.186609	+	0.186609i	0.607620	+	0.794228i	$0.292125\pi$
$620$		0			0
$621$	4.36739	+	4.36739i	0.175257	+	0.175257i
$622$		0			0
$623$		−	25.5918i		−	1.02531i
$624$		0			0
$625$	23.9556	−	7.15033i	0.958226	−	0.286013i
$626$		0			0
$627$	−0.397732	+	0.397732i	−0.0158839	+	0.0158839i
$628$		0			0
$629$	−41.3764	+	41.3764i	−1.64978	+	1.64978i
$630$		0			0
$631$		−	4.43412i		−	0.176519i	−0.996097	−	0.0882597i	$-0.971869\pi$
$631$		−	4.43412i		−	0.176519i	0.996097	−	0.0882597i	$-0.0281305\pi$
$632$		0			0
$633$	8.59487			0.341615
$634$		0			0
$635$	−2.38725	+	0.173418i	−0.0947351	+	0.00688187i
$636$		0			0
$637$	−1.83099	+	1.83099i	−0.0725464	+	0.0725464i
$638$		0			0
$639$	8.95735			0.354347
$640$		0			0
$641$	−29.2735			−1.15623			−0.578116	−	0.815954i	$-0.696212\pi$
$641$	−29.2735			−1.15623			−0.578116	+	0.815954i	$0.696212\pi$
$642$		0			0
$643$	5.69367	−	5.69367i	0.224536	−	0.224536i	−0.585869	−	0.810406i	$-0.699247\pi$
$643$	5.69367	−	5.69367i	0.224536	−	0.224536i	0.810406	+	0.585869i	$0.199247\pi$
$644$		0			0
$645$	−0.205656	−	2.83104i	−0.00809771	−	0.111472i
$646$		0			0
$647$	−2.78788			−0.109603			−0.0548015	−	0.998497i	$-0.517453\pi$
$647$	−2.78788			−0.109603			−0.0548015	+	0.998497i	$0.517453\pi$
$648$		0			0
$649$		−	10.2607i		−	0.402766i
$650$		0			0
$651$	3.79128	−	3.79128i	0.148592	−	0.148592i
$652$		0			0
$653$	−19.9931	+	19.9931i	−0.782389	+	0.782389i	−0.980233	−	0.197844i	$-0.936606\pi$
$653$	−19.9931	+	19.9931i	−0.782389	+	0.782389i	0.197844	+	0.980233i	$0.436606\pi$
$654$		0			0
$655$	−22.5481	+	26.0807i	−0.881027	+	1.01906i
$656$		0			0
$657$		−	0.174246i		−	0.00679799i
$658$		0			0
$659$	−6.26656	−	6.26656i	−0.244110	−	0.244110i	0.574438	−	0.818548i	$-0.305221\pi$
$659$	−6.26656	−	6.26656i	−0.244110	−	0.244110i	−0.818548	+	0.574438i	$0.805221\pi$
$660$		0			0
$661$	2.89073	−	2.89073i	0.112436	−	0.112436i	−0.648650	−	0.761087i	$-0.724666\pi$
$661$	2.89073	−	2.89073i	0.112436	−	0.112436i	0.761087	+	0.648650i	$0.224666\pi$
$662$		0			0
$663$	−11.9213			−0.462985
$664$		0			0
$665$	−2.57244	+	2.97546i	−0.0997550	+	0.115383i
$666$		0			0
$667$	−18.2283	−	18.2283i	−0.705803	−	0.705803i
$668$		0			0
$669$	−15.6125	−	15.6125i	−0.603614	−	0.603614i
$670$		0			0
$671$	−9.79420			−0.378101
$672$		0			0
$673$			30.9133i			1.19162i	0.803125	+	0.595810i	$0.203169\pi$
$673$			30.9133i			1.19162i	−0.803125	+	0.595810i	$0.796831\pi$
$674$		0			0
$675$	4.00938	+	2.98745i	0.154321	+	0.114987i
$676$		0			0
$677$	−5.28850	−	5.28850i	−0.203253	−	0.203253i	0.598139	−	0.801392i	$-0.295907\pi$
$677$	−5.28850	−	5.28850i	−0.203253	−	0.203253i	−0.801392	+	0.598139i	$0.795907\pi$
$678$		0			0
$679$		−	30.9757i		−	1.18874i
$680$		0			0
$681$			7.86189i			0.301268i
$682$		0			0
$683$	10.6055	+	10.6055i	0.405809	+	0.405809i	0.880274	−	0.474465i	$-0.157359\pi$
$683$	10.6055	+	10.6055i	0.405809	+	0.405809i	−0.474465	+	0.880274i	$0.657359\pi$
$684$		0			0
$685$	1.62897	+	22.4243i	0.0622399	+	0.856788i
$686$		0			0
$687$			16.7193i			0.637882i
$688$		0			0
$689$	0.330358			0.0125856
$690$		0			0
$691$	32.1363	+	32.1363i	1.22252	+	1.22252i	0.966732	+	0.255790i	$0.0823357\pi$
$691$	32.1363	+	32.1363i	1.22252	+	1.22252i	0.255790	+	0.966732i	$0.417664\pi$
$692$		0			0
$693$	−1.94990	−	1.94990i	−0.0740706	−	0.0740706i
$694$		0			0
$695$	−6.95587	−	6.01372i	−0.263851	−	0.228113i
$696$		0			0
$697$	92.4648			3.50235
$698$		0			0
$699$	−6.30756	+	6.30756i	−0.238574	+	0.238574i
$700$		0			0
$701$	−13.0526	−	13.0526i	−0.492989	−	0.492989i	0.416258	−	0.909247i	$-0.363341\pi$
$701$	−13.0526	−	13.0526i	−0.492989	−	0.492989i	−0.909247	+	0.416258i	$0.863341\pi$
$702$		0			0
$703$			4.68883i			0.176843i
$704$		0			0
$705$	6.03592	−	6.98155i	0.227326	−	0.262940i
$706$		0			0
$707$	−28.3545	+	28.3545i	−1.06638	+	1.06638i
$708$		0			0
$709$	7.03016	−	7.03016i	0.264023	−	0.264023i	−0.562663	−	0.826686i	$-0.690223\pi$
$709$	7.03016	−	7.03016i	0.264023	−	0.264023i	0.826686	+	0.562663i	$0.190223\pi$
$710$		0			0
$711$			3.06488i			0.114942i
$712$		0			0
$713$	11.2769			0.422325
$714$		0			0
$715$	−3.33978	+	0.242613i	−0.124901	+	0.00907321i
$716$		0			0
$717$	−16.2153	+	16.2153i	−0.605573	+	0.605573i
$718$		0			0
$719$	15.9753			0.595778			0.297889	−	0.954601i	$-0.403718\pi$
$719$	15.9753			0.595778			0.297889	+	0.954601i	$0.403718\pi$
$720$		0			0
$721$	42.7464			1.59196
$722$		0			0
$723$	−4.58369	+	4.58369i	−0.170469	+	0.170469i
$724$		0			0
$725$	−16.7341	−	12.4688i	−0.621489	−	0.463080i
$726$		0			0
$727$	−9.60073			−0.356071			−0.178036	−	0.984024i	$-0.556974\pi$
$727$	−9.60073			−0.356071			−0.178036	+	0.984024i	$0.556974\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−6.70992	+	6.70992i	−0.248175	+	0.248175i
$732$		0			0
$733$	5.23740	−	5.23740i	0.193448	−	0.193448i	−0.603736	−	0.797184i	$-0.706322\pi$
$733$	5.23740	−	5.23740i	0.193448	−	0.193448i	0.797184	+	0.603736i	$0.206322\pi$
$734$		0			0
$735$	−2.74655	−	2.37453i	−0.101308	−	0.0875860i
$736$		0			0
$737$			11.5305i			0.424731i
$738$		0			0
$739$	−18.0809	−	18.0809i	−0.665118	−	0.665118i	0.291464	−	0.956582i	$-0.405858\pi$
$739$	−18.0809	−	18.0809i	−0.665118	−	0.665118i	−0.956582	+	0.291464i	$0.905858\pi$
$740$		0			0
$741$	−0.675469	+	0.675469i	−0.0248140	+	0.0248140i
$742$		0			0
$743$	5.96005			0.218653			0.109326	−	0.994006i	$-0.465131\pi$
$743$	5.96005			0.218653			0.109326	+	0.994006i	$0.465131\pi$
$744$		0			0
$745$	−3.01731	−	2.60862i	−0.110546	−	0.0955725i
$746$		0			0
$747$	9.18751	+	9.18751i	0.336153	+	0.336153i
$748$		0			0
$749$	17.2162	+	17.2162i	0.629065	+	0.629065i
$750$		0			0
$751$	32.6552			1.19160			0.595802	−	0.803131i	$-0.296834\pi$
$751$	32.6552			1.19160			0.595802	+	0.803131i	$0.296834\pi$
$752$		0			0
$753$		−	20.3954i		−	0.743251i
$754$		0			0
$755$	45.6606	−	3.31694i	1.66176	−	0.120716i
$756$		0			0
$757$	34.0760	+	34.0760i	1.23851	+	1.23851i	0.960609	+	0.277903i	$0.0896395\pi$
$757$	34.0760	+	34.0760i	1.23851	+	1.23851i	0.277903	+	0.960609i	$0.410361\pi$
$758$		0			0
$759$		−	5.79986i		−	0.210521i
$760$		0			0
$761$			29.5888i			1.07259i	0.844030	+	0.536296i	$0.180177\pi$
$761$			29.5888i			1.07259i	−0.844030	+	0.536296i	$0.819823\pi$
$762$		0			0
$763$	14.4371	+	14.4371i	0.522659	+	0.522659i
$764$		0			0
$765$	−1.21106	−	16.6713i	−0.0437859	−	0.602752i
$766$		0			0
$767$		−	17.4257i		−	0.629206i
$768$		0			0
$769$	29.1544			1.05133			0.525667	−	0.850690i	$-0.323816\pi$
$769$	29.1544			1.05133			0.525667	+	0.850690i	$0.323816\pi$
$770$		0			0
$771$	−0.136994	−	0.136994i	−0.00493373	−	0.00493373i
$772$		0			0
$773$	−16.3728	−	16.3728i	−0.588889	−	0.588889i	0.348441	−	0.937331i	$-0.386711\pi$
$773$	−16.3728	−	16.3728i	−0.588889	−	0.588889i	−0.937331	+	0.348441i	$0.886711\pi$
$774$		0			0
$775$	9.03318	−	1.31936i	0.324482	−	0.0473929i
$776$		0			0
$777$	−22.9872			−0.824662
$778$		0			0
$779$	5.23912	−	5.23912i	0.187711	−	0.187711i
$780$		0			0
$781$	−5.94764	−	5.94764i	−0.212823	−	0.212823i
$782$		0			0
$783$		−	4.17374i		−	0.149157i
$784$		0			0
$785$	−19.4568	−	16.8214i	−0.694443	−	0.600383i
$786$		0			0
$787$	−27.4334	+	27.4334i	−0.977894	+	0.977894i	−0.999761	−	0.0218667i	$-0.993039\pi$
$787$	−27.4334	+	27.4334i	−0.977894	+	0.977894i	0.0218667	+	0.999761i	$0.493039\pi$
$788$		0			0
$789$	11.7173	−	11.7173i	0.417148	−	0.417148i
$790$		0			0
$791$			37.6867i			1.33999i
$792$		0			0
$793$	−16.6335			−0.590673
$794$		0			0
$795$	0.0335604	+	0.461989i	0.00119026	+	0.0163850i
$796$		0			0
$797$	−1.30833	+	1.30833i	−0.0463434	+	0.0463434i	−0.729899	−	0.683555i	$-0.760433\pi$
$797$	−1.30833	+	1.30833i	−0.0463434	+	0.0463434i	0.683555	+	0.729899i	$0.260433\pi$
$798$		0			0
$799$	−30.8530			−1.09150
$800$		0			0
$801$	8.71473			0.307920
$802$		0			0
$803$	−0.115699	+	0.115699i	−0.00408292	+	0.00408292i
$804$		0			0
$805$	−2.93847	−	40.4507i	−0.103567	−	1.42570i
$806$		0			0
$807$	−10.0322			−0.353149
$808$		0			0
$809$			5.40398i			0.189994i	0.995478	+	0.0949970i	$0.0302841\pi$
$809$			5.40398i			0.189994i	−0.995478	+	0.0949970i	$0.969716\pi$
$810$		0			0
$811$	5.63507	−	5.63507i	0.197874	−	0.197874i	−0.601214	−	0.799088i	$-0.705316\pi$
$811$	5.63507	−	5.63507i	0.197874	−	0.197874i	0.799088	+	0.601214i	$0.205316\pi$
$812$		0			0
$813$	−1.85459	+	1.85459i	−0.0650432	+	0.0650432i
$814$		0			0
$815$	9.78282	+	8.45776i	0.342677	+	0.296262i
$816$		0			0
$817$			0.760378i			0.0266023i
$818$		0			0
$819$	−3.31152	−	3.31152i	−0.115714	−	0.115714i
$820$		0			0
$821$	11.6911	−	11.6911i	0.408022	−	0.408022i	−0.473027	−	0.881048i	$-0.656839\pi$
$821$	11.6911	−	11.6911i	0.408022	−	0.408022i	0.881048	+	0.473027i	$0.156839\pi$
$822$		0			0
$823$	−12.7721			−0.445207			−0.222604	−	0.974909i	$-0.571456\pi$
$823$	−12.7721			−0.445207			−0.222604	+	0.974909i	$0.571456\pi$
$824$		0			0
$825$	−0.678563	−	4.64587i	−0.0236245	−	0.161748i
$826$		0			0
$827$	−0.00790410	−	0.00790410i	−0.000274852	−	0.000274852i	0.706969	−	0.707244i	$-0.250062\pi$
$827$	−0.00790410	−	0.00790410i	−0.000274852	−	0.000274852i	−0.707244	+	0.706969i	$0.750062\pi$
$828$		0			0
$829$	2.93843	+	2.93843i	0.102056	+	0.102056i	0.756291	−	0.654235i	$-0.227009\pi$
$829$	2.93843	+	2.93843i	0.102056	+	0.102056i	−0.654235	+	0.756291i	$0.727009\pi$
$830$		0			0
$831$	11.2788			0.391258
$832$		0			0
$833$			12.1376i			0.420542i
$834$		0			0
$835$	1.54372	+	21.2508i	0.0534228	+	0.735413i
$836$		0			0
$837$	1.29104	+	1.29104i	0.0446249	+	0.0446249i
$838$		0			0
$839$			39.0990i			1.34985i	0.737888	+	0.674923i	$0.235823\pi$
$839$			39.0990i			1.34985i	−0.737888	+	0.674923i	$0.764177\pi$
$840$		0			0
$841$		−	11.5799i		−	0.399308i
$842$		0			0
$843$	7.05586	+	7.05586i	0.243017	+	0.243017i
$844$		0			0
$845$	23.3205	−	1.69408i	0.802250	−	0.0582781i
$846$		0			0
$847$		−	29.7133i		−	1.02096i
$848$		0			0
$849$	28.8579			0.990399
$850$		0			0
$851$	−34.1870	−	34.1870i	−1.17192	−	1.17192i
$852$		0			0
$853$	−0.788780	−	0.788780i	−0.0270073	−	0.0270073i	0.693474	−	0.720481i	$-0.256079\pi$
$853$	−0.788780	−	0.788780i	−0.0270073	−	0.0270073i	−0.720481	+	0.693474i	$0.756079\pi$
$854$		0			0
$855$	−1.01323	−	0.875989i	−0.0346517	−	0.0299582i
$856$		0			0
$857$	45.0264			1.53807			0.769036	−	0.639206i	$-0.220737\pi$
$857$	45.0264			1.53807			0.769036	+	0.639206i	$0.220737\pi$
$858$		0			0
$859$	−21.5188	+	21.5188i	−0.734212	+	0.734212i	−0.971451	−	0.237239i	$-0.923757\pi$
$859$	−21.5188	+	21.5188i	−0.734212	+	0.734212i	0.237239	+	0.971451i	$0.423757\pi$
$860$		0			0
$861$	25.6851	+	25.6851i	0.875344	+	0.875344i
$862$		0			0
$863$		−	8.30436i		−	0.282684i	−0.989961	−	0.141342i	$-0.954858\pi$
$863$		−	8.30436i		−	0.282684i	0.989961	−	0.141342i	$-0.0451417\pi$
$864$		0			0
$865$	14.7894	+	12.7862i	0.502855	+	0.434744i
$866$		0			0
$867$	−27.4922	+	27.4922i	−0.933684	+	0.933684i
$868$		0			0
$869$	2.03507	−	2.03507i	0.0690351	−	0.0690351i
$870$		0			0
$871$			19.5823i			0.663520i
$872$		0			0
$873$	10.5481			0.357000
$874$		0			0
$875$	−7.08639	−	32.0585i	−0.239564	−	1.08377i
$876$		0			0
$877$	−17.6134	+	17.6134i	−0.594764	+	0.594764i	−0.938914	−	0.344151i	$-0.888167\pi$
$877$	−17.6134	+	17.6134i	−0.594764	+	0.594764i	0.344151	+	0.938914i	$0.388167\pi$
$878$		0			0
$879$	−6.58866			−0.222230
$880$		0			0
$881$	32.5717			1.09737			0.548684	−	0.836030i	$-0.315129\pi$
$881$	32.5717			1.09737			0.548684	+	0.836030i	$0.315129\pi$
$882$		0			0
$883$	−11.6327	+	11.6327i	−0.391472	+	0.391472i	−0.875212	−	0.483740i	$-0.839278\pi$
$883$	−11.6327	+	11.6327i	−0.391472	+	0.391472i	0.483740	+	0.875212i	$0.339278\pi$
$884$		0			0
$885$	24.3690	−	1.77024i	0.819153	−	0.0595060i
$886$		0			0
$887$	40.0203			1.34375			0.671875	−	0.740665i	$-0.265489\pi$
$887$	40.0203			1.34375			0.671875	+	0.740665i	$0.265489\pi$
$888$		0			0
$889$			3.14342i			0.105427i
$890$		0			0
$891$	0.663996	−	0.663996i	0.0222447	−	0.0222447i
$892$		0			0
$893$	−1.74815	+	1.74815i	−0.0584997	+	0.0584997i
$894$		0			0
$895$	−21.4156	+	24.7708i	−0.715845	+	0.827995i
$896$		0			0
$897$		−	9.84991i		−	0.328879i
$898$		0			0
$899$	−5.38846	−	5.38846i	−0.179715	−	0.179715i
$900$		0			0
$901$	1.09497	−	1.09497i	0.0364787	−	0.0364787i
$902$		0			0
$903$	−3.72779			−0.124053
$904$		0			0
$905$	14.3057	+	12.3680i	0.475536	+	0.411126i
$906$		0			0
$907$	5.81050	+	5.81050i	0.192934	+	0.192934i	0.796963	−	0.604028i	$-0.206439\pi$
$907$	5.81050	+	5.81050i	0.192934	+	0.192934i	−0.604028	+	0.796963i	$0.706439\pi$
$908$		0			0
$909$	−9.65550	−	9.65550i	−0.320253	−	0.320253i
$910$		0			0
$911$	−10.4809			−0.347248			−0.173624	−	0.984812i	$-0.555548\pi$
$911$	−10.4809			−0.347248			−0.173624	+	0.984812i	$0.555548\pi$
$912$		0			0
$913$		−	12.2009i		−	0.403792i
$914$		0			0
$915$	−1.68976	−	23.2611i	−0.0558619	−	0.768989i
$916$		0			0
$917$	32.0161	+	32.0161i	1.05726	+	1.05726i
$918$		0			0
$919$			51.8755i			1.71121i	0.517626	+	0.855607i	$0.326816\pi$
$919$			51.8755i			1.71121i	−0.517626	+	0.855607i	$0.673184\pi$
$920$		0			0
$921$		−	12.8055i		−	0.421956i
$922$		0			0
$923$	−10.1009	−	10.1009i	−0.332475	−	0.332475i
$924$		0			0
$925$	−31.3847	−	23.3851i	−1.03192	−	0.768898i
$926$		0			0
$927$			14.5564i			0.478094i
$928$		0			0
$929$	−5.54673			−0.181982			−0.0909912	−	0.995852i	$-0.529004\pi$
$929$	−5.54673			−0.181982			−0.0909912	+	0.995852i	$0.529004\pi$
$930$		0			0
$931$	0.687724	+	0.687724i	0.0225393	+	0.0225393i
$932$		0			0
$933$	2.39956	+	2.39956i	0.0785581	+	0.0785581i
$934$		0			0
$935$	−10.2655	+	11.8738i	−0.335719	+	0.388315i
$936$		0			0
$937$	9.31790			0.304402			0.152201	−	0.988350i	$-0.451364\pi$
$937$	9.31790			0.304402			0.152201	+	0.988350i	$0.451364\pi$
$938$		0			0
$939$	7.70346	−	7.70346i	0.251393	−	0.251393i
$940$		0			0
$941$	−21.9832	−	21.9832i	−0.716630	−	0.716630i	0.251283	−	0.967914i	$-0.419147\pi$
$941$	−21.9832	−	21.9832i	−0.716630	−	0.716630i	−0.967914	+	0.251283i	$0.919147\pi$
$942$		0			0
$943$			76.3986i			2.48788i
$944$		0			0
$945$	4.29458	−	4.96740i	0.139703	−	0.161590i
$946$		0			0
$947$	−15.4966	+	15.4966i	−0.503572	+	0.503572i	−0.912546	−	0.408974i	$-0.865887\pi$
$947$	−15.4966	+	15.4966i	−0.503572	+	0.503572i	0.408974	+	0.912546i	$0.365887\pi$
$948$		0			0
$949$	−0.196492	+	0.196492i	−0.00637839	+	0.00637839i
$950$		0			0
$951$			4.89001i			0.158569i
$952$		0			0
$953$	−5.72390			−0.185415			−0.0927076	−	0.995693i	$-0.529552\pi$
$953$	−5.72390			−0.185415			−0.0927076	+	0.995693i	$0.529552\pi$
$954$		0			0
$955$	−0.0656024	−	0.903075i	−0.00212284	−	0.0292228i
$956$		0			0
$957$	−2.77134	+	2.77134i	−0.0895848	+	0.0895848i
$958$		0			0
$959$	29.5273			0.953485
$960$		0			0
$961$	−27.6664			−0.892466
$962$		0			0
$963$	−5.86260	+	5.86260i	−0.188920	+	0.188920i
$964$		0			0
$965$	14.4733	−	1.05139i	0.465911	−	0.0338453i
$966$		0			0
$967$	−8.80514			−0.283154			−0.141577	−	0.989927i	$-0.545217\pi$
$967$	−8.80514			−0.283154			−0.141577	+	0.989927i	$0.545217\pi$
$968$		0			0
$969$			4.47767i			0.143844i
$970$		0			0
$971$	−26.8032	+	26.8032i	−0.860157	+	0.860157i	−0.991356	−	0.131199i	$-0.958117\pi$
$971$	−26.8032	+	26.8032i	−0.860157	+	0.860157i	0.131199	+	0.991356i	$0.458117\pi$
$972$		0			0
$973$	−8.53888	+	8.53888i	−0.273744	+	0.273744i
$974$		0			0
$975$	−1.15241	−	7.89009i	−0.0369065	−	0.252685i
$976$		0			0
$977$			36.2126i			1.15854i	0.815134	+	0.579272i	$0.196663\pi$
$977$			36.2126i			1.15854i	−0.815134	+	0.579272i	$0.803337\pi$
$978$		0			0
$979$	−5.78655	−	5.78655i	−0.184939	−	0.184939i
$980$		0			0
$981$	−4.91625	+	4.91625i	−0.156964	+	0.156964i
$982$		0			0
$983$	15.7547			0.502496			0.251248	−	0.967923i	$-0.419159\pi$
$983$	15.7547			0.502496			0.251248	+	0.967923i	$0.419159\pi$
$984$		0			0
$985$	−38.1425	+	44.1182i	−1.21532	+	1.40572i
$986$		0			0
$987$	−8.57040	−	8.57040i	−0.272799	−	0.272799i
$988$		0			0
$989$	−5.54404	−	5.54404i	−0.176290	−	0.176290i
$990$		0			0
$991$	−12.5049			−0.397230			−0.198615	−	0.980078i	$-0.563644\pi$
$991$	−12.5049			−0.397230			−0.198615	+	0.980078i	$0.563644\pi$
$992$		0			0
$993$			35.2487i			1.11859i
$994$		0			0
$995$	30.0397	−	2.18219i	0.952324	−	0.0691799i
$996$		0			0
$997$	−4.59749	−	4.59749i	−0.145604	−	0.145604i	0.630547	−	0.776151i	$-0.282831\pi$
$997$	−4.59749	−	4.59749i	−0.145604	−	0.145604i	−0.776151	+	0.630547i	$0.782831\pi$
$998$		0			0
$999$		−	7.82780i		−	0.247661i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.bl.b.289.14		48
4.3	odd	2		1920.2.bl.a.289.11		48
5.4	even	2	inner	1920.2.bl.b.289.11		48
8.3	odd	2		240.2.bl.a.109.9	✓	48
8.5	even	2		960.2.bl.a.529.6		48
16.3	odd	4		240.2.bl.a.229.16	yes	48
16.5	even	4	inner	1920.2.bl.b.1249.11		48
16.11	odd	4		1920.2.bl.a.1249.14		48
16.13	even	4		960.2.bl.a.49.13		48
20.19	odd	2		1920.2.bl.a.289.14		48
24.11	even	2		720.2.bm.h.109.16		48
40.19	odd	2		240.2.bl.a.109.16	yes	48
40.29	even	2		960.2.bl.a.529.13		48
48.35	even	4		720.2.bm.h.469.9		48
80.19	odd	4		240.2.bl.a.229.9	yes	48
80.29	even	4		960.2.bl.a.49.6		48
80.59	odd	4		1920.2.bl.a.1249.11		48
80.69	even	4	inner	1920.2.bl.b.1249.14		48
120.59	even	2		720.2.bm.h.109.9		48
240.179	even	4		720.2.bm.h.469.16		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.9	✓	48	8.3	odd	2
240.2.bl.a.109.16	yes	48	40.19	odd	2
240.2.bl.a.229.9	yes	48	80.19	odd	4
240.2.bl.a.229.16	yes	48	16.3	odd	4
720.2.bm.h.109.9		48	120.59	even	2
720.2.bm.h.109.16		48	24.11	even	2
720.2.bm.h.469.9		48	48.35	even	4
720.2.bm.h.469.16		48	240.179	even	4
960.2.bl.a.49.6		48	80.29	even	4
960.2.bl.a.49.13		48	16.13	even	4
960.2.bl.a.529.6		48	8.5	even	2
960.2.bl.a.529.13		48	40.29	even	2
1920.2.bl.a.289.11		48	4.3	odd	2
1920.2.bl.a.289.14		48	20.19	odd	2
1920.2.bl.a.1249.11		48	80.59	odd	4
1920.2.bl.a.1249.14		48	16.11	odd	4
1920.2.bl.b.289.11		48	5.4	even	2	inner
1920.2.bl.b.289.14		48	1.1	even	1	trivial
1920.2.bl.b.1249.11		48	16.5	even	4	inner
1920.2.bl.b.1249.14		48	80.69	even	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:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.bl (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(-0.162008 - 2.23019i) q^{5} -2.93661 q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{3} +(-0.162008 - 2.23019i) q^{5} -2.93661 q^{7} -1.00000i q^{9} +(-0.663996 + 0.663996i) q^{11} +(-1.12767 + 1.12767i) q^{13} +(-1.69154 - 1.46243i) q^{15} +7.47528i q^{17} +(0.423555 + 0.423555i) q^{19} +(-2.07650 + 2.07650i) q^{21} -6.17642 q^{23} +(-4.94751 + 0.722620i) q^{25} +(-0.707107 - 0.707107i) q^{27} +(2.95128 + 2.95128i) q^{29} -1.82581 q^{31} +0.939032i q^{33} +(0.475756 + 6.54921i) q^{35} +(5.53509 + 5.53509i) q^{37} +1.59476i q^{39} -12.3694i q^{41} +(0.897614 + 0.897614i) q^{43} +(-2.23019 + 0.162008i) q^{45} +4.12733i q^{47} +1.62370 q^{49} +(5.28582 + 5.28582i) q^{51} +(-0.146479 - 0.146479i) q^{53} +(1.58841 + 1.37327i) q^{55} +0.598997 q^{57} +(-7.72645 + 7.72645i) q^{59} +(7.37519 + 7.37519i) q^{61} +2.93661i q^{63} +(2.69760 + 2.33222i) q^{65} +(8.68265 - 8.68265i) q^{67} +(-4.36739 + 4.36739i) q^{69} +8.95735i q^{71} +0.174246 q^{73} +(-2.98745 + 4.00938i) q^{75} +(1.94990 - 1.94990i) q^{77} -3.06488 q^{79} -1.00000 q^{81} +(-9.18751 + 9.18751i) q^{83} +(16.6713 - 1.21106i) q^{85} +4.17374 q^{87} +8.71473i q^{89} +(3.31152 - 3.31152i) q^{91} +(-1.29104 + 1.29104i) q^{93} +(0.875989 - 1.01323i) q^{95} +10.5481i q^{97} +(0.663996 + 0.663996i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 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

L-functions

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