LMFDB - Embedded newform 384.7.l.a.31.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,7,Mod(31,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("384.31");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	384.l (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:	$88.3407681100$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.16
Character	$\chi$	$=$	384.31
Dual form			384.7.l.a.223.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(11.0227 + 11.0227i) q^{3} +(99.4317 + 99.4317i) q^{5} -407.926 q^{7} +243.000i q^{9} +O(q^{10})$	\(q+(11.0227 + 11.0227i) q^{3} +(99.4317 + 99.4317i) q^{5} -407.926 q^{7} +243.000i q^{9} +(1305.36 - 1305.36i) q^{11} +(1343.66 - 1343.66i) q^{13} +2192.01i q^{15} +4694.90 q^{17} +(-2519.26 - 2519.26i) q^{19} +(-4496.45 - 4496.45i) q^{21} -21920.1 q^{23} +4148.34i q^{25} +(-2678.52 + 2678.52i) q^{27} +(-11013.8 + 11013.8i) q^{29} -29355.4i q^{31} +28777.2 q^{33} +(-40560.8 - 40560.8i) q^{35} +(836.191 + 836.191i) q^{37} +29621.5 q^{39} -134247. i q^{41} +(94240.7 - 94240.7i) q^{43} +(-24161.9 + 24161.9i) q^{45} +22148.9i q^{47} +48754.4 q^{49} +(51750.5 + 51750.5i) q^{51} +(-53365.3 - 53365.3i) q^{53} +259588. q^{55} -55538.1i q^{57} +(-142793. + 142793. i) q^{59} +(-10444.7 + 10444.7i) q^{61} -99126.0i q^{63} +267204. q^{65} +(32487.9 + 32487.9i) q^{67} +(-241619. - 241619. i) q^{69} +231804. q^{71} +23177.3i q^{73} +(-45725.9 + 45725.9i) q^{75} +(-532490. + 532490. i) q^{77} -659707. i q^{79} -59049.0 q^{81} +(-575483. - 575483. i) q^{83} +(466822. + 466822. i) q^{85} -242804. q^{87} +1.12283e6i q^{89} +(-548113. + 548113. i) q^{91} +(323576. - 323576. i) q^{93} -500989. i q^{95} +751819. q^{97} +(317202. + 317202. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 2720 q^{11} - 3936 q^{19} - 26240 q^{23} - 66400 q^{29} + 162336 q^{35} + 7200 q^{37} + 340704 q^{43} + 806736 q^{49} + 80352 q^{51} - 443680 q^{53} - 232704 q^{55} - 886144 q^{59} + 326496 q^{61} - 372832 q^{65} - 962112 q^{67} - 541728 q^{69} - 534016 q^{71} - 1073088 q^{75} + 932960 q^{77} - 2834352 q^{81} - 2497760 q^{83} + 372000 q^{85} + 775008 q^{91} - 660960 q^{99}+O(q^{100}) $ 48 * q - 2720 * q^11 - 3936 * q^19 - 26240 * q^23 - 66400 * q^29 + 162336 * q^35 + 7200 * q^37 + 340704 * q^43 + 806736 * q^49 + 80352 * q^51 - 443680 * q^53 - 232704 * q^55 - 886144 * q^59 + 326496 * q^61 - 372832 * q^65 - 962112 * q^67 - 541728 * q^69 - 534016 * q^71 - 1073088 * q^75 + 932960 * q^77 - 2834352 * q^81 - 2497760 * q^83 + 372000 * q^85 + 775008 * q^91 - 660960 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	11.0227	+	11.0227i	0.408248	+	0.408248i
$3$	11.0227	+	11.0227i	0.408248	+	0.408248i
$4$		0			0
$5$	99.4317	+	99.4317i	0.795454	+	0.795454i	0.982375	−	0.186921i	$-0.0598509\pi$
$5$	99.4317	+	99.4317i	0.795454	+	0.795454i	−0.186921	+	0.982375i	$0.559851\pi$
$6$		0			0
$7$	−407.926			−1.18929			−0.594644	−	0.803989i	$-0.702707\pi$
$7$	−407.926			−1.18929			−0.594644	+	0.803989i	$0.702707\pi$
$8$		0			0
$9$			243.000i			0.333333i
$10$		0			0
$11$	1305.36	−	1305.36i	0.980736	−	0.980736i	−0.0190821	−	0.999818i	$-0.506074\pi$
$11$	1305.36	−	1305.36i	0.980736	−	0.980736i	0.999818	+	0.0190821i	$0.00607440\pi$
$12$		0			0
$13$	1343.66	−	1343.66i	0.611587	−	0.611587i	−0.331772	−	0.943360i	$-0.607647\pi$
$13$	1343.66	−	1343.66i	0.611587	−	0.611587i	0.943360	+	0.331772i	$0.107647\pi$
$14$		0			0
$15$			2192.01i			0.649485i
$16$		0			0
$17$	4694.90			0.955607			0.477804	−	0.878467i	$-0.341433\pi$
$17$	4694.90			0.955607			0.477804	+	0.878467i	$0.341433\pi$
$18$		0			0
$19$	−2519.26	−	2519.26i	−0.367293	−	0.367293i	0.499196	−	0.866489i	$-0.333629\pi$
$19$	−2519.26	−	2519.26i	−0.367293	−	0.367293i	−0.866489	+	0.499196i	$0.833629\pi$
$20$		0			0
$21$	−4496.45	−	4496.45i	−0.485525	−	0.485525i
$22$		0			0
$23$	−21920.1			−1.80161			−0.900803	−	0.434229i	$-0.857021\pi$
$23$	−21920.1			−1.80161			−0.900803	+	0.434229i	$0.857021\pi$
$24$		0			0
$25$			4148.34i			0.265494i
$26$		0			0
$27$	−2678.52	+	2678.52i	−0.136083	+	0.136083i
$28$		0			0
$29$	−11013.8	+	11013.8i	−0.451589	+	0.451589i	−0.895882	−	0.444293i	$-0.853455\pi$
$29$	−11013.8	+	11013.8i	−0.451589	+	0.451589i	0.444293	+	0.895882i	$0.353455\pi$
$30$		0			0
$31$		−	29355.4i		−	0.985378i	−0.870205	−	0.492689i	$-0.836014\pi$
$31$		−	29355.4i		−	0.985378i	0.870205	−	0.492689i	$-0.163986\pi$
$32$		0			0
$33$	28777.2			0.800767
$34$		0			0
$35$	−40560.8	−	40560.8i	−0.946024	−	0.946024i
$36$		0			0
$37$	836.191	+	836.191i	0.0165082	+	0.0165082i	0.715313	−	0.698804i	$-0.246284\pi$
$37$	836.191	+	836.191i	0.0165082	+	0.0165082i	−0.698804	+	0.715313i	$0.746284\pi$
$38$		0			0
$39$	29621.5			0.499359
$40$		0			0
$41$		−	134247.i		−	1.94785i	−0.226880	−	0.973923i	$-0.572853\pi$
$41$		−	134247.i		−	1.94785i	0.226880	−	0.973923i	$-0.427147\pi$
$42$		0			0
$43$	94240.7	−	94240.7i	1.18531	−	1.18531i	0.206964	−	0.978349i	$-0.433642\pi$
$43$	94240.7	−	94240.7i	1.18531	−	1.18531i	0.978349	−	0.206964i	$-0.0663584\pi$
$44$		0			0
$45$	−24161.9	+	24161.9i	−0.265151	+	0.265151i
$46$		0			0
$47$			22148.9i			0.213333i	0.994295	+	0.106666i	$0.0340177\pi$
$47$			22148.9i			0.213333i	−0.994295	+	0.106666i	$0.965982\pi$
$48$		0			0
$49$	48754.4			0.414406
$50$		0			0
$51$	51750.5	+	51750.5i	0.390125	+	0.390125i
$52$		0			0
$53$	−53365.3	−	53365.3i	−0.358452	−	0.358452i	0.504790	−	0.863242i	$-0.331570\pi$
$53$	−53365.3	−	53365.3i	−0.358452	−	0.358452i	−0.863242	+	0.504790i	$0.831570\pi$
$54$		0			0
$55$	259588.			1.56026
$56$		0			0
$57$		−	55538.1i		−	0.299893i
$58$		0			0
$59$	−142793.	+	142793.i	−0.695264	+	0.695264i	−0.963385	−	0.268121i	$-0.913597\pi$
$59$	−142793.	+	142793.i	−0.695264	+	0.695264i	0.268121	+	0.963385i	$0.413597\pi$
$60$		0			0
$61$	−10444.7	+	10444.7i	−0.0460156	+	0.0460156i	−0.729740	−	0.683725i	$-0.760359\pi$
$61$	−10444.7	+	10444.7i	−0.0460156	+	0.0460156i	0.683725	+	0.729740i	$0.260359\pi$
$62$		0			0
$63$		−	99126.0i		−	0.396429i
$64$		0			0
$65$	267204.			0.972979
$66$		0			0
$67$	32487.9	+	32487.9i	0.108018	+	0.108018i	0.759050	−	0.651032i	$-0.225664\pi$
$67$	32487.9	+	32487.9i	0.108018	+	0.108018i	−0.651032	+	0.759050i	$0.725664\pi$
$68$		0			0
$69$	−241619.	−	241619.i	−0.735502	−	0.735502i
$70$		0			0
$71$	231804.			0.647659			0.323830	−	0.946115i	$-0.395030\pi$
$71$	231804.			0.647659			0.323830	+	0.946115i	$0.395030\pi$
$72$		0			0
$73$			23177.3i			0.0595791i	0.999556	+	0.0297895i	$0.00948370\pi$
$73$			23177.3i			0.0595791i	−0.999556	+	0.0297895i	$0.990516\pi$
$74$		0			0
$75$	−45725.9	+	45725.9i	−0.108387	+	0.108387i
$76$		0			0
$77$	−532490.	+	532490.i	−1.16638	+	1.16638i
$78$		0			0
$79$		−	659707.i		−	1.33804i	−0.743244	−	0.669021i	$-0.766714\pi$
$79$		−	659707.i		−	1.33804i	0.743244	−	0.669021i	$-0.233286\pi$
$80$		0			0
$81$	−59049.0			−0.111111
$82$		0			0
$83$	−575483.	−	575483.i	−1.00646	−	1.00646i	−0.999979	−	0.00648579i	$-0.997935\pi$
$83$	−575483.	−	575483.i	−1.00646	−	1.00646i	−0.00648579	−	0.999979i	$-0.502065\pi$
$84$		0			0
$85$	466822.	+	466822.i	0.760142	+	0.760142i
$86$		0			0
$87$	−242804.			−0.368721
$88$		0			0
$89$			1.12283e6i			1.59274i	0.604810	+	0.796369i	$0.293249\pi$
$89$			1.12283e6i			1.59274i	−0.604810	+	0.796369i	$0.706751\pi$
$90$		0			0
$91$	−548113.	+	548113.i	−0.727354	+	0.727354i
$92$		0			0
$93$	323576.	−	323576.i	0.402279	−	0.402279i
$94$		0			0
$95$		−	500989.i		−	0.584328i
$96$		0			0
$97$	751819.			0.823755			0.411877	−	0.911239i	$-0.364873\pi$
$97$	751819.			0.823755			0.411877	+	0.911239i	$0.364873\pi$
$98$		0			0
$99$	317202.	+	317202.i	0.326912	+	0.326912i
$100$		0			0
$101$	426592.	+	426592.i	0.414046	+	0.414046i	0.883145	−	0.469100i	$-0.155422\pi$
$101$	426592.	+	426592.i	0.414046	+	0.414046i	−0.469100	+	0.883145i	$0.655422\pi$
$102$		0			0
$103$	2.03872e6			1.86572			0.932859	−	0.360241i	$-0.117306\pi$
$103$	2.03872e6			1.86572			0.932859	+	0.360241i	$0.117306\pi$
$104$		0			0
$105$		−	894179.i		−	0.772425i
$106$		0			0
$107$	−66558.3	+	66558.3i	−0.0543314	+	0.0543314i	−0.733750	−	0.679419i	$-0.762232\pi$
$107$	−66558.3	+	66558.3i	−0.0543314	+	0.0543314i	0.679419	+	0.733750i	$0.262232\pi$
$108$		0			0
$109$	1.43278e6	−	1.43278e6i	1.10637	−	1.10637i	0.112742	−	0.993624i	$-0.464037\pi$
$109$	1.43278e6	−	1.43278e6i	1.10637	−	1.10637i	0.993624	−	0.112742i	$-0.0359632\pi$
$110$		0			0
$111$			18434.2i			0.0134789i
$112$		0			0
$113$	2.33135e6			1.61574			0.807871	−	0.589360i	$-0.200620\pi$
$113$	2.33135e6			1.61574			0.807871	+	0.589360i	$0.200620\pi$
$114$		0			0
$115$	−2.17956e6	−	2.17956e6i	−1.43309	−	1.43309i
$116$		0			0
$117$	326509.	+	326509.i	0.203862	+	0.203862i
$118$		0			0
$119$	−1.91517e6			−1.13649
$120$		0			0
$121$		−	1.63637e6i		−	0.923685i
$122$		0			0
$123$	1.47977e6	−	1.47977e6i	0.795205	−	0.795205i
$124$		0			0
$125$	1.14114e6	−	1.14114e6i	0.584266	−	0.584266i
$126$		0			0
$127$		−	913501.i		−	0.445962i	−0.974823	−	0.222981i	$-0.928421\pi$
$127$		−	913501.i		−	0.445962i	0.974823	−	0.222981i	$-0.0715788\pi$
$128$		0			0
$129$	2.07757e6			0.967804
$130$		0			0
$131$	−91277.0	−	91277.0i	−0.0406020	−	0.0406020i	0.686514	−	0.727116i	$-0.259140\pi$
$131$	−91277.0	−	91277.0i	−0.0406020	−	0.0406020i	−0.727116	+	0.686514i	$0.759140\pi$
$132$		0			0
$133$	1.02767e6	+	1.02767e6i	0.436817	+	0.436817i
$134$		0			0
$135$	−532659.			−0.216495
$136$		0			0
$137$			837703.i			0.325783i	0.986644	+	0.162891i	$0.0520820\pi$
$137$			837703.i			0.325783i	−0.986644	+	0.162891i	$0.947918\pi$
$138$		0			0
$139$	1.30129e6	−	1.30129e6i	0.484540	−	0.484540i	−0.422038	−	0.906578i	$-0.638685\pi$
$139$	1.30129e6	−	1.30129e6i	0.484540	−	0.484540i	0.906578	+	0.422038i	$0.138685\pi$
$140$		0			0
$141$	−244140.	+	244140.i	−0.0870928	+	0.0870928i
$142$		0			0
$143$		−	3.50791e6i		−	1.19961i
$144$		0			0
$145$	−2.19024e6			−0.718436
$146$		0			0
$147$	537406.	+	537406.i	0.169180	+	0.169180i
$148$		0			0
$149$	276371.	+	276371.i	0.0835475	+	0.0835475i	0.747646	−	0.664098i	$-0.231184\pi$
$149$	276371.	+	276371.i	0.0835475	+	0.0835475i	−0.664098	+	0.747646i	$0.731184\pi$
$150$		0			0
$151$	−5.73959e6			−1.66706			−0.833528	−	0.552477i	$-0.813683\pi$
$151$	−5.73959e6			−1.66706			−0.833528	+	0.552477i	$0.813683\pi$
$152$		0			0
$153$			1.14086e6i			0.318536i
$154$		0			0
$155$	2.91886e6	−	2.91886e6i	0.783823	−	0.783823i
$156$		0			0
$157$	−1.38023e6	+	1.38023e6i	−0.356657	+	0.356657i	−0.862579	−	0.505922i	$-0.831152\pi$
$157$	−1.38023e6	+	1.38023e6i	−0.356657	+	0.356657i	0.505922	+	0.862579i	$0.331152\pi$
$158$		0			0
$159$		−	1.17646e6i		−	0.292675i
$160$		0			0
$161$	8.94179e6			2.14263
$162$		0			0
$163$	1.62992e6	+	1.62992e6i	0.376360	+	0.376360i	0.869787	−	0.493427i	$-0.164256\pi$
$163$	1.62992e6	+	1.62992e6i	0.376360	+	0.376360i	−0.493427	+	0.869787i	$0.664256\pi$
$164$		0			0
$165$	2.86136e6	+	2.86136e6i	0.636974	+	0.636974i
$166$		0			0
$167$	3.73108e6			0.801097			0.400549	−	0.916275i	$-0.368820\pi$
$167$	3.73108e6			0.801097			0.400549	+	0.916275i	$0.368820\pi$
$168$		0			0
$169$			1.21598e6i			0.251922i
$170$		0			0
$171$	612180.	−	612180.i	0.122431	−	0.122431i
$172$		0			0
$173$	2.05957e6	−	2.05957e6i	0.397776	−	0.397776i	−0.479672	−	0.877448i	$-0.659244\pi$
$173$	2.05957e6	−	2.05957e6i	0.397776	−	0.397776i	0.877448	+	0.479672i	$0.159244\pi$
$174$		0			0
$175$		−	1.69221e6i		−	0.315749i
$176$		0			0
$177$	−3.14792e6			−0.567681
$178$		0			0
$179$	−4.47273e6	−	4.47273e6i	−0.779854	−	0.779854i	0.199952	−	0.979806i	$-0.435922\pi$
$179$	−4.47273e6	−	4.47273e6i	−0.779854	−	0.779854i	−0.979806	+	0.199952i	$0.935922\pi$
$180$		0			0
$181$	6.94409e6	+	6.94409e6i	1.17106	+	1.17106i	0.981957	+	0.189104i	$0.0605582\pi$
$181$	6.94409e6	+	6.94409e6i	1.17106	+	1.17106i	0.189104	+	0.981957i	$0.439442\pi$
$182$		0			0
$183$	−230257.			−0.0375716
$184$		0			0
$185$			166288.i			0.0262631i
$186$		0			0
$187$	6.12853e6	−	6.12853e6i	0.937198	−	0.937198i
$188$		0			0
$189$	1.09264e6	−	1.09264e6i	0.161842	−	0.161842i
$190$		0			0
$191$			6.78277e6i			0.973435i	0.873560	+	0.486717i	$0.161806\pi$
$191$			6.78277e6i			0.973435i	−0.873560	+	0.486717i	$0.838194\pi$
$192$		0			0
$193$	−8.57451e6			−1.19272			−0.596359	−	0.802718i	$-0.703386\pi$
$193$	−8.57451e6			−1.19272			−0.596359	+	0.802718i	$0.703386\pi$
$194$		0			0
$195$	2.94531e6	+	2.94531e6i	0.397217	+	0.397217i
$196$		0			0
$197$	−7.04633e6	−	7.04633e6i	−0.921646	−	0.921646i	0.0754994	−	0.997146i	$-0.475945\pi$
$197$	−7.04633e6	−	7.04633e6i	−0.921646	−	0.921646i	−0.997146	+	0.0754994i	$0.975945\pi$
$198$		0			0
$199$	−7.06231e6			−0.896164			−0.448082	−	0.893992i	$-0.647893\pi$
$199$	−7.06231e6			−0.896164			−0.448082	+	0.893992i	$0.647893\pi$
$200$		0			0
$201$			716208.i			0.0881965i
$202$		0			0
$203$	4.49281e6	−	4.49281e6i	0.537069	−	0.537069i
$204$		0			0
$205$	1.33485e7	−	1.33485e7i	1.54942	−	1.54942i
$206$		0			0
$207$		−	5.32659e6i		−	0.600535i
$208$		0			0
$209$	−6.57708e6			−0.720434
$210$		0			0
$211$	−2.66095e6	−	2.66095e6i	−0.283263	−	0.283263i	0.551146	−	0.834409i	$-0.314191\pi$
$211$	−2.66095e6	−	2.66095e6i	−0.283263	−	0.283263i	−0.834409	+	0.551146i	$0.814191\pi$
$212$		0			0
$213$	2.55511e6	+	2.55511e6i	0.264406	+	0.264406i
$214$		0			0
$215$	1.87410e7			1.88572
$216$		0			0
$217$			1.19748e7i			1.17190i
$218$		0			0
$219$	−255476.	+	255476.i	−0.0243230	+	0.0243230i
$220$		0			0
$221$	6.30834e6	−	6.30834e6i	0.584437	−	0.584437i
$222$		0			0
$223$		−	1.70720e7i		−	1.53947i	−0.638364	−	0.769734i	$-0.720389\pi$
$223$		−	1.70720e7i		−	1.53947i	0.638364	−	0.769734i	$-0.279611\pi$
$224$		0			0
$225$	−1.00805e6			−0.0884979
$226$		0			0
$227$	−4.90006e6	−	4.90006e6i	−0.418913	−	0.418913i	0.465916	−	0.884829i	$-0.345725\pi$
$227$	−4.90006e6	−	4.90006e6i	−0.418913	−	0.418913i	−0.884829	+	0.465916i	$0.845725\pi$
$228$		0			0
$229$	−2.48757e6	−	2.48757e6i	−0.207142	−	0.207142i	0.595909	−	0.803052i	$-0.296792\pi$
$229$	−2.48757e6	−	2.48757e6i	−0.207142	−	0.207142i	−0.803052	+	0.595909i	$0.796792\pi$
$230$		0			0
$231$	−1.17390e7			−0.952343
$232$		0			0
$233$		−	1.30662e7i		−	1.03295i	−0.856301	−	0.516477i	$-0.827243\pi$
$233$		−	1.30662e7i		−	1.03295i	0.856301	−	0.516477i	$-0.172757\pi$
$234$		0			0
$235$	−2.20230e6	+	2.20230e6i	−0.169696	+	0.169696i
$236$		0			0
$237$	7.27175e6	−	7.27175e6i	0.546253	−	0.546253i
$238$		0			0
$239$		−	9.59298e6i		−	0.702684i	−0.936247	−	0.351342i	$-0.885725\pi$
$239$		−	9.59298e6i		−	0.702684i	0.936247	−	0.351342i	$-0.114275\pi$
$240$		0			0
$241$	1.87299e7			1.33809			0.669043	−	0.743224i	$-0.266704\pi$
$241$	1.87299e7			1.33809			0.669043	+	0.743224i	$0.266704\pi$
$242$		0			0
$243$	−650880.	−	650880.i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	4.84774e6	+	4.84774e6i	0.329641	+	0.329641i
$246$		0			0
$247$	−6.77004e6			−0.449263
$248$		0			0
$249$		−	1.26868e7i		−	0.821775i
$250$		0			0
$251$	−4.66553e6	+	4.66553e6i	−0.295039	+	0.295039i	−0.839067	−	0.544028i	$-0.816899\pi$
$251$	−4.66553e6	+	4.66553e6i	−0.295039	+	0.295039i	0.544028	+	0.839067i	$0.316899\pi$
$252$		0			0
$253$	−2.86136e7	+	2.86136e7i	−1.76690	+	1.76690i
$254$		0			0
$255$			1.02913e7i			0.620653i
$256$		0			0
$257$	2.54982e7			1.50214			0.751069	−	0.660224i	$-0.229539\pi$
$257$	2.54982e7			1.50214			0.751069	+	0.660224i	$0.229539\pi$
$258$		0			0
$259$	−341104.	−	341104.i	−0.0196330	−	0.0196330i
$260$		0			0
$261$	−2.67635e6	−	2.67635e6i	−0.150530	−	0.150530i
$262$		0			0
$263$	1.95340e7			1.07380			0.536901	−	0.843645i	$-0.319595\pi$
$263$	1.95340e7			1.07380			0.536901	+	0.843645i	$0.319595\pi$
$264$		0			0
$265$		−	1.06124e7i		−	0.570265i
$266$		0			0
$267$	−1.23766e7	+	1.23766e7i	−0.650233	+	0.650233i
$268$		0			0
$269$	−1.47261e6	+	1.47261e6i	−0.0756539	+	0.0756539i	−0.743921	−	0.668267i	$-0.767036\pi$
$269$	−1.47261e6	+	1.47261e6i	−0.0756539	+	0.0756539i	0.668267	+	0.743921i	$0.267036\pi$
$270$		0			0
$271$		−	1.71707e7i		−	0.862742i	−0.902175	−	0.431371i	$-0.858030\pi$
$271$		−	1.71707e7i		−	0.862742i	0.902175	−	0.431371i	$-0.141970\pi$
$272$		0			0
$273$	−1.20834e7			−0.593882
$274$		0			0
$275$	5.41507e6	+	5.41507e6i	0.260379	+	0.260379i
$276$		0			0
$277$	−4.08428e6	−	4.08428e6i	−0.192166	−	0.192166i	0.604465	−	0.796631i	$-0.293387\pi$
$277$	−4.08428e6	−	4.08428e6i	−0.192166	−	0.192166i	−0.796631	+	0.604465i	$0.793387\pi$
$278$		0			0
$279$	7.13336e6			0.328459
$280$		0			0
$281$			1.63532e7i			0.737028i	0.929622	+	0.368514i	$0.120133\pi$
$281$			1.63532e7i			0.737028i	−0.929622	+	0.368514i	$0.879867\pi$
$282$		0			0
$283$	−5.07476e6	+	5.07476e6i	−0.223901	+	0.223901i	−0.810139	−	0.586238i	$-0.800608\pi$
$283$	−5.07476e6	+	5.07476e6i	−0.223901	+	0.223901i	0.586238	+	0.810139i	$0.300608\pi$
$284$		0			0
$285$	5.52225e6	−	5.52225e6i	0.238551	−	0.238551i
$286$		0			0
$287$			5.47630e7i			2.31655i
$288$		0			0
$289$	−2.09549e6			−0.0868145
$290$		0			0
$291$	8.28707e6	+	8.28707e6i	0.336296	+	0.336296i
$292$		0			0
$293$	−1.82645e7	−	1.82645e7i	−0.726114	−	0.726114i	0.243730	−	0.969843i	$-0.421629\pi$
$293$	−1.82645e7	−	1.82645e7i	−0.726114	−	0.726114i	−0.969843	+	0.243730i	$0.921629\pi$
$294$		0			0
$295$	−2.83962e7			−1.10610
$296$		0			0
$297$			6.99285e6i			0.266922i
$298$		0			0
$299$	−2.94531e7	+	2.94531e7i	−1.10184	+	1.10184i
$300$		0			0
$301$	−3.84432e7	+	3.84432e7i	−1.40968	+	1.40968i
$302$		0			0
$303$			9.40438e6i			0.338067i
$304$		0			0
$305$	−2.07706e6			−0.0732066
$306$		0			0
$307$	−6.22745e6	−	6.22745e6i	−0.215226	−	0.215226i	0.591257	−	0.806483i	$-0.298632\pi$
$307$	−6.22745e6	−	6.22745e6i	−0.215226	−	0.215226i	−0.806483	+	0.591257i	$0.798632\pi$
$308$		0			0
$309$	2.24722e7	+	2.24722e7i	0.761676	+	0.761676i
$310$		0			0
$311$	−7.02088e6			−0.233405			−0.116703	−	0.993167i	$-0.537232\pi$
$311$	−7.02088e6			−0.233405			−0.116703	+	0.993167i	$0.537232\pi$
$312$		0			0
$313$			3.29834e7i			1.07563i	0.843063	+	0.537815i	$0.180750\pi$
$313$			3.29834e7i			1.07563i	−0.843063	+	0.537815i	$0.819250\pi$
$314$		0			0
$315$	9.85627e6	−	9.85627e6i	0.315341	−	0.315341i
$316$		0			0
$317$	−2.71810e7	+	2.71810e7i	−0.853274	+	0.853274i	−0.990535	−	0.137261i	$-0.956170\pi$
$317$	−2.71810e7	+	2.71810e7i	−0.853274	+	0.853274i	0.137261	+	0.990535i	$0.456170\pi$
$318$		0			0
$319$			2.87539e7i			0.885778i
$320$		0			0
$321$	−1.46730e6			−0.0443614
$322$		0			0
$323$	−1.18277e7	−	1.18277e7i	−0.350987	−	0.350987i
$324$		0			0
$325$	5.57395e6	+	5.57395e6i	0.162373	+	0.162373i
$326$		0			0
$327$	3.15861e7			0.903344
$328$		0			0
$329$		−	9.03509e6i		−	0.253714i
$330$		0			0
$331$	2.20689e7	−	2.20689e7i	0.608551	−	0.608551i	−0.334017	−	0.942567i	$-0.608404\pi$
$331$	2.20689e7	−	2.20689e7i	0.608551	−	0.608551i	0.942567	+	0.334017i	$0.108404\pi$
$332$		0			0
$333$	−203194.	+	203194.i	−0.00550274	+	0.00550274i
$334$		0			0
$335$			6.46065e6i			0.171847i
$336$		0			0
$337$	−6.38849e7			−1.66920			−0.834600	−	0.550857i	$-0.814301\pi$
$337$	−6.38849e7			−1.66920			−0.834600	+	0.550857i	$0.814301\pi$
$338$		0			0
$339$	2.56978e7	+	2.56978e7i	0.659624	+	0.659624i
$340$		0			0
$341$	−3.83193e7	−	3.83193e7i	−0.966396	−	0.966396i
$342$		0			0
$343$	2.81039e7			0.696440
$344$		0			0
$345$		−	4.80492e7i		−	1.17012i
$346$		0			0
$347$	−4.81137e7	+	4.81137e7i	−1.15154	+	1.15154i	−0.165299	+	0.986244i	$0.552859\pi$
$347$	−4.81137e7	+	4.81137e7i	−1.15154	+	1.15154i	−0.986244	+	0.165299i	$0.947141\pi$
$348$		0			0
$349$	−1.14069e7	+	1.14069e7i	−0.268344	+	0.268344i	−0.828433	−	0.560089i	$-0.810767\pi$
$349$	−1.14069e7	+	1.14069e7i	−0.268344	+	0.268344i	0.560089	+	0.828433i	$0.310767\pi$
$350$		0			0
$351$			7.19802e6i			0.166453i
$352$		0			0
$353$	1.97230e7			0.448382			0.224191	−	0.974545i	$-0.428026\pi$
$353$	1.97230e7			0.448382			0.224191	+	0.974545i	$0.428026\pi$
$354$		0			0
$355$	2.30487e7	+	2.30487e7i	0.515183	+	0.515183i
$356$		0			0
$357$	−2.11104e7	−	2.11104e7i	−0.463971	−	0.463971i
$358$		0			0
$359$	1.50385e7			0.325029			0.162514	−	0.986706i	$-0.448040\pi$
$359$	1.50385e7			0.325029			0.162514	+	0.986706i	$0.448040\pi$
$360$		0			0
$361$		−	3.43525e7i		−	0.730192i
$362$		0			0
$363$	1.80372e7	−	1.80372e7i	0.377093	−	0.377093i
$364$		0			0
$365$	−2.30456e6	+	2.30456e6i	−0.0473924	+	0.0473924i
$366$		0			0
$367$			4.43153e7i			0.896511i	0.893906	+	0.448255i	$0.147954\pi$
$367$			4.43153e7i			0.896511i	−0.893906	+	0.448255i	$0.852046\pi$
$368$		0			0
$369$	3.26221e7			0.649282
$370$		0			0
$371$	2.17691e7	+	2.17691e7i	0.426303	+	0.426303i
$372$		0			0
$373$	−6.45326e7	−	6.45326e7i	−1.24352	−	1.24352i	−0.958531	−	0.284989i	$-0.908010\pi$
$373$	−6.45326e7	−	6.45326e7i	−1.24352	−	1.24352i	−0.284989	−	0.958531i	$-0.591990\pi$
$374$		0			0
$375$	2.51570e7			0.477051
$376$		0			0
$377$			2.95975e7i			0.552372i
$378$		0			0
$379$	−7.13304e7	+	7.13304e7i	−1.31026	+	1.31026i	−0.389037	+	0.921222i	$0.627192\pi$
$379$	−7.13304e7	+	7.13304e7i	−1.31026	+	1.31026i	−0.921222	+	0.389037i	$0.872808\pi$
$380$		0			0
$381$	1.00693e7	−	1.00693e7i	0.182063	−	0.182063i
$382$		0			0
$383$		−	3.88466e7i		−	0.691444i	−0.938337	−	0.345722i	$-0.887634\pi$
$383$		−	3.88466e7i		−	0.691444i	0.938337	−	0.345722i	$-0.112366\pi$
$384$		0			0
$385$	−1.05893e8			−1.85560
$386$		0			0
$387$	2.29005e7	+	2.29005e7i	0.395104	+	0.395104i
$388$		0			0
$389$	3.00068e7	+	3.00068e7i	0.509766	+	0.509766i	0.914455	−	0.404688i	$-0.132620\pi$
$389$	3.00068e7	+	3.00068e7i	0.509766	+	0.509766i	−0.404688	+	0.914455i	$0.632620\pi$
$390$		0			0
$391$	−1.02913e8			−1.72163
$392$		0			0
$393$		−	2.01224e6i		−	0.0331514i
$394$		0			0
$395$	6.55958e7	−	6.55958e7i	1.06435	−	1.06435i
$396$		0			0
$397$	4.82007e7	−	4.82007e7i	0.770339	−	0.770339i	−0.207827	−	0.978166i	$-0.566639\pi$
$397$	4.82007e7	−	4.82007e7i	0.770339	−	0.770339i	0.978166	+	0.207827i	$0.0666391\pi$
$398$		0			0
$399$			2.26554e7i			0.356659i
$400$		0			0
$401$	−6.22689e7			−0.965691			−0.482845	−	0.875706i	$-0.660397\pi$
$401$	−6.22689e7			−0.965691			−0.482845	+	0.875706i	$0.660397\pi$
$402$		0			0
$403$	−3.94436e7	−	3.94436e7i	−0.602645	−	0.602645i
$404$		0			0
$405$	−5.87134e6	−	5.87134e6i	−0.0883838	−	0.0883838i
$406$		0			0
$407$	2.18306e6			0.0323804
$408$		0			0
$409$			2.73346e7i			0.399524i	0.979844	+	0.199762i	$0.0640168\pi$
$409$			2.73346e7i			0.399524i	−0.979844	+	0.199762i	$0.935983\pi$
$410$		0			0
$411$	−9.23375e6	+	9.23375e6i	−0.133000	+	0.133000i
$412$		0			0
$413$	5.82488e7	−	5.82488e7i	0.826869	−	0.826869i
$414$		0			0
$415$		−	1.14443e8i		−	1.60119i
$416$		0			0
$417$	2.86874e7			0.395625
$418$		0			0
$419$	7.07426e7	+	7.07426e7i	0.961698	+	0.961698i	0.999293	−	0.0375948i	$-0.0119696\pi$
$419$	7.07426e7	+	7.07426e7i	0.961698	+	0.961698i	−0.0375948	+	0.999293i	$0.511970\pi$
$420$		0			0
$421$	3.49174e7	+	3.49174e7i	0.467946	+	0.467946i	0.901249	−	0.433302i	$-0.142652\pi$
$421$	3.49174e7	+	3.49174e7i	0.467946	+	0.467946i	−0.433302	+	0.901249i	$0.642652\pi$
$422$		0			0
$423$	−5.38217e6			−0.0711109
$424$		0			0
$425$			1.94760e7i			0.253708i
$426$		0			0
$427$	4.26065e6	−	4.26065e6i	0.0547258	−	0.0547258i
$428$		0			0
$429$	3.86667e7	−	3.86667e7i	0.489739	−	0.489739i
$430$		0			0
$431$			1.08295e8i			1.35262i	0.736618	+	0.676310i	$0.236422\pi$
$431$			1.08295e8i			1.35262i	−0.736618	+	0.676310i	$0.763578\pi$
$432$		0			0
$433$	−1.27495e8			−1.57047			−0.785234	−	0.619199i	$-0.787457\pi$
$433$	−1.27495e8			−1.57047			−0.785234	+	0.619199i	$0.787457\pi$
$434$		0			0
$435$	−2.41424e7	−	2.41424e7i	−0.293300	−	0.293300i
$436$		0			0
$437$	5.52225e7	+	5.52225e7i	0.661716	+	0.661716i
$438$		0			0
$439$	4.08483e7			0.482815			0.241407	−	0.970424i	$-0.422391\pi$
$439$	4.08483e7			0.482815			0.241407	+	0.970424i	$0.422391\pi$
$440$		0			0
$441$			1.18473e7i			0.138135i
$442$		0			0
$443$	1.64430e7	−	1.64430e7i	0.189134	−	0.189134i	−0.606188	−	0.795322i	$-0.707302\pi$
$443$	1.64430e7	−	1.64430e7i	0.189134	−	0.189134i	0.795322	+	0.606188i	$0.207302\pi$
$444$		0			0
$445$	−1.11645e8	+	1.11645e8i	−1.26695	+	1.26695i
$446$		0			0
$447$			6.09271e6i			0.0682163i
$448$		0			0
$449$	−1.73176e7			−0.191315			−0.0956574	−	0.995414i	$-0.530495\pi$
$449$	−1.73176e7			−0.191315			−0.0956574	+	0.995414i	$0.530495\pi$
$450$		0			0
$451$	−1.75241e8	−	1.75241e8i	−1.91032	−	1.91032i
$452$		0			0
$453$	−6.32658e7	−	6.32658e7i	−0.680573	−	0.680573i
$454$		0			0
$455$	−1.09000e8			−1.15715
$456$		0			0
$457$			1.27366e8i			1.33445i	0.744854	+	0.667227i	$0.232519\pi$
$457$			1.27366e8i			1.33445i	−0.744854	+	0.667227i	$0.767481\pi$
$458$		0			0
$459$	−1.25754e7	+	1.25754e7i	−0.130042	+	0.130042i
$460$		0			0
$461$	−2.64080e7	+	2.64080e7i	−0.269546	+	0.269546i	−0.828917	−	0.559371i	$-0.811043\pi$
$461$	−2.64080e7	+	2.64080e7i	−0.269546	+	0.269546i	0.559371	+	0.828917i	$0.311043\pi$
$462$		0			0
$463$		−	1.72733e7i		−	0.174034i	−0.996207	−	0.0870169i	$-0.972267\pi$
$463$		−	1.72733e7i		−	0.174034i	0.996207	−	0.0870169i	$-0.0277334\pi$
$464$		0			0
$465$	6.43474e7			0.639989
$466$		0			0
$467$	6.75616e7	+	6.75616e7i	0.663360	+	0.663360i	0.956170	−	0.292811i	$-0.0945905\pi$
$467$	6.75616e7	+	6.75616e7i	0.663360	+	0.663360i	−0.292811	+	0.956170i	$0.594591\pi$
$468$		0			0
$469$	−1.32526e7	−	1.32526e7i	−0.128465	−	0.128465i
$470$		0			0
$471$	−3.04276e7			−0.291209
$472$		0			0
$473$		−	2.46036e8i		−	2.32496i
$474$		0			0
$475$	1.04507e7	−	1.04507e7i	0.0975139	−	0.0975139i
$476$		0			0
$477$	1.29678e7	−	1.29678e7i	0.119484	−	0.119484i
$478$		0			0
$479$			9.57983e7i			0.871669i	0.900027	+	0.435834i	$0.143547\pi$
$479$			9.57983e7i			0.871669i	−0.900027	+	0.435834i	$0.856453\pi$
$480$		0			0
$481$	2.24711e6			0.0201924
$482$		0			0
$483$	9.85627e7	+	9.85627e7i	0.874724	+	0.874724i
$484$		0			0
$485$	7.47546e7	+	7.47546e7i	0.655259	+	0.655259i
$486$		0			0
$487$	−2.47709e6			−0.0214464			−0.0107232	−	0.999943i	$-0.503413\pi$
$487$	−2.47709e6			−0.0214464			−0.0107232	+	0.999943i	$0.503413\pi$
$488$		0			0
$489$			3.59322e7i			0.307296i
$490$		0			0
$491$	8.25602e7	−	8.25602e7i	0.697472	−	0.697472i	−0.266393	−	0.963865i	$-0.585832\pi$
$491$	8.25602e7	−	8.25602e7i	0.697472	−	0.697472i	0.963865	+	0.266393i	$0.0858319\pi$
$492$		0			0
$493$	−5.17087e7	+	5.17087e7i	−0.431542	+	0.431542i
$494$		0			0
$495$			6.30800e7i			0.520087i
$496$		0			0
$497$	−9.45590e7			−0.770253
$498$		0			0
$499$	1.35012e7	+	1.35012e7i	0.108661	+	0.108661i	0.759347	−	0.650686i	$-0.225519\pi$
$499$	1.35012e7	+	1.35012e7i	0.108661	+	0.108661i	−0.650686	+	0.759347i	$0.725519\pi$
$500$		0			0
$501$	4.11266e7	+	4.11266e7i	0.327047	+	0.327047i
$502$		0			0
$503$	8.70792e6			0.0684243			0.0342122	−	0.999415i	$-0.489108\pi$
$503$	8.70792e6			0.0684243			0.0342122	+	0.999415i	$0.489108\pi$
$504$		0			0
$505$			8.48335e7i			0.658708i
$506$		0			0
$507$	−1.34034e7	+	1.34034e7i	−0.102847	+	0.102847i
$508$		0			0
$509$	1.73915e8	−	1.73915e8i	1.31882	−	1.31882i	0.404102	−	0.914714i	$-0.367584\pi$
$509$	1.73915e8	−	1.73915e8i	1.31882	−	1.31882i	0.914714	−	0.404102i	$-0.132416\pi$
$510$		0			0
$511$		−	9.45460e6i		−	0.0708566i
$512$		0			0
$513$	1.34958e7			0.0999644
$514$		0			0
$515$	2.02714e8	+	2.02714e8i	1.48409	+	1.48409i
$516$		0			0
$517$	2.89122e7	+	2.89122e7i	0.209223	+	0.209223i
$518$		0			0
$519$	4.54041e7			0.324783
$520$		0			0
$521$		−	2.29977e7i		−	0.162619i	−0.996689	−	0.0813093i	$-0.974090\pi$
$521$		−	2.29977e7i		−	0.162619i	0.996689	−	0.0813093i	$-0.0259102\pi$
$522$		0			0
$523$	1.12981e8	−	1.12981e8i	0.789768	−	0.789768i	−0.191688	−	0.981456i	$-0.561396\pi$
$523$	1.12981e8	−	1.12981e8i	0.789768	−	0.789768i	0.981456	+	0.191688i	$0.0613962\pi$
$524$		0			0
$525$	1.86528e7	−	1.86528e7i	0.128904	−	0.128904i
$526$		0			0
$527$		−	1.37821e8i		−	0.941635i
$528$		0			0
$529$	3.32456e8			2.24578
$530$		0			0
$531$	−3.46986e7	−	3.46986e7i	−0.231755	−	0.231755i
$532$		0			0
$533$	−1.80383e8	−	1.80383e8i	−1.19128	−	1.19128i
$534$		0			0
$535$	−1.32360e7			−0.0864362
$536$		0			0
$537$		−	9.86031e7i		−	0.636748i
$538$		0			0
$539$	6.36421e7	−	6.36421e7i	0.406423	−	0.406423i
$540$		0			0
$541$	−7.13958e7	+	7.13958e7i	−0.450900	+	0.450900i	−0.895653	−	0.444753i	$-0.853291\pi$
$541$	−7.13958e7	+	7.13958e7i	−0.450900	+	0.450900i	0.444753	+	0.895653i	$0.353291\pi$
$542$		0			0
$543$			1.53085e8i			0.956167i
$544$		0			0
$545$	2.84927e8			1.76013
$546$		0			0
$547$	−1.27198e8	−	1.27198e8i	−0.777176	−	0.777176i	0.202174	−	0.979350i	$-0.435199\pi$
$547$	−1.27198e8	−	1.27198e8i	−0.777176	−	0.777176i	−0.979350	+	0.202174i	$0.935199\pi$
$548$		0			0
$549$	−2.53805e6	−	2.53805e6i	−0.0153385	−	0.0153385i
$550$		0			0
$551$	5.54932e7			0.331730
$552$		0			0
$553$			2.69111e8i			1.59132i
$554$		0			0
$555$	−1.83294e6	+	1.83294e6i	−0.0107218	+	0.0107218i
$556$		0			0
$557$	1.50060e7	−	1.50060e7i	0.0868360	−	0.0868360i	−0.662355	−	0.749191i	$-0.730443\pi$
$557$	1.50060e7	−	1.50060e7i	0.0868360	−	0.0868360i	0.749191	+	0.662355i	$0.230443\pi$
$558$		0			0
$559$		−	2.53254e8i		−	1.44984i
$560$		0			0
$561$	1.35106e8			0.765219
$562$		0			0
$563$	−2.42642e8	−	2.42642e8i	−1.35969	−	1.35969i	−0.874293	−	0.485398i	$-0.838675\pi$
$563$	−2.42642e8	−	2.42642e8i	−1.35969	−	1.35969i	−0.485398	−	0.874293i	$-0.661325\pi$
$564$		0			0
$565$	2.31810e8	+	2.31810e8i	1.28525	+	1.28525i
$566$		0			0
$567$	2.40876e7			0.132143
$568$		0			0
$569$			3.09405e7i			0.167954i	0.996468	+	0.0839771i	$0.0267623\pi$
$569$			3.09405e7i			0.167954i	−0.996468	+	0.0839771i	$0.973238\pi$
$570$		0			0
$571$	−7.48080e7	+	7.48080e7i	−0.401827	+	0.401827i	−0.878877	−	0.477049i	$-0.841706\pi$
$571$	−7.48080e7	+	7.48080e7i	−0.401827	+	0.401827i	0.477049	+	0.878877i	$0.341706\pi$
$572$		0			0
$573$	−7.47644e7	+	7.47644e7i	−0.397403	+	0.397403i
$574$		0			0
$575$		−	9.09322e7i		−	0.478315i
$576$		0			0
$577$	−2.47348e8			−1.28760			−0.643800	−	0.765194i	$-0.722643\pi$
$577$	−2.47348e8			−1.28760			−0.643800	+	0.765194i	$0.722643\pi$
$578$		0			0
$579$	−9.45143e7	−	9.45143e7i	−0.486925	−	0.486925i
$580$		0			0
$581$	2.34755e8	+	2.34755e8i	1.19698	+	1.19698i
$582$		0			0
$583$	−1.39322e8			−0.703094
$584$		0			0
$585$			6.49307e7i			0.324326i
$586$		0			0
$587$	−2.03302e8	+	2.03302e8i	−1.00514	+	1.00514i	−0.00515608	+	0.999987i	$0.501641\pi$
$587$	−2.03302e8	+	2.03302e8i	−1.00514	+	1.00514i	−0.999987	+	0.00515608i	$0.998359\pi$
$588$		0			0
$589$	−7.39539e7	+	7.39539e7i	−0.361922	+	0.361922i
$590$		0			0
$591$		−	1.55339e8i		−	0.752521i
$592$		0			0
$593$	1.11781e8			0.536050			0.268025	−	0.963412i	$-0.413629\pi$
$593$	1.11781e8			0.536050			0.268025	+	0.963412i	$0.413629\pi$
$594$		0			0
$595$	−1.90429e8	−	1.90429e8i	−0.904027	−	0.904027i
$596$		0			0
$597$	−7.78457e7	−	7.78457e7i	−0.365857	−	0.365857i
$598$		0			0
$599$	−2.83959e7			−0.132122			−0.0660611	−	0.997816i	$-0.521043\pi$
$599$	−2.83959e7			−0.132122			−0.0660611	+	0.997816i	$0.521043\pi$
$600$		0			0
$601$		−	2.58943e8i		−	1.19284i	−0.802674	−	0.596419i	$-0.796590\pi$
$601$		−	2.58943e8i		−	1.19284i	0.802674	−	0.596419i	$-0.203410\pi$
$602$		0			0
$603$	−7.89455e6	+	7.89455e6i	−0.0360061	+	0.0360061i
$604$		0			0
$605$	1.62707e8	−	1.62707e8i	0.734749	−	0.734749i
$606$		0			0
$607$		−	1.96421e8i		−	0.878257i	−0.898424	−	0.439128i	$-0.855287\pi$
$607$		−	1.96421e8i		−	0.878257i	0.898424	−	0.439128i	$-0.144713\pi$
$608$		0			0
$609$	9.90459e7			0.438515
$610$		0			0
$611$	2.97605e7	+	2.97605e7i	0.130472	+	0.130472i
$612$		0			0
$613$	−1.23504e8	−	1.23504e8i	−0.536166	−	0.536166i	0.386234	−	0.922401i	$-0.373776\pi$
$613$	−1.23504e8	−	1.23504e8i	−0.536166	−	0.536166i	−0.922401	+	0.386234i	$0.873776\pi$
$614$		0			0
$615$	2.94272e8			1.26510
$616$		0			0
$617$		−	3.88338e8i		−	1.65331i	−0.562708	−	0.826656i	$-0.690240\pi$
$617$		−	3.88338e8i		−	1.65331i	0.562708	−	0.826656i	$-0.309760\pi$
$618$		0			0
$619$	−1.12499e8	+	1.12499e8i	−0.474327	+	0.474327i	−0.903312	−	0.428985i	$-0.858871\pi$
$619$	−1.12499e8	+	1.12499e8i	−0.474327	+	0.474327i	0.428985	+	0.903312i	$0.358871\pi$
$620$		0			0
$621$	5.87134e7	−	5.87134e7i	0.245167	−	0.245167i
$622$		0			0
$623$		−	4.58032e8i		−	1.89423i
$624$		0			0
$625$	2.91750e8			1.19501
$626$		0			0
$627$	−7.24972e7	−	7.24972e7i	−0.294116	−	0.294116i
$628$		0			0
$629$	3.92583e6	+	3.92583e6i	0.0157754	+	0.0157754i
$630$		0			0
$631$	1.38596e8			0.551648			0.275824	−	0.961208i	$-0.411049\pi$
$631$	1.38596e8			0.551648			0.275824	+	0.961208i	$0.411049\pi$
$632$		0			0
$633$		−	5.86617e7i		−	0.231283i
$634$		0			0
$635$	9.08310e7	−	9.08310e7i	0.354742	−	0.354742i
$636$		0			0
$637$	6.55093e7	−	6.55093e7i	0.253445	−	0.253445i
$638$		0			0
$639$			5.63285e7i			0.215886i
$640$		0			0
$641$	−3.56878e7			−0.135502			−0.0677510	−	0.997702i	$-0.521582\pi$
$641$	−3.56878e7			−0.135502			−0.0677510	+	0.997702i	$0.521582\pi$
$642$		0			0
$643$	−2.52804e8	−	2.52804e8i	−0.950935	−	0.950935i	0.0479167	−	0.998851i	$-0.484742\pi$
$643$	−2.52804e8	−	2.52804e8i	−0.950935	−	0.950935i	−0.998851	+	0.0479167i	$0.984742\pi$
$644$		0			0
$645$	2.06577e8	+	2.06577e8i	0.769843	+	0.769843i
$646$		0			0
$647$	2.04039e8			0.753358			0.376679	−	0.926344i	$-0.377066\pi$
$647$	2.04039e8			0.753358			0.376679	+	0.926344i	$0.377066\pi$
$648$		0			0
$649$			3.72791e8i			1.36374i
$650$		0			0
$651$	−1.31995e8	+	1.31995e8i	−0.478426	+	0.478426i
$652$		0			0
$653$	1.26644e8	−	1.26644e8i	0.454826	−	0.454826i	−0.442127	−	0.896953i	$-0.645776\pi$
$653$	1.26644e8	−	1.26644e8i	0.454826	−	0.454826i	0.896953	+	0.442127i	$0.145776\pi$
$654$		0			0
$655$		−	1.81517e7i		−	0.0645941i
$656$		0			0
$657$	−5.63208e6			−0.0198597
$658$		0			0
$659$	3.22381e8	+	3.22381e8i	1.12645	+	1.12645i	0.990750	+	0.135702i	$0.0433291\pi$
$659$	3.22381e8	+	3.22381e8i	1.12645	+	1.12645i	0.135702	+	0.990750i	$0.456671\pi$
$660$		0			0
$661$	−3.01517e8	−	3.01517e8i	−1.04402	−	1.04402i	−0.998986	−	0.0450302i	$-0.985662\pi$
$661$	−3.01517e8	−	3.01517e8i	−1.04402	−	1.04402i	−0.0450302	−	0.998986i	$-0.514338\pi$
$662$		0			0
$663$	1.39070e8			0.477191
$664$		0			0
$665$			2.04366e8i			0.694935i
$666$		0			0
$667$	2.41424e8	−	2.41424e8i	0.813585	−	0.813585i
$668$		0			0
$669$	1.88180e8	−	1.88180e8i	0.628485	−	0.628485i
$670$		0			0
$671$			2.72681e7i			0.0902583i
$672$		0			0
$673$	4.20736e8			1.38027			0.690135	−	0.723680i	$-0.257551\pi$
$673$	4.20736e8			1.38027			0.690135	+	0.723680i	$0.257551\pi$
$674$		0			0
$675$	−1.11114e7	−	1.11114e7i	−0.0361291	−	0.0361291i
$676$		0			0
$677$	2.79557e8	+	2.79557e8i	0.900957	+	0.900957i	0.995519	−	0.0945619i	$-0.0301450\pi$
$677$	2.79557e8	+	2.79557e8i	0.900957	+	0.900957i	−0.0945619	+	0.995519i	$0.530145\pi$
$678$		0			0
$679$	−3.06686e8			−0.979682
$680$		0			0
$681$		−	1.08024e8i		−	0.342041i
$682$		0			0
$683$	−1.74053e7	+	1.74053e7i	−0.0546286	+	0.0546286i	−0.733893	−	0.679265i	$-0.762299\pi$
$683$	−1.74053e7	+	1.74053e7i	−0.0546286	+	0.0546286i	0.679265	+	0.733893i	$0.262299\pi$
$684$		0			0
$685$	−8.32943e7	+	8.32943e7i	−0.259145	+	0.259145i
$686$		0			0
$687$		−	5.48395e7i		−	0.169131i
$688$		0			0
$689$	−1.43409e8			−0.438450
$690$		0			0
$691$	2.86023e8	+	2.86023e8i	0.866895	+	0.866895i	0.992127	−	0.125233i	$-0.0399678\pi$
$691$	2.86023e8	+	2.86023e8i	0.866895	+	0.866895i	−0.125233	+	0.992127i	$0.539968\pi$
$692$		0			0
$693$	−1.29395e8	−	1.29395e8i	−0.388792	−	0.388792i
$694$		0			0
$695$	2.58779e8			0.770858
$696$		0			0
$697$		−	6.30278e8i		−	1.86138i
$698$		0			0
$699$	1.44025e8	−	1.44025e8i	0.421701	−	0.421701i
$700$		0			0
$701$	−3.30099e8	+	3.30099e8i	−0.958275	+	0.958275i	−0.999164	−	0.0408890i	$-0.986981\pi$
$701$	−3.30099e8	+	3.30099e8i	−0.958275	+	0.958275i	0.0408890	+	0.999164i	$0.486981\pi$
$702$		0			0
$703$		−	4.21316e6i		−	0.0121267i
$704$		0			0
$705$	−4.85506e7			−0.138557
$706$		0			0
$707$	−1.74018e8	−	1.74018e8i	−0.492419	−	0.492419i
$708$		0			0
$709$	−2.96521e8	−	2.96521e8i	−0.831988	−	0.831988i	0.155800	−	0.987789i	$-0.450204\pi$
$709$	−2.96521e8	−	2.96521e8i	−0.831988	−	0.831988i	−0.987789	+	0.155800i	$0.950204\pi$
$710$		0			0
$711$	1.60309e8			0.446014
$712$		0			0
$713$			6.43474e8i			1.77526i
$714$		0			0
$715$	3.48798e8	−	3.48798e8i	0.954235	−	0.954235i
$716$		0			0
$717$	1.05741e8	−	1.05741e8i	0.286869	−	0.286869i
$718$		0			0
$719$			3.98405e8i			1.07186i	0.844263	+	0.535929i	$0.180039\pi$
$719$			3.98405e8i			1.07186i	−0.844263	+	0.535929i	$0.819961\pi$
$720$		0			0
$721$	−8.31647e8			−2.21888
$722$		0			0
$723$	2.06454e8	+	2.06454e8i	0.546271	+	0.546271i
$724$		0			0
$725$	−4.56890e7	−	4.56890e7i	−0.119894	−	0.119894i
$726$		0			0
$727$	−2.05758e8			−0.535492			−0.267746	−	0.963490i	$-0.586279\pi$
$727$	−2.05758e8			−0.535492			−0.267746	+	0.963490i	$0.586279\pi$
$728$		0			0
$729$		−	1.43489e7i		−	0.0370370i
$730$		0			0
$731$	4.42450e8	−	4.42450e8i	1.13269	−	1.13269i
$732$		0			0
$733$	−2.65126e8	+	2.65126e8i	−0.673194	+	0.673194i	−0.958451	−	0.285257i	$-0.907921\pi$
$733$	−2.65126e8	+	2.65126e8i	−0.673194	+	0.673194i	0.285257	+	0.958451i	$0.407921\pi$
$734$		0			0
$735$			1.06870e8i			0.269151i
$736$		0			0
$737$	8.48167e7			0.211875
$738$		0			0
$739$	2.74561e8	+	2.74561e8i	0.680307	+	0.680307i	0.960069	−	0.279762i	$-0.0902556\pi$
$739$	2.74561e8	+	2.74561e8i	0.680307	+	0.680307i	−0.279762	+	0.960069i	$0.590256\pi$
$740$		0			0
$741$	−7.46242e7	−	7.46242e7i	−0.183411	−	0.183411i
$742$		0			0
$743$	−1.16840e8			−0.284856			−0.142428	−	0.989805i	$-0.545491\pi$
$743$	−1.16840e8			−0.284856			−0.142428	+	0.989805i	$0.545491\pi$
$744$		0			0
$745$			5.49601e7i			0.132916i
$746$		0			0
$747$	1.39842e8	−	1.39842e8i	0.335488	−	0.335488i
$748$		0			0
$749$	2.71508e7	−	2.71508e7i	0.0646157	−	0.0646157i
$750$		0			0
$751$			1.91673e8i			0.452524i	0.974066	+	0.226262i	$0.0726506\pi$
$751$			1.91673e8i			0.452524i	−0.974066	+	0.226262i	$0.927349\pi$
$752$		0			0
$753$	−1.02853e8			−0.240898
$754$		0			0
$755$	−5.70698e8	−	5.70698e8i	−1.32607	−	1.32607i
$756$		0			0
$757$	−4.62970e7	−	4.62970e7i	−0.106725	−	0.106725i	0.651728	−	0.758453i	$-0.274044\pi$
$757$	−4.62970e7	−	4.62970e7i	−0.106725	−	0.106725i	−0.758453	+	0.651728i	$0.774044\pi$
$758$		0			0
$759$	−6.30800e8			−1.44267
$760$		0			0
$761$			2.39507e8i			0.543456i	0.962374	+	0.271728i	$0.0875951\pi$
$761$			2.39507e8i			0.543456i	−0.962374	+	0.271728i	$0.912405\pi$
$762$		0			0
$763$	−5.84466e8	+	5.84466e8i	−1.31579	+	1.31579i
$764$		0			0
$765$	−1.13438e8	+	1.13438e8i	−0.253381	+	0.253381i
$766$		0			0
$767$			3.83729e8i			0.850429i
$768$		0			0
$769$	2.57776e8			0.566844			0.283422	−	0.958995i	$-0.408530\pi$
$769$	2.57776e8			0.566844			0.283422	+	0.958995i	$0.408530\pi$
$770$		0			0
$771$	2.81059e8	+	2.81059e8i	0.613245	+	0.613245i
$772$		0			0
$773$	2.50765e8	+	2.50765e8i	0.542911	+	0.542911i	0.924381	−	0.381470i	$-0.124582\pi$
$773$	2.50765e8	+	2.50765e8i	0.542911	+	0.542911i	−0.381470	+	0.924381i	$0.624582\pi$
$774$		0			0
$775$	1.21776e8			0.261612
$776$		0			0
$777$		−	7.51977e6i		−	0.0160303i
$778$		0			0
$779$	−3.38204e8	+	3.38204e8i	−0.715429	+	0.715429i
$780$		0			0
$781$	3.02588e8	−	3.02588e8i	0.635183	−	0.635183i
$782$		0			0
$783$		−	5.90013e7i		−	0.122907i
$784$		0			0
$785$	−2.74476e8			−0.567409
$786$		0			0
$787$	1.66806e8	+	1.66806e8i	0.342205	+	0.342205i	0.857196	−	0.514991i	$-0.172205\pi$
$787$	1.66806e8	+	1.66806e8i	0.342205	+	0.342205i	−0.514991	+	0.857196i	$0.672205\pi$
$788$		0			0
$789$	2.15318e8	+	2.15318e8i	0.438378	+	0.438378i
$790$		0			0
$791$	−9.51017e8			−1.92158
$792$		0			0
$793$			2.80681e7i			0.0562851i
$794$		0			0
$795$	1.16977e8	−	1.16977e8i	0.232810	−	0.232810i
$796$		0			0
$797$	−2.34716e8	+	2.34716e8i	−0.463625	+	0.463625i	−0.899842	−	0.436216i	$-0.856318\pi$
$797$	−2.34716e8	+	2.34716e8i	−0.463625	+	0.463625i	0.436216	+	0.899842i	$0.356318\pi$
$798$		0			0
$799$			1.03987e8i			0.203862i
$800$		0			0
$801$	−2.72848e8			−0.530913
$802$		0			0
$803$	3.02547e7	+	3.02547e7i	0.0584313	+	0.0584313i
$804$		0			0
$805$	8.89097e8	+	8.89097e8i	1.70436	+	1.70436i
$806$		0			0
$807$	−3.24643e7			−0.0617711
$808$		0			0
$809$		−	9.79685e8i		−	1.85030i	−0.379607	−	0.925148i	$-0.623941\pi$
$809$		−	9.79685e8i		−	1.85030i	0.379607	−	0.925148i	$-0.376059\pi$
$810$		0			0
$811$	7.93471e7	−	7.93471e7i	0.148754	−	0.148754i	−0.628807	−	0.777561i	$-0.716457\pi$
$811$	7.93471e7	−	7.93471e7i	0.148754	−	0.148754i	0.777561	+	0.628807i	$0.216457\pi$
$812$		0			0
$813$	1.89268e8	−	1.89268e8i	0.352213	−	0.352213i
$814$		0			0
$815$			3.24131e8i			0.598753i
$816$		0			0
$817$	−4.74833e8			−0.870713
$818$		0			0
$819$	−1.33191e8	−	1.33191e8i	−0.242451	−	0.242451i
$820$		0			0
$821$	−6.94135e8	−	6.94135e8i	−1.25434	−	1.25434i	−0.953756	−	0.300581i	$-0.902819\pi$
$821$	−6.94135e8	−	6.94135e8i	−1.25434	−	1.25434i	−0.300581	−	0.953756i	$-0.597181\pi$
$822$		0			0
$823$	2.35319e8			0.422141			0.211070	−	0.977471i	$-0.432305\pi$
$823$	2.35319e8			0.422141			0.211070	+	0.977471i	$0.432305\pi$
$824$		0			0
$825$			1.19378e8i			0.212599i
$826$		0			0
$827$	−4.16675e8	+	4.16675e8i	−0.736683	+	0.736683i	−0.971934	−	0.235252i	$-0.924409\pi$
$827$	−4.16675e8	+	4.16675e8i	−0.736683	+	0.736683i	0.235252	+	0.971934i	$0.424409\pi$
$828$		0			0
$829$	2.08455e8	−	2.08455e8i	0.365889	−	0.365889i	−0.500087	−	0.865975i	$-0.666699\pi$
$829$	2.08455e8	−	2.08455e8i	0.365889	−	0.365889i	0.865975	+	0.500087i	$0.166699\pi$
$830$		0			0
$831$		−	9.00396e7i		−	0.156903i
$832$		0			0
$833$	2.28897e8			0.396009
$834$		0			0
$835$	3.70988e8	+	3.70988e8i	0.637236	+	0.637236i
$836$		0			0
$837$	7.86289e7	+	7.86289e7i	0.134093	+	0.134093i
$838$		0			0
$839$	−5.73096e7			−0.0970379			−0.0485189	−	0.998822i	$-0.515450\pi$
$839$	−5.73096e7			−0.0970379			−0.0485189	+	0.998822i	$0.515450\pi$
$840$		0			0
$841$			3.52216e8i			0.592135i
$842$		0			0
$843$	−1.80257e8	+	1.80257e8i	−0.300891	+	0.300891i
$844$		0			0
$845$	−1.20907e8	+	1.20907e8i	−0.200392	+	0.200392i
$846$		0			0
$847$			6.67515e8i			1.09853i
$848$		0			0
$849$	−1.11875e8			−0.182814
$850$		0			0
$851$	−1.83294e7	−	1.83294e7i	−0.0297413	−	0.0297413i
$852$		0			0
$853$	2.08222e8	+	2.08222e8i	0.335490	+	0.335490i	0.854667	−	0.519177i	$-0.173761\pi$
$853$	2.08222e8	+	2.08222e8i	0.335490	+	0.335490i	−0.519177	+	0.854667i	$0.673761\pi$
$854$		0			0
$855$	1.21740e8			0.194776
$856$		0			0
$857$		−	3.23257e7i		−	0.0513577i	−0.999670	−	0.0256788i	$-0.991825\pi$
$857$		−	3.23257e7i		−	0.0513577i	0.999670	−	0.0256788i	$-0.00817472\pi$
$858$		0			0
$859$	1.26896e8	−	1.26896e8i	0.200202	−	0.200202i	−0.599884	−	0.800087i	$-0.704787\pi$
$859$	1.26896e8	−	1.26896e8i	0.200202	−	0.200202i	0.800087	+	0.599884i	$0.204787\pi$
$860$		0			0
$861$	−6.03636e8	+	6.03636e8i	−0.945727	+	0.945727i
$862$		0			0
$863$			2.95082e8i			0.459103i	0.973296	+	0.229552i	$0.0737260\pi$
$863$			2.95082e8i			0.459103i	−0.973296	+	0.229552i	$0.926274\pi$
$864$		0			0
$865$	4.09574e8			0.632825
$866$		0			0
$867$	−2.30980e7	−	2.30980e7i	−0.0354419	−	0.0354419i
$868$		0			0
$869$	−8.61154e8	−	8.61154e8i	−1.31227	−	1.31227i
$870$		0			0
$871$	8.73051e7			0.132125
$872$		0			0
$873$			1.82692e8i			0.274585i
$874$		0			0
$875$	−4.65502e8	+	4.65502e8i	−0.694860	+	0.694860i
$876$		0			0
$877$	7.00284e8	−	7.00284e8i	1.03819	−	1.03819i	0.0389459	−	0.999241i	$-0.487600\pi$
$877$	7.00284e8	−	7.00284e8i	1.03819	−	1.03819i	0.999241	−	0.0389459i	$-0.0124000\pi$
$878$		0			0
$879$		−	4.02648e8i		−	0.592869i
$880$		0			0
$881$	−4.48321e8			−0.655635			−0.327817	−	0.944741i	$-0.606313\pi$
$881$	−4.48321e8			−0.655635			−0.327817	+	0.944741i	$0.606313\pi$
$882$		0			0
$883$	1.06421e7	+	1.06421e7i	0.0154577	+	0.0154577i	0.714793	−	0.699336i	$-0.246521\pi$
$883$	1.06421e7	+	1.06421e7i	0.0154577	+	0.0154577i	−0.699336	+	0.714793i	$0.746521\pi$
$884$		0			0
$885$	−3.13003e8	−	3.13003e8i	−0.451564	−	0.451564i
$886$		0			0
$887$	2.84309e8			0.407399			0.203700	−	0.979033i	$-0.434703\pi$
$887$	2.84309e8			0.407399			0.203700	+	0.979033i	$0.434703\pi$
$888$		0			0
$889$			3.72641e8i			0.530377i
$890$		0			0
$891$	−7.70802e7	+	7.70802e7i	−0.108971	+	0.108971i
$892$		0			0
$893$	5.57987e7	−	5.57987e7i	0.0783555	−	0.0783555i
$894$		0			0
$895$		−	8.89462e8i		−	1.24068i
$896$		0			0
$897$	−6.49307e8			−0.899648
$898$		0			0
$899$	3.23314e8	+	3.23314e8i	0.444986	+	0.444986i
$900$		0			0
$901$	−2.50545e8	−	2.50545e8i	−0.342540	−	0.342540i
$902$		0			0
$903$	−8.47496e8			−1.15100
$904$		0			0
$905$			1.38093e9i			1.86305i
$906$		0			0
$907$	1.92149e8	−	1.92149e8i	0.257523	−	0.257523i	−0.566523	−	0.824046i	$-0.691712\pi$
$907$	1.92149e8	−	1.92149e8i	0.257523	−	0.257523i	0.824046	+	0.566523i	$0.191712\pi$
$908$		0			0
$909$	−1.03662e8	+	1.03662e8i	−0.138015	+	0.138015i
$910$		0			0
$911$		−	2.51367e8i		−	0.332470i	−0.986086	−	0.166235i	$-0.946839\pi$
$911$		−	2.51367e8i		−	0.332470i	0.986086	−	0.166235i	$-0.0531611\pi$
$912$		0			0
$913$	−1.50243e9			−1.97415
$914$		0			0
$915$	−2.28949e7	−	2.28949e7i	−0.0298865	−	0.0298865i
$916$		0			0
$917$	3.72343e7	+	3.72343e7i	0.0482875	+	0.0482875i
$918$		0			0
$919$	−1.72821e8			−0.222664			−0.111332	−	0.993783i	$-0.535512\pi$
$919$	−1.72821e8			−0.222664			−0.111332	+	0.993783i	$0.535512\pi$
$920$		0			0
$921$		−	1.37287e8i		−	0.175731i
$922$		0			0
$923$	3.11466e8	−	3.11466e8i	0.396100	−	0.396100i
$924$		0			0
$925$	−3.46880e6	+	3.46880e6i	−0.00438283	+	0.00438283i
$926$		0			0
$927$			4.95409e8i			0.621906i
$928$		0			0
$929$	9.34033e6			0.0116497			0.00582486	−	0.999983i	$-0.498146\pi$
$929$	9.34033e6			0.0116497			0.00582486	+	0.999983i	$0.498146\pi$
$930$		0			0
$931$	−1.22825e8	−	1.22825e8i	−0.152208	−	0.152208i
$932$		0			0
$933$	−7.73891e7	−	7.73891e7i	−0.0952873	−	0.0952873i
$934$		0			0
$935$	1.21874e9			1.49100
$936$		0			0
$937$		−	9.90524e8i		−	1.20406i	−0.798475	−	0.602028i	$-0.794360\pi$
$937$		−	9.90524e8i		−	1.20406i	0.798475	−	0.602028i	$-0.205640\pi$
$938$		0			0
$939$	−3.63567e8	+	3.63567e8i	−0.439124	+	0.439124i
$940$		0			0
$941$	4.16273e8	−	4.16273e8i	0.499585	−	0.499585i	−0.411723	−	0.911309i	$-0.635073\pi$
$941$	4.16273e8	−	4.16273e8i	0.499585	−	0.499585i	0.911309	+	0.411723i	$0.135073\pi$
$942$		0			0
$943$			2.94272e9i			3.50925i
$944$		0			0
$945$	2.17285e8			0.257475
$946$		0			0
$947$	4.75744e8	+	4.75744e8i	0.560174	+	0.560174i	0.929357	−	0.369183i	$-0.120362\pi$
$947$	4.75744e8	+	4.75744e8i	0.560174	+	0.560174i	−0.369183	+	0.929357i	$0.620362\pi$
$948$		0			0
$949$	3.11423e7	+	3.11423e7i	0.0364378	+	0.0364378i
$950$		0			0
$951$	−5.99217e8			−0.696695
$952$		0			0
$953$		−	5.32360e8i		−	0.615073i	−0.951536	−	0.307537i	$-0.900495\pi$
$953$		−	5.32360e8i		−	0.615073i	0.951536	−	0.307537i	$-0.0995046\pi$
$954$		0			0
$955$	−6.74422e8	+	6.74422e8i	−0.774322	+	0.774322i
$956$		0			0
$957$	−3.16946e8	+	3.16946e8i	−0.361618	+	0.361618i
$958$		0			0
$959$		−	3.41721e8i		−	0.387450i
$960$		0			0
$961$	2.57641e7			0.0290299
$962$		0			0
$963$	−1.61737e7	−	1.61737e7i	−0.0181105	−	0.0181105i
$964$		0			0
$965$	−8.52579e8	−	8.52579e8i	−0.948752	−	0.948752i
$966$		0			0
$967$	1.34706e9			1.48973			0.744864	−	0.667216i	$-0.232514\pi$
$967$	1.34706e9			1.48973			0.744864	+	0.667216i	$0.232514\pi$
$968$		0			0
$969$		−	2.60746e8i		−	0.286580i
$970$		0			0
$971$	2.98809e8	−	2.98809e8i	0.326390	−	0.326390i	−0.524822	−	0.851212i	$-0.675868\pi$
$971$	2.98809e8	−	2.98809e8i	0.326390	−	0.326390i	0.851212	+	0.524822i	$0.175868\pi$
$972$		0			0
$973$	−5.30829e8	+	5.30829e8i	−0.576257	+	0.576257i
$974$		0			0
$975$			1.22880e8i			0.132577i
$976$		0			0
$977$	4.33270e8			0.464595			0.232298	−	0.972645i	$-0.425376\pi$
$977$	4.33270e8			0.464595			0.232298	+	0.972645i	$0.425376\pi$
$978$		0			0
$979$	1.46570e9	+	1.46570e9i	1.56206	+	1.56206i
$980$		0			0
$981$	3.48165e8	+	3.48165e8i	0.368789	+	0.368789i
$982$		0			0
$983$	1.37975e9			1.45258			0.726288	−	0.687391i	$-0.241244\pi$
$983$	1.37975e9			1.45258			0.726288	+	0.687391i	$0.241244\pi$
$984$		0			0
$985$		−	1.40126e9i		−	1.46625i
$986$		0			0
$987$	9.95911e7	−	9.95911e7i	0.103578	−	0.103578i
$988$		0			0
$989$	−2.06577e9	+	2.06577e9i	−2.13547	+	2.13547i
$990$		0			0
$991$		−	1.16289e9i		−	1.19486i	−0.801922	−	0.597428i	$-0.796189\pi$
$991$		−	1.16289e9i		−	1.19486i	0.801922	−	0.597428i	$-0.203811\pi$
$992$		0			0
$993$	4.86518e8			0.496879
$994$		0			0
$995$	−7.02218e8	−	7.02218e8i	−0.712857	−	0.712857i
$996$		0			0
$997$	3.50811e8	+	3.50811e8i	0.353987	+	0.353987i	0.861591	−	0.507604i	$-0.169469\pi$
$997$	3.50811e8	+	3.50811e8i	0.353987	+	0.353987i	−0.507604	+	0.861591i	$0.669469\pi$
$998$		0			0
$999$	−4.47950e6			−0.00449297

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.7.l.a.31.16		48
4.3	odd	2		384.7.l.b.31.9		48
8.3	odd	2		48.7.l.a.43.10	yes	48
8.5	even	2		192.7.l.a.79.9		48
16.3	odd	4	inner	384.7.l.a.223.16		48
16.5	even	4		48.7.l.a.19.10	✓	48
16.11	odd	4		192.7.l.a.175.9		48
16.13	even	4		384.7.l.b.223.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.l.a.19.10	✓	48	16.5	even	4
48.7.l.a.43.10	yes	48	8.3	odd	2
192.7.l.a.79.9		48	8.5	even	2
192.7.l.a.175.9		48	16.11	odd	4
384.7.l.a.31.16		48	1.1	even	1	trivial
384.7.l.a.223.16		48	16.3	odd	4	inner
384.7.l.b.31.9		48	4.3	odd	2
384.7.l.b.223.9		48	16.13	even	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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	384.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(11.0227 + 11.0227i) q^{3} +(99.4317 + 99.4317i) q^{5} -407.926 q^{7} +243.000i q^{9} +O(q^{10})\)	\(q+(11.0227 + 11.0227i) q^{3} +(99.4317 + 99.4317i) q^{5} -407.926 q^{7} +243.000i q^{9} +(1305.36 - 1305.36i) q^{11} +(1343.66 - 1343.66i) q^{13} +2192.01i q^{15} +4694.90 q^{17} +(-2519.26 - 2519.26i) q^{19} +(-4496.45 - 4496.45i) q^{21} -21920.1 q^{23} +4148.34i q^{25} +(-2678.52 + 2678.52i) q^{27} +(-11013.8 + 11013.8i) q^{29} -29355.4i q^{31} +28777.2 q^{33} +(-40560.8 - 40560.8i) q^{35} +(836.191 + 836.191i) q^{37} +29621.5 q^{39} -134247. i q^{41} +(94240.7 - 94240.7i) q^{43} +(-24161.9 + 24161.9i) q^{45} +22148.9i q^{47} +48754.4 q^{49} +(51750.5 + 51750.5i) q^{51} +(-53365.3 - 53365.3i) q^{53} +259588. q^{55} -55538.1i q^{57} +(-142793. + 142793. i) q^{59} +(-10444.7 + 10444.7i) q^{61} -99126.0i q^{63} +267204. q^{65} +(32487.9 + 32487.9i) q^{67} +(-241619. - 241619. i) q^{69} +231804. q^{71} +23177.3i q^{73} +(-45725.9 + 45725.9i) q^{75} +(-532490. + 532490. i) q^{77} -659707. i q^{79} -59049.0 q^{81} +(-575483. - 575483. i) q^{83} +(466822. + 466822. i) q^{85} -242804. q^{87} +1.12283e6i q^{89} +(-548113. + 548113. i) q^{91} +(323576. - 323576. i) q^{93} -500989. i q^{95} +751819. q^{97} +(317202. + 317202. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 2720 q^{11} - 3936 q^{19} - 26240 q^{23} - 66400 q^{29} + 162336 q^{35} + 7200 q^{37} + 340704 q^{43} + 806736 q^{49} + 80352 q^{51} - 443680 q^{53} - 232704 q^{55} - 886144 q^{59} + 326496 q^{61} - 372832 q^{65} - 962112 q^{67} - 541728 q^{69} - 534016 q^{71} - 1073088 q^{75} + 932960 q^{77} - 2834352 q^{81} - 2497760 q^{83} + 372000 q^{85} + 775008 q^{91} - 660960 q^{99}+O(q^{100}) \) 48 * q - 2720 * q^11 - 3936 * q^19 - 26240 * q^23 - 66400 * q^29 + 162336 * q^35 + 7200 * q^37 + 340704 * q^43 + 806736 * q^49 + 80352 * q^51 - 443680 * q^53 - 232704 * q^55 - 886144 * q^59 + 326496 * q^61 - 372832 * q^65 - 962112 * q^67 - 541728 * q^69 - 534016 * q^71 - 1073088 * q^75 + 932960 * q^77 - 2834352 * q^81 - 2497760 * q^83 + 372000 * q^85 + 775008 * q^91 - 660960 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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