LMFDB - Embedded newform 384.7.l.a.31.2

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			31.2
Character	$\chi$	$=$	384.31
Dual form			384.7.l.a.223.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.0227 - 11.0227i) q^{3} +(-107.837 - 107.837i) q^{5} -5.36994 q^{7} +243.000i q^{9} +O(q^{10})$	\(q+(-11.0227 - 11.0227i) q^{3} +(-107.837 - 107.837i) q^{5} -5.36994 q^{7} +243.000i q^{9} +(-48.9517 + 48.9517i) q^{11} +(2118.46 - 2118.46i) q^{13} +2377.30i q^{15} -3884.97 q^{17} +(-5877.62 - 5877.62i) q^{19} +(59.1913 + 59.1913i) q^{21} +3237.03 q^{23} +7632.48i q^{25} +(2678.52 - 2678.52i) q^{27} +(30583.8 - 30583.8i) q^{29} -54018.7i q^{31} +1079.16 q^{33} +(579.076 + 579.076i) q^{35} +(-33650.8 - 33650.8i) q^{37} -46702.3 q^{39} -29052.0i q^{41} +(-24548.9 + 24548.9i) q^{43} +(26204.3 - 26204.3i) q^{45} +58193.1i q^{47} -117620. q^{49} +(42822.9 + 42822.9i) q^{51} +(-27071.8 - 27071.8i) q^{53} +10557.6 q^{55} +129575. i q^{57} +(225328. - 225328. i) q^{59} +(1789.71 - 1789.71i) q^{61} -1304.90i q^{63} -456895. q^{65} +(122582. + 122582. i) q^{67} +(-35680.9 - 35680.9i) q^{69} +213921. q^{71} +337380. i q^{73} +(84130.6 - 84130.6i) q^{75} +(262.868 - 262.868i) q^{77} +715537. i q^{79} -59049.0 q^{81} +(338143. + 338143. i) q^{83} +(418942. + 418942. i) q^{85} -674232. q^{87} -527375. i q^{89} +(-11376.0 + 11376.0i) q^{91} +(-595432. + 595432. i) q^{93} +1.26765e6i q^{95} -1.55143e6 q^{97} +(-11895.3 - 11895.3i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−107.837	−	107.837i	−0.862693	−	0.862693i	0.128957	−	0.991650i	$-0.458837\pi$
$5$	−107.837	−	107.837i	−0.862693	−	0.862693i	−0.991650	+	0.128957i	$0.958837\pi$
$6$		0			0
$7$	−5.36994			−0.0156558			−0.00782790	−	0.999969i	$-0.502492\pi$
$7$	−5.36994			−0.0156558			−0.00782790	+	0.999969i	$0.502492\pi$
$8$		0			0
$9$			243.000i			0.333333i
$10$		0			0
$11$	−48.9517	+	48.9517i	−0.0367781	+	0.0367781i	−0.725257	−	0.688479i	$-0.758279\pi$
$11$	−48.9517	+	48.9517i	−0.0367781	+	0.0367781i	0.688479	+	0.725257i	$0.258279\pi$
$12$		0			0
$13$	2118.46	−	2118.46i	0.964252	−	0.964252i	−0.0351311	−	0.999383i	$-0.511185\pi$
$13$	2118.46	−	2118.46i	0.964252	−	0.964252i	0.999383	+	0.0351311i	$0.0111849\pi$
$14$		0			0
$15$			2377.30i			0.704386i
$16$		0			0
$17$	−3884.97			−0.790753			−0.395377	−	0.918519i	$-0.629386\pi$
$17$	−3884.97			−0.790753			−0.395377	+	0.918519i	$0.629386\pi$
$18$		0			0
$19$	−5877.62	−	5877.62i	−0.856921	−	0.856921i	0.134053	−	0.990974i	$-0.457201\pi$
$19$	−5877.62	−	5877.62i	−0.856921	−	0.856921i	−0.990974	+	0.134053i	$0.957201\pi$
$20$		0			0
$21$	59.1913	+	59.1913i	0.00639146	+	0.00639146i
$22$		0			0
$23$	3237.03			0.266050			0.133025	−	0.991113i	$-0.457531\pi$
$23$	3237.03			0.266050			0.133025	+	0.991113i	$0.457531\pi$
$24$		0			0
$25$			7632.48i			0.488479i
$26$		0			0
$27$	2678.52	−	2678.52i	0.136083	−	0.136083i
$28$		0			0
$29$	30583.8	−	30583.8i	1.25400	−	1.25400i	0.300087	−	0.953912i	$-0.402984\pi$
$29$	30583.8	−	30583.8i	1.25400	−	1.25400i	0.953912	−	0.300087i	$-0.0970157\pi$
$30$		0			0
$31$		−	54018.7i		−	1.81326i	−0.421932	−	0.906628i	$-0.638648\pi$
$31$		−	54018.7i		−	1.81326i	0.421932	−	0.906628i	$-0.361352\pi$
$32$		0			0
$33$	1079.16			0.0300292
$34$		0			0
$35$	579.076	+	579.076i	0.0135062	+	0.0135062i
$36$		0			0
$37$	−33650.8	−	33650.8i	−0.664339	−	0.664339i	0.292060	−	0.956400i	$-0.405659\pi$
$37$	−33650.8	−	33650.8i	−0.664339	−	0.664339i	−0.956400	+	0.292060i	$0.905659\pi$
$38$		0			0
$39$	−46702.3			−0.787308
$40$		0			0
$41$		−	29052.0i		−	0.421526i	−0.977537	−	0.210763i	$-0.932405\pi$
$41$		−	29052.0i		−	0.421526i	0.977537	−	0.210763i	$-0.0675949\pi$
$42$		0			0
$43$	−24548.9	+	24548.9i	−0.308764	+	0.308764i	−0.844430	−	0.535666i	$-0.820061\pi$
$43$	−24548.9	+	24548.9i	−0.308764	+	0.308764i	0.535666	+	0.844430i	$0.320061\pi$
$44$		0			0
$45$	26204.3	−	26204.3i	0.287564	−	0.287564i
$46$		0			0
$47$			58193.1i			0.560503i	0.959927	+	0.280251i	$0.0904178\pi$
$47$			58193.1i			0.560503i	−0.959927	+	0.280251i	$0.909582\pi$
$48$		0			0
$49$	−117620.			−0.999755
$50$		0			0
$51$	42822.9	+	42822.9i	0.322824	+	0.322824i
$52$		0			0
$53$	−27071.8	−	27071.8i	−0.181840	−	0.181840i	0.610317	−	0.792157i	$-0.291042\pi$
$53$	−27071.8	−	27071.8i	−0.181840	−	0.181840i	−0.792157	+	0.610317i	$0.791042\pi$
$54$		0			0
$55$	10557.6			0.0634565
$56$		0			0
$57$			129575.i			0.699673i
$58$		0			0
$59$	225328.	−	225328.i	1.09713	−	1.09713i	0.102387	−	0.994745i	$-0.467352\pi$
$59$	225328.	−	225328.i	1.09713	−	1.09713i	0.994745	−	0.102387i	$-0.0326481\pi$
$60$		0			0
$61$	1789.71	−	1789.71i	0.00788485	−	0.00788485i	−0.703153	−	0.711038i	$-0.748225\pi$
$61$	1789.71	−	1789.71i	0.00788485	−	0.00788485i	0.711038	+	0.703153i	$0.248225\pi$
$62$		0			0
$63$		−	1304.90i		−	0.00521860i
$64$		0			0
$65$	−456895.			−1.66371
$66$		0			0
$67$	122582.	+	122582.i	0.407571	+	0.407571i	0.880891	−	0.473320i	$-0.156944\pi$
$67$	122582.	+	122582.i	0.407571	+	0.407571i	−0.473320	+	0.880891i	$0.656944\pi$
$68$		0			0
$69$	−35680.9	−	35680.9i	−0.108615	−	0.108615i
$70$		0			0
$71$	213921.			0.597692			0.298846	−	0.954301i	$-0.403398\pi$
$71$	213921.			0.597692			0.298846	+	0.954301i	$0.403398\pi$
$72$		0			0
$73$			337380.i			0.867263i	0.901090	+	0.433631i	$0.142768\pi$
$73$			337380.i			0.867263i	−0.901090	+	0.433631i	$0.857232\pi$
$74$		0			0
$75$	84130.6	−	84130.6i	0.199421	−	0.199421i
$76$		0			0
$77$	262.868	−	262.868i	0.000575791	−	0.000575791i
$78$		0			0
$79$			715537.i			1.45128i	0.688075	+	0.725639i	$0.258456\pi$
$79$			715537.i			1.45128i	−0.688075	+	0.725639i	$0.741544\pi$
$80$		0			0
$81$	−59049.0			−0.111111
$82$		0			0
$83$	338143.	+	338143.i	0.591380	+	0.591380i	0.938004	−	0.346624i	$-0.112672\pi$
$83$	338143.	+	338143.i	0.591380	+	0.591380i	−0.346624	+	0.938004i	$0.612672\pi$
$84$		0			0
$85$	418942.	+	418942.i	0.682177	+	0.682177i
$86$		0			0
$87$	−674232.			−1.02389
$88$		0			0
$89$		−	527375.i		−	0.748083i	−0.927412	−	0.374041i	$-0.877972\pi$
$89$		−	527375.i		−	0.748083i	0.927412	−	0.374041i	$-0.122028\pi$
$90$		0			0
$91$	−11376.0	+	11376.0i	−0.0150961	+	0.0150961i
$92$		0			0
$93$	−595432.	+	595432.i	−0.740258	+	0.740258i
$94$		0			0
$95$			1.26765e6i			1.47852i
$96$		0			0
$97$	−1.55143e6			−1.69987			−0.849937	−	0.526884i	$-0.823360\pi$
$97$	−1.55143e6			−1.69987			−0.849937	+	0.526884i	$0.823360\pi$
$98$		0			0
$99$	−11895.3	−	11895.3i	−0.0122594	−	0.0122594i
$100$		0			0
$101$	−1.16299e6	−	1.16299e6i	−1.12879	−	1.12879i	−0.990375	−	0.138413i	$-0.955800\pi$
$101$	−1.16299e6	−	1.16299e6i	−1.12879	−	1.12879i	−0.138413	−	0.990375i	$-0.544200\pi$
$102$		0			0
$103$	−1.22358e6			−1.11975			−0.559873	−	0.828578i	$-0.689150\pi$
$103$	−1.22358e6			−1.11975			−0.559873	+	0.828578i	$0.689150\pi$
$104$		0			0
$105$		−	12766.0i		−	0.0110277i
$106$		0			0
$107$	421967.	−	421967.i	0.344450	−	0.344450i	−0.513587	−	0.858038i	$-0.671684\pi$
$107$	421967.	−	421967.i	0.344450	−	0.344450i	0.858038	+	0.513587i	$0.171684\pi$
$108$		0			0
$109$	966244.	−	966244.i	0.746118	−	0.746118i	−0.227630	−	0.973748i	$-0.573098\pi$
$109$	966244.	−	966244.i	0.746118	−	0.746118i	0.973748	+	0.227630i	$0.0730976\pi$
$110$		0			0
$111$			741845.i			0.542431i
$112$		0			0
$113$	1.34165e6			0.929833			0.464916	−	0.885355i	$-0.346084\pi$
$113$	1.34165e6			0.929833			0.464916	+	0.885355i	$0.346084\pi$
$114$		0			0
$115$	−349071.	−	349071.i	−0.229520	−	0.229520i
$116$		0			0
$117$	514786.	+	514786.i	0.321417	+	0.321417i
$118$		0			0
$119$	20862.1			0.0123799
$120$		0			0
$121$			1.76677e6i			0.997295i
$122$		0			0
$123$	−320232.	+	320232.i	−0.172087	+	0.172087i
$124$		0			0
$125$	−861886.	+	861886.i	−0.441286	+	0.441286i
$126$		0			0
$127$			512988.i			0.250435i	0.992129	+	0.125218i	$0.0399629\pi$
$127$			512988.i			0.250435i	−0.992129	+	0.125218i	$0.960037\pi$
$128$		0			0
$129$	541191.			0.252105
$130$		0			0
$131$	1.55668e6	+	1.55668e6i	0.692444	+	0.692444i	0.962769	−	0.270325i	$-0.0871312\pi$
$131$	1.55668e6	+	1.55668e6i	0.692444	+	0.692444i	−0.270325	+	0.962769i	$0.587131\pi$
$132$		0			0
$133$	31562.5	+	31562.5i	0.0134158	+	0.0134158i
$134$		0			0
$135$	−577685.			−0.234795
$136$		0			0
$137$		−	24036.2i		−	0.00934768i	−0.999989	−	0.00467384i	$-0.998512\pi$
$137$		−	24036.2i		−	0.00934768i	0.999989	−	0.00467384i	$-0.00148773\pi$
$138$		0			0
$139$	−3.76939e6	+	3.76939e6i	−1.40355	+	1.40355i	−0.615086	+	0.788460i	$0.710879\pi$
$139$	−3.76939e6	+	3.76939e6i	−1.40355	+	1.40355i	−0.788460	+	0.615086i	$0.789121\pi$
$140$		0			0
$141$	641445.	−	641445.i	0.228824	−	0.228824i
$142$		0			0
$143$			207404.i			0.0709267i
$144$		0			0
$145$	−6.59610e6			−2.16363
$146$		0			0
$147$	1.29649e6	+	1.29649e6i	0.408148	+	0.408148i
$148$		0			0
$149$	−2.54711e6	−	2.54711e6i	−0.769998	−	0.769998i	0.208108	−	0.978106i	$-0.433269\pi$
$149$	−2.54711e6	−	2.54711e6i	−0.769998	−	0.769998i	−0.978106	+	0.208108i	$0.933269\pi$
$150$		0			0
$151$	4.85437e6			1.40995			0.704973	−	0.709235i	$-0.250959\pi$
$151$	4.85437e6			1.40995			0.704973	+	0.709235i	$0.250959\pi$
$152$		0			0
$153$		−	944048.i		−	0.263584i
$154$		0			0
$155$	−5.82519e6	+	5.82519e6i	−1.56428	+	1.56428i
$156$		0			0
$157$	−4.73206e6	+	4.73206e6i	−1.22279	+	1.22279i	−0.256151	+	0.966637i	$0.582454\pi$
$157$	−4.73206e6	+	4.73206e6i	−1.22279	+	1.22279i	−0.966637	+	0.256151i	$0.917546\pi$
$158$		0			0
$159$			596809.i			0.148472i
$160$		0			0
$161$	−17382.7			−0.00416523
$162$		0			0
$163$	2.25527e6	+	2.25527e6i	0.520758	+	0.520758i	0.917800	−	0.397042i	$-0.129963\pi$
$163$	2.25527e6	+	2.25527e6i	0.520758	+	0.520758i	−0.397042	+	0.917800i	$0.629963\pi$
$164$		0			0
$165$	−116373.	−	116373.i	−0.0259060	−	0.0259060i
$166$		0			0
$167$	5.96746e6			1.28127			0.640634	−	0.767846i	$-0.278671\pi$
$167$	5.96746e6			1.28127			0.640634	+	0.767846i	$0.278671\pi$
$168$		0			0
$169$		−	4.14894e6i		−	0.859562i
$170$		0			0
$171$	1.42826e6	−	1.42826e6i	0.285640	−	0.285640i
$172$		0			0
$173$	−6.11242e6	+	6.11242e6i	−1.18052	+	1.18052i	−0.200916	+	0.979609i	$0.564392\pi$
$173$	−6.11242e6	+	6.11242e6i	−1.18052	+	1.18052i	−0.979609	+	0.200916i	$0.935608\pi$
$174$		0			0
$175$		−	40986.0i		−	0.00764753i
$176$		0			0
$177$	−4.96744e6			−0.895804
$178$		0			0
$179$	−328581.	−	328581.i	−0.0572906	−	0.0572906i	0.677881	−	0.735172i	$-0.262898\pi$
$179$	−328581.	−	328581.i	−0.0572906	−	0.0572906i	−0.735172	+	0.677881i	$0.762898\pi$
$180$		0			0
$181$	−1.85271e6	−	1.85271e6i	−0.312444	−	0.312444i	0.533412	−	0.845856i	$-0.320910\pi$
$181$	−1.85271e6	−	1.85271e6i	−0.312444	−	0.312444i	−0.845856	+	0.533412i	$0.820910\pi$
$182$		0			0
$183$	−39454.9			−0.00643795
$184$		0			0
$185$			7.25758e6i			1.14624i
$186$		0			0
$187$	190176.	−	190176.i	0.0290824	−	0.0290824i
$188$		0			0
$189$	−14383.5	+	14383.5i	−0.00213049	+	0.00213049i
$190$		0			0
$191$			8.50584e6i			1.22072i	0.792123	+	0.610361i	$0.208976\pi$
$191$			8.50584e6i			1.22072i	−0.792123	+	0.610361i	$0.791024\pi$
$192$		0			0
$193$	4.58702e6			0.638056			0.319028	−	0.947745i	$-0.396644\pi$
$193$	4.58702e6			0.638056			0.319028	+	0.947745i	$0.396644\pi$
$194$		0			0
$195$	5.03622e6	+	5.03622e6i	0.679205	+	0.679205i
$196$		0			0
$197$	−5.84236e6	−	5.84236e6i	−0.764169	−	0.764169i	0.212904	−	0.977073i	$-0.431708\pi$
$197$	−5.84236e6	−	5.84236e6i	−0.764169	−	0.764169i	−0.977073	+	0.212904i	$0.931708\pi$
$198$		0			0
$199$	−2.72449e6			−0.345721			−0.172861	−	0.984946i	$-0.555301\pi$
$199$	−2.72449e6			−0.345721			−0.172861	+	0.984946i	$0.555301\pi$
$200$		0			0
$201$		−	2.70238e6i		−	0.332780i
$202$		0			0
$203$	−164233.	+	164233.i	−0.0196324	+	0.0196324i
$204$		0			0
$205$	−3.13287e6	+	3.13287e6i	−0.363648	+	0.363648i
$206$		0			0
$207$			786599.i			0.0886834i
$208$		0			0
$209$	575439.			0.0630319
$210$		0			0
$211$	4.15605e6	+	4.15605e6i	0.442419	+	0.442419i	0.892824	−	0.450405i	$-0.148720\pi$
$211$	4.15605e6	+	4.15605e6i	0.442419	+	0.442419i	−0.450405	+	0.892824i	$0.648720\pi$
$212$		0			0
$213$	−2.35798e6	−	2.35798e6i	−0.244007	−	0.244007i
$214$		0			0
$215$	5.29454e6			0.532737
$216$		0			0
$217$			290077.i			0.0283880i
$218$		0			0
$219$	3.71884e6	−	3.71884e6i	0.354059	−	0.354059i
$220$		0			0
$221$	−8.23016e6	+	8.23016e6i	−0.762485	+	0.762485i
$222$		0			0
$223$			2.24265e6i			0.202230i	0.994875	+	0.101115i	$0.0322411\pi$
$223$			2.24265e6i			0.202230i	−0.994875	+	0.101115i	$0.967759\pi$
$224$		0			0
$225$	−1.85469e6			−0.162826
$226$		0			0
$227$	−1.51072e7	−	1.51072e7i	−1.29154	−	1.29154i	−0.933837	−	0.357700i	$-0.883561\pi$
$227$	−1.51072e7	−	1.51072e7i	−1.29154	−	1.29154i	−0.357700	−	0.933837i	$-0.616439\pi$
$228$		0			0
$229$	−4.67653e6	−	4.67653e6i	−0.389419	−	0.389419i	0.485061	−	0.874480i	$-0.338797\pi$
$229$	−4.67653e6	−	4.67653e6i	−0.389419	−	0.389419i	−0.874480	+	0.485061i	$0.838797\pi$
$230$		0			0
$231$	−5795.02			−0.000470131
$232$		0			0
$233$		−	1.98032e7i		−	1.56555i	−0.622304	−	0.782776i	$-0.713803\pi$
$233$		−	1.98032e7i		−	1.56555i	0.622304	−	0.782776i	$-0.286197\pi$
$234$		0			0
$235$	6.27535e6	−	6.27535e6i	0.483542	−	0.483542i
$236$		0			0
$237$	7.88715e6	−	7.88715e6i	0.592482	−	0.592482i
$238$		0			0
$239$			3.78826e6i			0.277489i	0.990328	+	0.138745i	$0.0443067\pi$
$239$			3.78826e6i			0.277489i	−0.990328	+	0.138745i	$0.955693\pi$
$240$		0			0
$241$	−1.52426e7			−1.08895			−0.544475	−	0.838777i	$-0.683271\pi$
$241$	−1.52426e7			−1.08895			−0.544475	+	0.838777i	$0.683271\pi$
$242$		0			0
$243$	650880.	+	650880.i	0.0453609	+	0.0453609i
$244$		0			0
$245$	1.26838e7	+	1.26838e7i	0.862482	+	0.862482i
$246$		0			0
$247$	−2.49030e7			−1.65257
$248$		0			0
$249$		−	7.45451e6i		−	0.482860i
$250$		0			0
$251$	−1.55084e7	+	1.55084e7i	−0.980720	+	0.980720i	−0.999818	−	0.0190975i	$-0.993921\pi$
$251$	−1.55084e7	+	1.55084e7i	−0.980720	+	0.980720i	0.0190975	+	0.999818i	$0.493921\pi$
$252$		0			0
$253$	−158458.	+	158458.i	−0.00978483	+	0.00978483i
$254$		0			0
$255$		−	9.23575e6i		−	0.556996i
$256$		0			0
$257$	2.30378e7			1.35720			0.678598	−	0.734510i	$-0.262588\pi$
$257$	2.30378e7			1.35720			0.678598	+	0.734510i	$0.262588\pi$
$258$		0			0
$259$	180703.	+	180703.i	0.0104008	+	0.0104008i
$260$		0			0
$261$	7.43186e6	+	7.43186e6i	0.418000	+	0.418000i
$262$		0			0
$263$	1.14678e7			0.630395			0.315198	−	0.949026i	$-0.397929\pi$
$263$	1.14678e7			0.630395			0.315198	+	0.949026i	$0.397929\pi$
$264$		0			0
$265$			5.83866e6i			0.313744i
$266$		0			0
$267$	−5.81310e6	+	5.81310e6i	−0.305403	+	0.305403i
$268$		0			0
$269$	1.81452e7	−	1.81452e7i	0.932191	−	0.932191i	−0.0656520	−	0.997843i	$-0.520913\pi$
$269$	1.81452e7	−	1.81452e7i	0.932191	−	0.932191i	0.997843	+	0.0656520i	$0.0209127\pi$
$270$		0			0
$271$		−	1.68065e7i		−	0.844441i	−0.906493	−	0.422221i	$-0.861251\pi$
$271$		−	1.68065e7i		−	0.844441i	0.906493	−	0.422221i	$-0.138749\pi$
$272$		0			0
$273$	250789.			0.0123259
$274$		0			0
$275$	−373623.	−	373623.i	−0.0179653	−	0.0179653i
$276$		0			0
$277$	1.32183e7	+	1.32183e7i	0.621922	+	0.621922i	0.946022	−	0.324101i	$-0.105062\pi$
$277$	1.32183e7	+	1.32183e7i	0.621922	+	0.621922i	−0.324101	+	0.946022i	$0.605062\pi$
$278$		0			0
$279$	1.31265e7			0.604418
$280$		0			0
$281$			3.78604e7i			1.70634i	0.521632	+	0.853170i	$0.325323\pi$
$281$			3.78604e7i			1.70634i	−0.521632	+	0.853170i	$0.674677\pi$
$282$		0			0
$283$	2.50461e7	−	2.50461e7i	1.10505	−	1.10505i	0.111254	−	0.993792i	$-0.464513\pi$
$283$	2.50461e7	−	2.50461e7i	1.10505	−	1.10505i	0.993792	−	0.111254i	$-0.0354866\pi$
$284$		0			0
$285$	1.39729e7	−	1.39729e7i	0.603603	−	0.603603i
$286$		0			0
$287$			156008.i			0.00659933i
$288$		0			0
$289$	−9.04457e6			−0.374709
$290$		0			0
$291$	1.71010e7	+	1.71010e7i	0.693971	+	0.693971i
$292$		0			0
$293$	−2.24773e7	−	2.24773e7i	−0.893596	−	0.893596i	0.101263	−	0.994860i	$-0.467711\pi$
$293$	−2.24773e7	−	2.24773e7i	−0.893596	−	0.893596i	−0.994860	+	0.101263i	$0.967711\pi$
$294$		0			0
$295$	−4.85972e7			−1.89298
$296$		0			0
$297$			262236.i			0.0100097i
$298$		0			0
$299$	6.85753e6	−	6.85753e6i	0.256539	−	0.256539i
$300$		0			0
$301$	131826.	−	131826.i	0.00483395	−	0.00483395i
$302$		0			0
$303$			2.56386e7i			0.921651i
$304$		0			0
$305$	−385993.			−0.0136044
$306$		0			0
$307$	−2.44973e7	−	2.44973e7i	−0.846650	−	0.846650i	0.143063	−	0.989714i	$-0.454305\pi$
$307$	−2.44973e7	−	2.44973e7i	−0.846650	−	0.846650i	−0.989714	+	0.143063i	$0.954305\pi$
$308$		0			0
$309$	1.34871e7	+	1.34871e7i	0.457134	+	0.457134i
$310$		0			0
$311$	2.12390e7			0.706078			0.353039	−	0.935609i	$-0.385148\pi$
$311$	2.12390e7			0.706078			0.353039	+	0.935609i	$0.385148\pi$
$312$		0			0
$313$			3.85664e7i			1.25770i	0.777527	+	0.628849i	$0.216474\pi$
$313$			3.85664e7i			1.25770i	−0.777527	+	0.628849i	$0.783526\pi$
$314$		0			0
$315$	−140716.	+	140716.i	−0.00450205	+	0.00450205i
$316$		0			0
$317$	2.55878e7	−	2.55878e7i	0.803257	−	0.803257i	−0.180346	−	0.983603i	$-0.557722\pi$
$317$	2.55878e7	−	2.55878e7i	0.803257	−	0.803257i	0.983603	+	0.180346i	$0.0577218\pi$
$318$		0			0
$319$			2.99425e6i			0.0922394i
$320$		0			0
$321$	−9.30243e6			−0.281243
$322$		0			0
$323$	2.28344e7	+	2.28344e7i	0.677613	+	0.677613i
$324$		0			0
$325$	1.61691e7	+	1.61691e7i	0.471017	+	0.471017i
$326$		0			0
$327$	−2.13012e7			−0.609203
$328$		0			0
$329$		−	312493.i		−	0.00877512i
$330$		0			0
$331$	4.02071e6	−	4.02071e6i	0.110871	−	0.110871i	−0.649495	−	0.760366i	$-0.725020\pi$
$331$	4.02071e6	−	4.02071e6i	0.110871	−	0.110871i	0.760366	+	0.649495i	$0.225020\pi$
$332$		0			0
$333$	8.17714e6	−	8.17714e6i	0.221446	−	0.221446i
$334$		0			0
$335$		−	2.64377e7i		−	0.703218i
$336$		0			0
$337$	1.58536e7			0.414226			0.207113	−	0.978317i	$-0.433593\pi$
$337$	1.58536e7			0.414226			0.207113	+	0.978317i	$0.433593\pi$
$338$		0			0
$339$	−1.47886e7	−	1.47886e7i	−0.379603	−	0.379603i
$340$		0			0
$341$	2.64431e6	+	2.64431e6i	0.0666881	+	0.0666881i
$342$		0			0
$343$	1.26338e6			0.0313078
$344$		0			0
$345$			7.69541e6i			0.187402i
$346$		0			0
$347$	3.19130e7	−	3.19130e7i	0.763798	−	0.763798i	−0.213208	−	0.977007i	$-0.568391\pi$
$347$	3.19130e7	−	3.19130e7i	0.763798	−	0.763798i	0.977007	+	0.213208i	$0.0683913\pi$
$348$		0			0
$349$	−2.14408e7	+	2.14408e7i	−0.504388	+	0.504388i	−0.912798	−	0.408411i	$-0.866083\pi$
$349$	−2.14408e7	+	2.14408e7i	−0.504388	+	0.504388i	0.408411	+	0.912798i	$0.366083\pi$
$350$		0			0
$351$		−	1.13487e7i		−	0.262436i
$352$		0			0
$353$	4.67083e7			1.06187			0.530933	−	0.847414i	$-0.321841\pi$
$353$	4.67083e7			1.06187			0.530933	+	0.847414i	$0.321841\pi$
$354$		0			0
$355$	−2.30685e7	−	2.30685e7i	−0.515625	−	0.515625i
$356$		0			0
$357$	−229956.	−	229956.i	−0.00505406	−	0.00505406i
$358$		0			0
$359$	2.17927e7			0.471006			0.235503	−	0.971874i	$-0.424326\pi$
$359$	2.17927e7			0.471006			0.235503	+	0.971874i	$0.424326\pi$
$360$		0			0
$361$			2.20470e7i			0.468627i
$362$		0			0
$363$	1.94746e7	−	1.94746e7i	0.407144	−	0.407144i
$364$		0			0
$365$	3.63819e7	−	3.63819e7i	0.748182	−	0.748182i
$366$		0			0
$367$		−	8.36110e7i		−	1.69147i	−0.533600	−	0.845737i	$-0.679161\pi$
$367$		−	8.36110e7i		−	1.69147i	0.533600	−	0.845737i	$-0.320839\pi$
$368$		0			0
$369$	7.05964e6			0.140509
$370$		0			0
$371$	145374.	+	145374.i	0.00284685	+	0.00284685i
$372$		0			0
$373$	3.88117e7	+	3.88117e7i	0.747887	+	0.747887i	0.974082	−	0.226195i	$-0.0726287\pi$
$373$	3.88117e7	+	3.88117e7i	0.747887	+	0.747887i	−0.226195	+	0.974082i	$0.572629\pi$
$374$		0			0
$375$	1.90006e7			0.360308
$376$		0			0
$377$		−	1.29581e8i		−	2.41834i
$378$		0			0
$379$	−5.20448e7	+	5.20448e7i	−0.956004	+	0.956004i	−0.999072	−	0.0430678i	$-0.986287\pi$
$379$	−5.20448e7	+	5.20448e7i	−0.956004	+	0.956004i	0.0430678	+	0.999072i	$0.486287\pi$
$380$		0			0
$381$	5.65451e6	−	5.65451e6i	0.102240	−	0.102240i
$382$		0			0
$383$			1.32415e7i			0.235691i	0.993032	+	0.117845i	$0.0375987\pi$
$383$			1.32415e7i			0.235691i	−0.993032	+	0.117845i	$0.962401\pi$
$384$		0			0
$385$	−56693.5			−0.000993462
$386$		0			0
$387$	−5.96538e6	−	5.96538e6i	−0.102921	−	0.102921i
$388$		0			0
$389$	2.91185e6	+	2.91185e6i	0.0494675	+	0.0494675i	0.731408	−	0.681940i	$-0.238864\pi$
$389$	2.91185e6	+	2.91185e6i	0.0494675	+	0.0494675i	−0.681940	+	0.731408i	$0.738864\pi$
$390$		0			0
$391$	−1.25758e7			−0.210380
$392$		0			0
$393$		−	3.43176e7i		−	0.565378i
$394$		0			0
$395$	7.71611e7	−	7.71611e7i	1.25201	−	1.25201i
$396$		0			0
$397$	−1.15219e7	+	1.15219e7i	−0.184142	+	0.184142i	−0.793158	−	0.609016i	$-0.791565\pi$
$397$	−1.15219e7	+	1.15219e7i	−0.184142	+	0.184142i	0.609016	+	0.793158i	$0.291565\pi$
$398$		0			0
$399$		−	695808.i		−	0.0109539i
$400$		0			0
$401$	7.10441e7			1.10178			0.550890	−	0.834578i	$-0.314288\pi$
$401$	7.10441e7			1.10178			0.550890	+	0.834578i	$0.314288\pi$
$402$		0			0
$403$	−1.14436e8	−	1.14436e8i	−1.74843	−	1.74843i
$404$		0			0
$405$	6.36765e6	+	6.36765e6i	0.0958548	+	0.0958548i
$406$		0			0
$407$	3.29452e6			0.0488663
$408$		0			0
$409$		−	1.89990e7i		−	0.277691i	−0.990314	−	0.138845i	$-0.955661\pi$
$409$		−	1.89990e7i		−	0.277691i	0.990314	−	0.138845i	$-0.0443391\pi$
$410$		0			0
$411$	−264944.	+	264944.i	−0.00381617	+	0.00381617i
$412$		0			0
$413$	−1.21000e6	+	1.21000e6i	−0.0171765	+	0.0171765i
$414$		0			0
$415$		−	7.29285e7i		−	1.02036i
$416$		0			0
$417$	8.30977e7			1.14599
$418$		0			0
$419$	−3.56420e7	−	3.56420e7i	−0.484529	−	0.484529i	0.422045	−	0.906575i	$-0.361312\pi$
$419$	−3.56420e7	−	3.56420e7i	−0.484529	−	0.484529i	−0.906575	+	0.422045i	$0.861312\pi$
$420$		0			0
$421$	−4.15849e7	−	4.15849e7i	−0.557301	−	0.557301i	0.371237	−	0.928538i	$-0.378934\pi$
$421$	−4.15849e7	−	4.15849e7i	−0.557301	−	0.557301i	−0.928538	+	0.371237i	$0.878934\pi$
$422$		0			0
$423$	−1.41409e7			−0.186834
$424$		0			0
$425$		−	2.96520e7i		−	0.386266i
$426$		0			0
$427$	−9610.64	+	9610.64i	−0.000123444	+	0.000123444i
$428$		0			0
$429$	2.28616e6	−	2.28616e6i	0.0289557	−	0.0289557i
$430$		0			0
$431$		−	6.32371e7i		−	0.789842i	−0.918715	−	0.394921i	$-0.870772\pi$
$431$		−	6.32371e7i		−	0.789842i	0.918715	−	0.394921i	$-0.129228\pi$
$432$		0			0
$433$	4.88658e6			0.0601924			0.0300962	−	0.999547i	$-0.490419\pi$
$433$	4.88658e6			0.0601924			0.0300962	+	0.999547i	$0.490419\pi$
$434$		0			0
$435$	7.27069e7	+	7.27069e7i	0.883299	+	0.883299i
$436$		0			0
$437$	−1.90261e7	−	1.90261e7i	−0.227984	−	0.227984i
$438$		0			0
$439$	−1.89631e7			−0.224138			−0.112069	−	0.993700i	$-0.535748\pi$
$439$	−1.89631e7			−0.224138			−0.112069	+	0.993700i	$0.535748\pi$
$440$		0			0
$441$		−	2.85817e7i		−	0.333252i
$442$		0			0
$443$	−7.56690e7	+	7.56690e7i	−0.870376	+	0.870376i	−0.992513	−	0.122137i	$-0.961025\pi$
$443$	−7.56690e7	+	7.56690e7i	−0.870376	+	0.870376i	0.122137	+	0.992513i	$0.461025\pi$
$444$		0			0
$445$	−5.68704e7	+	5.68704e7i	−0.645366	+	0.645366i
$446$		0			0
$447$			5.61522e7i			0.628701i
$448$		0			0
$449$	−3.34359e7			−0.369381			−0.184690	−	0.982797i	$-0.559128\pi$
$449$	−3.34359e7			−0.369381			−0.184690	+	0.982797i	$0.559128\pi$
$450$		0			0
$451$	1.42214e6	+	1.42214e6i	0.0155029	+	0.0155029i
$452$		0			0
$453$	−5.35083e7	−	5.35083e7i	−0.575608	−	0.575608i
$454$		0			0
$455$	2.45350e6			0.0260467
$456$		0			0
$457$			5.54209e7i			0.580664i	0.956926	+	0.290332i	$0.0937657\pi$
$457$			5.54209e7i			0.580664i	−0.956926	+	0.290332i	$0.906234\pi$
$458$		0			0
$459$	−1.04060e7	+	1.04060e7i	−0.107608	+	0.107608i
$460$		0			0
$461$	−2.76199e7	+	2.76199e7i	−0.281916	+	0.281916i	−0.833873	−	0.551957i	$-0.813881\pi$
$461$	−2.76199e7	+	2.76199e7i	−0.281916	+	0.281916i	0.551957	+	0.833873i	$0.313881\pi$
$462$		0			0
$463$		−	6.48037e7i		−	0.652915i	−0.945212	−	0.326457i	$-0.894145\pi$
$463$		−	6.48037e7i		−	0.652915i	0.945212	−	0.326457i	$-0.105855\pi$
$464$		0			0
$465$	1.28419e8			1.27723
$466$		0			0
$467$	1.01369e8	+	1.01369e8i	0.995297	+	0.995297i	0.999989	−	0.00469233i	$-0.00149362\pi$
$467$	1.01369e8	+	1.01369e8i	0.995297	+	0.995297i	−0.00469233	+	0.999989i	$0.501494\pi$
$468$		0			0
$469$	−658260.	−	658260.i	−0.00638085	−	0.00638085i
$470$		0			0
$471$	1.04320e8			0.998402
$472$		0			0
$473$		−	2.40342e6i		−	0.0227115i
$474$		0			0
$475$	4.48608e7	−	4.48608e7i	0.418588	−	0.418588i
$476$		0			0
$477$	6.57845e6	−	6.57845e6i	0.0606133	−	0.0606133i
$478$		0			0
$479$			5.97214e7i			0.543404i	0.962381	+	0.271702i	$0.0875866\pi$
$479$			5.97214e7i			0.543404i	−0.962381	+	0.271702i	$0.912413\pi$
$480$		0			0
$481$	−1.42576e8			−1.28118
$482$		0			0
$483$	191604.	+	191604.i	0.00170045	+	0.00170045i
$484$		0			0
$485$	1.67301e8	+	1.67301e8i	1.46647	+	1.46647i
$486$		0			0
$487$	8.93709e7			0.773765			0.386882	−	0.922129i	$-0.373552\pi$
$487$	8.93709e7			0.773765			0.386882	+	0.922129i	$0.373552\pi$
$488$		0			0
$489$		−	4.97184e7i		−	0.425197i
$490$		0			0
$491$	−5.33343e7	+	5.33343e7i	−0.450570	+	0.450570i	−0.895544	−	0.444974i	$-0.853213\pi$
$491$	−5.33343e7	+	5.33343e7i	−0.450570	+	0.450570i	0.444974	+	0.895544i	$0.353213\pi$
$492$		0			0
$493$	−1.18817e8	+	1.18817e8i	−0.991604	+	0.991604i
$494$		0			0
$495$			2.56549e6i			0.0211522i
$496$		0			0
$497$	−1.14874e6			−0.00935736
$498$		0			0
$499$	−1.13240e8	−	1.13240e8i	−0.911379	−	0.911379i	0.0850014	−	0.996381i	$-0.472911\pi$
$499$	−1.13240e8	−	1.13240e8i	−0.911379	−	0.911379i	−0.996381	+	0.0850014i	$0.972911\pi$
$500$		0			0
$501$	−6.57776e7	−	6.57776e7i	−0.523076	−	0.523076i
$502$		0			0
$503$	4.14356e7			0.325589			0.162794	−	0.986660i	$-0.447949\pi$
$503$	4.14356e7			0.325589			0.162794	+	0.986660i	$0.447949\pi$
$504$		0			0
$505$			2.50826e8i			1.94760i
$506$		0			0
$507$	−4.57326e7	+	4.57326e7i	−0.350915	+	0.350915i
$508$		0			0
$509$	7.15789e7	−	7.15789e7i	0.542790	−	0.542790i	−0.381556	−	0.924346i	$-0.624612\pi$
$509$	7.15789e7	−	7.15789e7i	0.542790	−	0.542790i	0.924346	+	0.381556i	$0.124612\pi$
$510$		0			0
$511$		−	1.81171e6i		−	0.0135777i
$512$		0			0
$513$	−3.14866e7			−0.233224
$514$		0			0
$515$	1.31946e8	+	1.31946e8i	0.965997	+	0.965997i
$516$		0			0
$517$	−2.84865e6	−	2.84865e6i	−0.0206142	−	0.0206142i
$518$		0			0
$519$	1.34751e8			0.963894
$520$		0			0
$521$			7.24342e7i			0.512189i	0.966652	+	0.256095i	$0.0824358\pi$
$521$			7.24342e7i			0.512189i	−0.966652	+	0.256095i	$0.917564\pi$
$522$		0			0
$523$	−1.89689e8	+	1.89689e8i	−1.32598	+	1.32598i	−0.417135	+	0.908845i	$0.636966\pi$
$523$	−1.89689e8	+	1.89689e8i	−1.32598	+	1.32598i	−0.908845	+	0.417135i	$0.863034\pi$
$524$		0			0
$525$	−451776.	+	451776.i	−0.00312209	+	0.00312209i
$526$		0			0
$527$			2.09861e8i			1.43384i
$528$		0			0
$529$	−1.37558e8			−0.929217
$530$		0			0
$531$	5.47547e7	+	5.47547e7i	0.365711	+	0.365711i
$532$		0			0
$533$	−6.15455e7	−	6.15455e7i	−0.406457	−	0.406457i
$534$		0			0
$535$	−9.10069e7			−0.594310
$536$		0			0
$537$			7.24370e6i			0.0467776i
$538$		0			0
$539$	5.75770e6	−	5.75770e6i	0.0367691	−	0.0367691i
$540$		0			0
$541$	1.36734e8	−	1.36734e8i	0.863545	−	0.863545i	−0.128203	−	0.991748i	$-0.540921\pi$
$541$	1.36734e8	−	1.36734e8i	0.863545	−	0.863545i	0.991748	+	0.128203i	$0.0409209\pi$
$542$		0			0
$543$			4.08438e7i			0.255110i
$544$		0			0
$545$	−2.08393e8			−1.28734
$546$		0			0
$547$	5.12718e7	+	5.12718e7i	0.313269	+	0.313269i	0.846175	−	0.532906i	$-0.178900\pi$
$547$	5.12718e7	+	5.12718e7i	0.313269	+	0.313269i	−0.532906	+	0.846175i	$0.678900\pi$
$548$		0			0
$549$	434900.	+	434900.i	0.00262828	+	0.00262828i
$550$		0			0
$551$	−3.59520e8			−2.14916
$552$		0			0
$553$		−	3.84239e6i		−	0.0227209i
$554$		0			0
$555$	7.99981e7	−	7.99981e7i	0.467951	−	0.467951i
$556$		0			0
$557$	−5.82264e7	+	5.82264e7i	−0.336941	+	0.336941i	−0.855215	−	0.518274i	$-0.826575\pi$
$557$	−5.82264e7	+	5.82264e7i	−0.336941	+	0.336941i	0.518274	+	0.855215i	$0.326575\pi$
$558$		0			0
$559$			1.04012e8i			0.595452i
$560$		0			0
$561$	−4.19250e6			−0.0237457
$562$		0			0
$563$	8.25505e6	+	8.25505e6i	0.0462588	+	0.0462588i	0.729858	−	0.683599i	$-0.239586\pi$
$563$	8.25505e6	+	8.25505e6i	0.0462588	+	0.0462588i	−0.683599	+	0.729858i	$0.739586\pi$
$564$		0			0
$565$	−1.44679e8	−	1.44679e8i	−0.802160	−	0.802160i
$566$		0			0
$567$	317090.			0.00173953
$568$		0			0
$569$			8.93722e7i			0.485138i	0.970134	+	0.242569i	$0.0779902\pi$
$569$			8.93722e7i			0.485138i	−0.970134	+	0.242569i	$0.922010\pi$
$570$		0			0
$571$	−3.04844e7	+	3.04844e7i	−0.163746	+	0.163746i	−0.784224	−	0.620478i	$-0.786939\pi$
$571$	−3.04844e7	+	3.04844e7i	−0.163746	+	0.163746i	0.620478	+	0.784224i	$0.286939\pi$
$572$		0			0
$573$	9.37573e7	−	9.37573e7i	0.498358	−	0.498358i
$574$		0			0
$575$			2.47066e7i			0.129960i
$576$		0			0
$577$	−5.99952e7			−0.312312			−0.156156	−	0.987732i	$-0.549910\pi$
$577$	−5.99952e7			−0.312312			−0.156156	+	0.987732i	$0.549910\pi$
$578$		0			0
$579$	−5.05613e7	−	5.05613e7i	−0.260485	−	0.260485i
$580$		0			0
$581$	−1.81581e6	−	1.81581e6i	−0.00925853	−	0.00925853i
$582$		0			0
$583$	2.65042e6			0.0133755
$584$		0			0
$585$		−	1.11026e8i		−	0.554569i
$586$		0			0
$587$	9.99854e7	−	9.99854e7i	0.494336	−	0.494336i	−0.415333	−	0.909669i	$-0.636335\pi$
$587$	9.99854e7	−	9.99854e7i	0.494336	−	0.494336i	0.909669	+	0.415333i	$0.136335\pi$
$588$		0			0
$589$	−3.17501e8	+	3.17501e8i	−1.55382	+	1.55382i
$590$		0			0
$591$			1.28797e8i			0.623941i
$592$		0			0
$593$	−1.00872e8			−0.483734			−0.241867	−	0.970309i	$-0.577760\pi$
$593$	−1.00872e8			−0.483734			−0.241867	+	0.970309i	$0.577760\pi$
$594$		0			0
$595$	−2.24970e6	−	2.24970e6i	−0.0106800	−	0.0106800i
$596$		0			0
$597$	3.00313e7	+	3.00313e7i	0.141140	+	0.141140i
$598$		0			0
$599$	−3.34581e7			−0.155676			−0.0778379	−	0.996966i	$-0.524802\pi$
$599$	−3.34581e7			−0.155676			−0.0778379	+	0.996966i	$0.524802\pi$
$600$		0			0
$601$		−	1.30304e8i		−	0.600251i	−0.953900	−	0.300126i	$-0.902971\pi$
$601$		−	1.30304e8i		−	0.600251i	0.953900	−	0.300126i	$-0.0970286\pi$
$602$		0			0
$603$	−2.97875e7	+	2.97875e7i	−0.135857	+	0.135857i
$604$		0			0
$605$	1.90522e8	−	1.90522e8i	0.860359	−	0.860359i
$606$		0			0
$607$			3.04854e8i			1.36309i	0.731775	+	0.681546i	$0.238692\pi$
$607$			3.04854e8i			1.36309i	−0.731775	+	0.681546i	$0.761308\pi$
$608$		0			0
$609$	3.62058e6			0.0160298
$610$		0			0
$611$	1.23280e8	+	1.23280e8i	0.540466	+	0.540466i
$612$		0			0
$613$	6.47373e7	+	6.47373e7i	0.281043	+	0.281043i	0.833525	−	0.552482i	$-0.186319\pi$
$613$	6.47373e7	+	6.47373e7i	0.281043	+	0.281043i	−0.552482	+	0.833525i	$0.686319\pi$
$614$		0			0
$615$	6.90654e7			0.296917
$616$		0			0
$617$		−	1.34382e8i		−	0.572117i	−0.958212	−	0.286059i	$-0.907655\pi$
$617$		−	1.34382e8i		−	0.572117i	0.958212	−	0.286059i	$-0.0923452\pi$
$618$		0			0
$619$	1.65022e8	−	1.65022e8i	0.695776	−	0.695776i	−0.267720	−	0.963497i	$-0.586270\pi$
$619$	1.65022e8	−	1.65022e8i	0.695776	−	0.695776i	0.963497	+	0.267720i	$0.0862703\pi$
$620$		0			0
$621$	8.67045e6	−	8.67045e6i	0.0362049	−	0.0362049i
$622$		0			0
$623$			2.83197e6i			0.0117118i
$624$		0			0
$625$	3.05143e8			1.24987
$626$		0			0
$627$	−6.34289e6	−	6.34289e6i	−0.0257327	−	0.0257327i
$628$		0			0
$629$	1.30732e8	+	1.30732e8i	0.525329	+	0.525329i
$630$		0			0
$631$	−3.33511e8			−1.32746			−0.663731	−	0.747971i	$-0.731028\pi$
$631$	−3.33511e8			−1.32746			−0.663731	+	0.747971i	$0.731028\pi$
$632$		0			0
$633$		−	9.16219e7i		−	0.361234i
$634$		0			0
$635$	5.53189e7	−	5.53189e7i	0.216049	−	0.216049i
$636$		0			0
$637$	−2.49174e8	+	2.49174e8i	−0.964015	+	0.964015i
$638$		0			0
$639$			5.19827e7i			0.199231i
$640$		0			0
$641$	−2.80056e8			−1.06334			−0.531669	−	0.846952i	$-0.678435\pi$
$641$	−2.80056e8			−1.06334			−0.531669	+	0.846952i	$0.678435\pi$
$642$		0			0
$643$	−3.76599e7	−	3.76599e7i	−0.141660	−	0.141660i	0.632721	−	0.774380i	$-0.281938\pi$
$643$	−3.76599e7	−	3.76599e7i	−0.141660	−	0.141660i	−0.774380	+	0.632721i	$0.781938\pi$
$644$		0			0
$645$	−5.83602e7	−	5.83602e7i	−0.217489	−	0.217489i
$646$		0			0
$647$	−2.17484e8			−0.802999			−0.401500	−	0.915859i	$-0.631511\pi$
$647$	−2.17484e8			−0.802999			−0.401500	+	0.915859i	$0.631511\pi$
$648$		0			0
$649$			2.20604e7i			0.0807009i
$650$		0			0
$651$	3.19743e6	−	3.19743e6i	0.0115893	−	0.0115893i
$652$		0			0
$653$	1.83718e7	−	1.83718e7i	0.0659800	−	0.0659800i	−0.673347	−	0.739327i	$-0.735144\pi$
$653$	1.83718e7	−	1.83718e7i	0.0659800	−	0.0659800i	0.739327	+	0.673347i	$0.235144\pi$
$654$		0			0
$655$		−	3.35734e8i		−	1.19473i
$656$		0			0
$657$	−8.19833e7			−0.289088
$658$		0			0
$659$	2.77669e8	+	2.77669e8i	0.970221	+	0.970221i	0.999569	−	0.0293478i	$-0.00934305\pi$
$659$	2.77669e8	+	2.77669e8i	0.970221	+	0.970221i	−0.0293478	+	0.999569i	$0.509343\pi$
$660$		0			0
$661$	−9.11648e7	−	9.11648e7i	−0.315662	−	0.315662i	0.531436	−	0.847098i	$-0.321653\pi$
$661$	−9.11648e7	−	9.11648e7i	−0.315662	−	0.315662i	−0.847098	+	0.531436i	$0.821653\pi$
$662$		0			0
$663$	1.81437e8			0.622567
$664$		0			0
$665$		−	6.80718e6i		−	0.0231474i
$666$		0			0
$667$	9.90007e7	−	9.90007e7i	0.333627	−	0.333627i
$668$		0			0
$669$	2.47200e7	−	2.47200e7i	0.0825602	−	0.0825602i
$670$		0			0
$671$			175219.i			0.000579980i
$672$		0			0
$673$	−5.24674e8			−1.72125			−0.860626	−	0.509238i	$-0.829927\pi$
$673$	−5.24674e8			−1.72125			−0.860626	+	0.509238i	$0.829927\pi$
$674$		0			0
$675$	2.04437e7	+	2.04437e7i	0.0664736	+	0.0664736i
$676$		0			0
$677$	−4.13584e8	−	4.13584e8i	−1.33290	−	1.33290i	−0.902764	−	0.430136i	$-0.858466\pi$
$677$	−4.13584e8	−	4.13584e8i	−1.33290	−	1.33290i	−0.430136	−	0.902764i	$-0.641534\pi$
$678$		0			0
$679$	8.33109e6			0.0266129
$680$		0			0
$681$			3.33045e8i			1.05454i
$682$		0			0
$683$	−1.09574e8	+	1.09574e8i	−0.343911	+	0.343911i	−0.857836	−	0.513924i	$-0.828191\pi$
$683$	−1.09574e8	+	1.09574e8i	−0.343911	+	0.343911i	0.513924	+	0.857836i	$0.328191\pi$
$684$		0			0
$685$	−2.59198e6	+	2.59198e6i	−0.00806418	+	0.00806418i
$686$		0			0
$687$			1.03096e8i			0.317959i
$688$		0			0
$689$	−1.14701e8			−0.350679
$690$		0			0
$691$	−2.60873e8	−	2.60873e8i	−0.790669	−	0.790669i	0.190934	−	0.981603i	$-0.438848\pi$
$691$	−2.60873e8	−	2.60873e8i	−0.790669	−	0.790669i	−0.981603	+	0.190934i	$0.938848\pi$
$692$		0			0
$693$	63876.8	+	63876.8i	0.000191930	+	0.000191930i
$694$		0			0
$695$	8.12957e8			2.42166
$696$		0			0
$697$			1.12866e8i			0.333323i
$698$		0			0
$699$	−2.18285e8	+	2.18285e8i	−0.639134	+	0.639134i
$700$		0			0
$701$	5.66448e7	−	5.66448e7i	0.164439	−	0.164439i	−0.620091	−	0.784530i	$-0.712904\pi$
$701$	5.66448e7	−	5.66448e7i	0.164439	−	0.164439i	0.784530	+	0.620091i	$0.212904\pi$
$702$		0			0
$703$			3.95573e8i			1.13857i
$704$		0			0
$705$	−1.38343e8			−0.394810
$706$		0			0
$707$	6.24519e6	+	6.24519e6i	0.0176721	+	0.0176721i
$708$		0			0
$709$	−2.04815e8	−	2.04815e8i	−0.574676	−	0.574676i	0.358755	−	0.933432i	$-0.383201\pi$
$709$	−2.04815e8	−	2.04815e8i	−0.574676	−	0.574676i	−0.933432	+	0.358755i	$0.883201\pi$
$710$		0			0
$711$	−1.73875e8			−0.483760
$712$		0			0
$713$		−	1.74860e8i		−	0.482417i
$714$		0			0
$715$	2.23658e7	−	2.23658e7i	0.0611880	−	0.0611880i
$716$		0			0
$717$	4.17569e7	−	4.17569e7i	0.113285	−	0.113285i
$718$		0			0
$719$			6.77714e8i			1.82331i	0.410959	+	0.911654i	$0.365194\pi$
$719$			6.77714e8i			1.82331i	−0.410959	+	0.911654i	$0.634806\pi$
$720$		0			0
$721$	6.57054e6			0.0175305
$722$		0			0
$723$	1.68015e8	+	1.68015e8i	0.444562	+	0.444562i
$724$		0			0
$725$	2.33430e8	+	2.33430e8i	0.612552	+	0.612552i
$726$		0			0
$727$	−3.48046e8			−0.905802			−0.452901	−	0.891561i	$-0.649611\pi$
$727$	−3.48046e8			−0.905802			−0.452901	+	0.891561i	$0.649611\pi$
$728$		0			0
$729$		−	1.43489e7i		−	0.0370370i
$730$		0			0
$731$	9.53718e7	−	9.53718e7i	0.244156	−	0.244156i
$732$		0			0
$733$	−1.36324e7	+	1.36324e7i	−0.0346146	+	0.0346146i	−0.724202	−	0.689588i	$-0.757792\pi$
$733$	−1.36324e7	+	1.36324e7i	−0.0346146	+	0.0346146i	0.689588	+	0.724202i	$0.257792\pi$
$734$		0			0
$735$		−	2.79619e8i		−	0.704213i
$736$		0			0
$737$	−1.20012e7			−0.0299794
$738$		0			0
$739$	2.89963e8	+	2.89963e8i	0.718470	+	0.718470i	0.968292	−	0.249821i	$-0.0803719\pi$
$739$	2.89963e8	+	2.89963e8i	0.718470	+	0.718470i	−0.249821	+	0.968292i	$0.580372\pi$
$740$		0			0
$741$	2.74499e8	+	2.74499e8i	0.674661	+	0.674661i
$742$		0			0
$743$	5.94522e8			1.44944			0.724722	−	0.689041i	$-0.241968\pi$
$743$	5.94522e8			1.44944			0.724722	+	0.689041i	$0.241968\pi$
$744$		0			0
$745$			5.49344e8i			1.32854i
$746$		0			0
$747$	−8.21689e7	+	8.21689e7i	−0.197127	+	0.197127i
$748$		0			0
$749$	−2.26594e6	+	2.26594e6i	−0.00539265	+	0.00539265i
$750$		0			0
$751$		−	5.29349e8i		−	1.24975i	−0.780726	−	0.624874i	$-0.785150\pi$
$751$		−	5.29349e8i		−	1.24975i	0.780726	−	0.624874i	$-0.214850\pi$
$752$		0			0
$753$	3.41888e8			0.800755
$754$		0			0
$755$	−5.23479e8	−	5.23479e8i	−1.21635	−	1.21635i
$756$		0			0
$757$	2.90978e8	+	2.90978e8i	0.670768	+	0.670768i	0.957893	−	0.287125i	$-0.0926996\pi$
$757$	2.90978e8	+	2.90978e8i	0.670768	+	0.670768i	−0.287125	+	0.957893i	$0.592700\pi$
$758$		0			0
$759$	3.49328e6			0.00798928
$760$		0			0
$761$		−	1.25159e8i		−	0.283994i	−0.989867	−	0.141997i	$-0.954648\pi$
$761$		−	1.25159e8i		−	0.283994i	0.989867	−	0.141997i	$-0.0453524\pi$
$762$		0			0
$763$	−5.18867e6	+	5.18867e6i	−0.0116811	+	0.0116811i
$764$		0			0
$765$	−1.01803e8	+	1.01803e8i	−0.227392	+	0.227392i
$766$		0			0
$767$		−	9.54696e8i		−	2.11582i
$768$		0			0
$769$	2.33480e8			0.513418			0.256709	−	0.966489i	$-0.417362\pi$
$769$	2.33480e8			0.513418			0.256709	+	0.966489i	$0.417362\pi$
$770$		0			0
$771$	−2.53939e8	−	2.53939e8i	−0.554073	−	0.554073i
$772$		0			0
$773$	−1.82416e8	−	1.82416e8i	−0.394934	−	0.394934i	0.481507	−	0.876442i	$-0.340089\pi$
$773$	−1.82416e8	−	1.82416e8i	−0.394934	−	0.394934i	−0.876442	+	0.481507i	$0.840089\pi$
$774$		0			0
$775$	4.12297e8			0.885737
$776$		0			0
$777$		−	3.98367e6i		−	0.00849219i
$778$		0			0
$779$	−1.70757e8	+	1.70757e8i	−0.361215	+	0.361215i
$780$		0			0
$781$	−1.04718e7	+	1.04718e7i	−0.0219820	+	0.0219820i
$782$		0			0
$783$		−	1.63838e8i		−	0.341295i
$784$		0			0
$785$	1.02058e9			2.10978
$786$		0			0
$787$	5.04645e8	+	5.04645e8i	1.03529	+	1.03529i	0.999354	+	0.0359348i	$0.0114409\pi$
$787$	5.04645e8	+	5.04645e8i	1.03529	+	1.03529i	0.0359348	+	0.999354i	$0.488559\pi$
$788$		0			0
$789$	−1.26406e8	−	1.26406e8i	−0.257358	−	0.257358i
$790$		0			0
$791$	−7.20460e6			−0.0145573
$792$		0			0
$793$		−	7.58287e6i		−	0.0152060i
$794$		0			0
$795$	6.43578e7	−	6.43578e7i	0.128086	−	0.128086i
$796$		0			0
$797$	−1.49530e8	+	1.49530e8i	−0.295362	+	0.295362i	−0.839194	−	0.543832i	$-0.816973\pi$
$797$	−1.49530e8	+	1.49530e8i	−0.295362	+	0.295362i	0.543832	+	0.839194i	$0.316973\pi$
$798$		0			0
$799$		−	2.26078e8i		−	0.443219i
$800$		0			0
$801$	1.28152e8			0.249361
$802$		0			0
$803$	−1.65153e7	−	1.65153e7i	−0.0318963	−	0.0318963i
$804$		0			0
$805$	1.87449e6	+	1.87449e6i	0.00359332	+	0.00359332i
$806$		0			0
$807$	−4.00018e8			−0.761130
$808$		0			0
$809$		−	6.79235e8i		−	1.28285i	−0.767187	−	0.641423i	$-0.778344\pi$
$809$		−	6.79235e8i		−	1.28285i	0.767187	−	0.641423i	$-0.221656\pi$
$810$		0			0
$811$	−6.71312e8	+	6.71312e8i	−1.25852	+	1.25852i	−0.306727	+	0.951798i	$0.599234\pi$
$811$	−6.71312e8	+	6.71312e8i	−1.25852	+	1.25852i	−0.951798	+	0.306727i	$0.900766\pi$
$812$		0			0
$813$	−1.85253e8	+	1.85253e8i	−0.344742	+	0.344742i
$814$		0			0
$815$		−	4.86402e8i		−	0.898509i
$816$		0			0
$817$	2.88578e8			0.529173
$818$		0			0
$819$	−2.76437e6	−	2.76437e6i	−0.00503204	−	0.00503204i
$820$		0			0
$821$	1.13933e8	+	1.13933e8i	0.205882	+	0.205882i	0.802515	−	0.596632i	$-0.203495\pi$
$821$	1.13933e8	+	1.13933e8i	0.205882	+	0.205882i	−0.596632	+	0.802515i	$0.703495\pi$
$822$		0			0
$823$	−3.09924e8			−0.555975			−0.277987	−	0.960585i	$-0.589667\pi$
$823$	−3.09924e8			−0.555975			−0.277987	+	0.960585i	$0.589667\pi$
$824$		0			0
$825$			8.23667e6i			0.0146686i
$826$		0			0
$827$	−2.49487e8	+	2.49487e8i	−0.441095	+	0.441095i	−0.892380	−	0.451285i	$-0.850966\pi$
$827$	−2.49487e8	+	2.49487e8i	−0.441095	+	0.441095i	0.451285	+	0.892380i	$0.350966\pi$
$828$		0			0
$829$	6.63974e8	−	6.63974e8i	1.16543	−	1.16543i	0.182165	−	0.983268i	$-0.441690\pi$
$829$	6.63974e8	−	6.63974e8i	1.16543	−	1.16543i	0.983268	−	0.182165i	$-0.0583104\pi$
$830$		0			0
$831$		−	2.91402e8i		−	0.507797i
$832$		0			0
$833$	4.56951e8			0.790560
$834$		0			0
$835$	−6.43511e8	−	6.43511e8i	−1.10534	−	1.10534i
$836$		0			0
$837$	−1.44690e8	−	1.44690e8i	−0.246753	−	0.246753i
$838$		0			0
$839$	−4.18417e7			−0.0708473			−0.0354237	−	0.999372i	$-0.511278\pi$
$839$	−4.18417e7			−0.0708473			−0.0354237	+	0.999372i	$0.511278\pi$
$840$		0			0
$841$		−	1.27591e9i		−	2.14503i
$842$		0			0
$843$	4.17324e8	−	4.17324e8i	0.696611	−	0.696611i
$844$		0			0
$845$	−4.47408e8	+	4.47408e8i	−0.741539	+	0.741539i
$846$		0			0
$847$		−	9.48744e6i		−	0.0156135i
$848$		0			0
$849$	−5.52151e8			−0.902266
$850$		0			0
$851$	−1.08929e8	−	1.08929e8i	−0.176748	−	0.176748i
$852$		0			0
$853$	6.18731e8	+	6.18731e8i	0.996908	+	0.996908i	0.999995	−	0.00308725i	$-0.000982702\pi$
$853$	6.18731e8	+	6.18731e8i	0.996908	+	0.996908i	−0.00308725	+	0.999995i	$0.500983\pi$
$854$		0			0
$855$	−3.08038e8			−0.492840
$856$		0			0
$857$			9.35284e8i			1.48594i	0.669325	+	0.742970i	$0.266583\pi$
$857$			9.35284e8i			1.48594i	−0.669325	+	0.742970i	$0.733417\pi$
$858$		0			0
$859$	3.05653e8	−	3.05653e8i	0.482225	−	0.482225i	−0.423617	−	0.905841i	$-0.639240\pi$
$859$	3.05653e8	−	3.05653e8i	0.482225	−	0.482225i	0.905841	+	0.423617i	$0.139240\pi$
$860$		0			0
$861$	1.71963e6	−	1.71963e6i	0.00269417	−	0.00269417i
$862$		0			0
$863$			1.52011e8i			0.236506i	0.992984	+	0.118253i	$0.0377293\pi$
$863$			1.52011e8i			0.236506i	−0.992984	+	0.118253i	$0.962271\pi$
$864$		0			0
$865$	1.31829e9			2.03686
$866$		0			0
$867$	9.96956e7	+	9.96956e7i	0.152974	+	0.152974i
$868$		0			0
$869$	−3.50267e7	−	3.50267e7i	−0.0533753	−	0.0533753i
$870$		0			0
$871$	5.19372e8			0.786002
$872$		0			0
$873$		−	3.76997e8i		−	0.566625i
$874$		0			0
$875$	4.62828e6	−	4.62828e6i	0.00690868	−	0.00690868i
$876$		0			0
$877$	6.76555e8	−	6.76555e8i	1.00301	−	1.00301i	0.00301200	−	0.999995i	$-0.499041\pi$
$877$	6.76555e8	−	6.76555e8i	1.00301	−	1.00301i	0.999995	−	0.00301200i	$-0.000958752\pi$
$878$		0			0
$879$			4.95521e8i			0.729618i
$880$		0			0
$881$	5.67082e8			0.829313			0.414656	−	0.909978i	$-0.363902\pi$
$881$	5.67082e8			0.829313			0.414656	+	0.909978i	$0.363902\pi$
$882$		0			0
$883$	−2.70776e8	−	2.70776e8i	−0.393303	−	0.393303i	0.482560	−	0.875863i	$-0.339707\pi$
$883$	−2.70776e8	−	2.70776e8i	−0.393303	−	0.393303i	−0.875863	+	0.482560i	$0.839707\pi$
$884$		0			0
$885$	5.35673e8	+	5.35673e8i	0.772804	+	0.772804i
$886$		0			0
$887$	−8.61154e8			−1.23399			−0.616993	−	0.786969i	$-0.711649\pi$
$887$	−8.61154e8			−1.23399			−0.616993	+	0.786969i	$0.711649\pi$
$888$		0			0
$889$		−	2.75471e6i		−	0.00392077i
$890$		0			0
$891$	2.89055e6	−	2.89055e6i	0.00408646	−	0.00408646i
$892$		0			0
$893$	3.42037e8	−	3.42037e8i	0.480307	−	0.480307i
$894$		0			0
$895$			7.08661e7i			0.0988484i
$896$		0			0
$897$	−1.51177e8			−0.209464
$898$		0			0
$899$	−1.65210e9	−	1.65210e9i	−2.27382	−	2.27382i
$900$		0			0
$901$	1.05173e8	+	1.05173e8i	0.143791	+	0.143791i
$902$		0			0
$903$	−2.90616e6			−0.00394690
$904$		0			0
$905$			3.99581e8i			0.539087i
$906$		0			0
$907$	4.01148e8	−	4.01148e8i	0.537629	−	0.537629i	−0.385203	−	0.922832i	$-0.625868\pi$
$907$	4.01148e8	−	4.01148e8i	0.537629	−	0.537629i	0.922832	+	0.385203i	$0.125868\pi$
$908$		0			0
$909$	2.82607e8	−	2.82607e8i	0.376263	−	0.376263i
$910$		0			0
$911$		−	9.73411e7i		−	0.128748i	−0.997926	−	0.0643741i	$-0.979495\pi$
$911$		−	9.73411e7i		−	0.128748i	0.997926	−	0.0643741i	$-0.0205051\pi$
$912$		0			0
$913$	−3.31054e7			−0.0434997
$914$		0			0
$915$	4.25469e6	+	4.25469e6i	0.00555398	+	0.00555398i
$916$		0			0
$917$	−8.35927e6	−	8.35927e6i	−0.0108408	−	0.0108408i
$918$		0			0
$919$	7.96503e8			1.02622			0.513110	−	0.858323i	$-0.328493\pi$
$919$	7.96503e8			1.02622			0.513110	+	0.858323i	$0.328493\pi$
$920$		0			0
$921$			5.40054e8i			0.691287i
$922$		0			0
$923$	4.53183e8	−	4.53183e8i	0.576326	−	0.576326i
$924$		0			0
$925$	2.56839e8	−	2.56839e8i	0.324516	−	0.324516i
$926$		0			0
$927$		−	2.97329e8i		−	0.373249i
$928$		0			0
$929$	7.73176e7			0.0964342			0.0482171	−	0.998837i	$-0.484646\pi$
$929$	7.73176e7			0.0964342			0.0482171	+	0.998837i	$0.484646\pi$
$930$		0			0
$931$	6.91327e8	+	6.91327e8i	0.856711	+	0.856711i
$932$		0			0
$933$	−2.34111e8	−	2.34111e8i	−0.288255	−	0.288255i
$934$		0			0
$935$	−4.10159e7			−0.0501784
$936$		0			0
$937$		−	1.24173e9i		−	1.50941i	−0.656063	−	0.754706i	$-0.727780\pi$
$937$		−	1.24173e9i		−	1.50941i	0.656063	−	0.754706i	$-0.272220\pi$
$938$		0			0
$939$	4.25106e8	−	4.25106e8i	0.513453	−	0.513453i
$940$		0			0
$941$	−6.89816e8	+	6.89816e8i	−0.827874	+	0.827874i	−0.987222	−	0.159349i	$-0.949061\pi$
$941$	−6.89816e8	+	6.89816e8i	−0.827874	+	0.827874i	0.159349	+	0.987222i	$0.449061\pi$
$942$		0			0
$943$		−	9.40423e7i		−	0.112147i
$944$		0			0
$945$	3.10213e6			0.00367591
$946$		0			0
$947$	5.78686e8	+	5.78686e8i	0.681386	+	0.681386i	0.960313	−	0.278926i	$-0.0899785\pi$
$947$	5.78686e8	+	5.78686e8i	0.681386	+	0.681386i	−0.278926	+	0.960313i	$0.589979\pi$
$948$		0			0
$949$	7.14726e8	+	7.14726e8i	0.836260	+	0.836260i
$950$		0			0
$951$	−5.64093e8			−0.655857
$952$		0			0
$953$			1.10265e9i			1.27397i	0.770875	+	0.636986i	$0.219819\pi$
$953$			1.10265e9i			1.27397i	−0.770875	+	0.636986i	$0.780181\pi$
$954$		0			0
$955$	9.17241e8	−	9.17241e8i	1.05311	−	1.05311i
$956$		0			0
$957$	3.30048e7	−	3.30048e7i	0.0376566	−	0.0376566i
$958$		0			0
$959$			129073.i			0.000146345i
$960$		0			0
$961$	−2.03052e9			−2.28790
$962$		0			0
$963$	1.02538e8	+	1.02538e8i	0.114817	+	0.114817i
$964$		0			0
$965$	−4.94649e8	−	4.94649e8i	−0.550446	−	0.550446i
$966$		0			0
$967$	7.32629e8			0.810223			0.405111	−	0.914267i	$-0.367233\pi$
$967$	7.32629e8			0.810223			0.405111	+	0.914267i	$0.367233\pi$
$968$		0			0
$969$		−	5.03393e8i		−	0.553269i
$970$		0			0
$971$	6.01418e8	−	6.01418e8i	0.656930	−	0.656930i	−0.297723	−	0.954652i	$-0.596227\pi$
$971$	6.01418e8	−	6.01418e8i	0.656930	−	0.656930i	0.954652	+	0.297723i	$0.0962270\pi$
$972$		0			0
$973$	2.02414e7	−	2.02414e7i	0.0219736	−	0.0219736i
$974$		0			0
$975$		−	3.56455e8i		−	0.384583i
$976$		0			0
$977$	6.27375e8			0.672734			0.336367	−	0.941731i	$-0.390802\pi$
$977$	6.27375e8			0.672734			0.336367	+	0.941731i	$0.390802\pi$
$978$		0			0
$979$	2.58159e7	+	2.58159e7i	0.0275131	+	0.0275131i
$980$		0			0
$981$	2.34797e8	+	2.34797e8i	0.248706	+	0.248706i
$982$		0			0
$983$	−7.60602e8			−0.800750			−0.400375	−	0.916351i	$-0.631120\pi$
$983$	−7.60602e8			−0.800750			−0.400375	+	0.916351i	$0.631120\pi$
$984$		0			0
$985$			1.26004e9i			1.31849i
$986$		0			0
$987$	−3.44452e6	+	3.44452e6i	−0.00358243	+	0.00358243i
$988$		0			0
$989$	−7.94656e7	+	7.94656e7i	−0.0821468	+	0.0821468i
$990$		0			0
$991$			1.26374e8i			0.129848i	0.997890	+	0.0649240i	$0.0206805\pi$
$991$			1.26374e8i			0.129848i	−0.997890	+	0.0649240i	$0.979319\pi$
$992$		0			0
$993$	−8.86382e7			−0.0905260
$994$		0			0
$995$	2.93800e8	+	2.93800e8i	0.298251	+	0.298251i
$996$		0			0
$997$	−1.36158e9	−	1.36158e9i	−1.37391	−	1.37391i	−0.854563	−	0.519348i	$-0.826175\pi$
$997$	−1.36158e9	−	1.36158e9i	−1.37391	−	1.37391i	−0.519348	−	0.854563i	$-0.673825\pi$
$998$		0			0
$999$	−1.80268e8			−0.180810

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.7.l.a.31.2		48
4.3	odd	2		384.7.l.b.31.23		48
8.3	odd	2		48.7.l.a.43.8	yes	48
8.5	even	2		192.7.l.a.79.23		48
16.3	odd	4	inner	384.7.l.a.223.2		48
16.5	even	4		48.7.l.a.19.8	✓	48
16.11	odd	4		192.7.l.a.175.23		48
16.13	even	4		384.7.l.b.223.23		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.l.a.19.8	✓	48	16.5	even	4
48.7.l.a.43.8	yes	48	8.3	odd	2
192.7.l.a.79.23		48	8.5	even	2
192.7.l.a.175.23		48	16.11	odd	4
384.7.l.a.31.2		48	1.1	even	1	trivial
384.7.l.a.223.2		48	16.3	odd	4	inner
384.7.l.b.31.23		48	4.3	odd	2
384.7.l.b.223.23		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)

\(f(q)\)	\(=\)	\(q+(-11.0227 - 11.0227i) q^{3} +(-107.837 - 107.837i) q^{5} -5.36994 q^{7} +243.000i q^{9} +O(q^{10})\)	\(q+(-11.0227 - 11.0227i) q^{3} +(-107.837 - 107.837i) q^{5} -5.36994 q^{7} +243.000i q^{9} +(-48.9517 + 48.9517i) q^{11} +(2118.46 - 2118.46i) q^{13} +2377.30i q^{15} -3884.97 q^{17} +(-5877.62 - 5877.62i) q^{19} +(59.1913 + 59.1913i) q^{21} +3237.03 q^{23} +7632.48i q^{25} +(2678.52 - 2678.52i) q^{27} +(30583.8 - 30583.8i) q^{29} -54018.7i q^{31} +1079.16 q^{33} +(579.076 + 579.076i) q^{35} +(-33650.8 - 33650.8i) q^{37} -46702.3 q^{39} -29052.0i q^{41} +(-24548.9 + 24548.9i) q^{43} +(26204.3 - 26204.3i) q^{45} +58193.1i q^{47} -117620. q^{49} +(42822.9 + 42822.9i) q^{51} +(-27071.8 - 27071.8i) q^{53} +10557.6 q^{55} +129575. i q^{57} +(225328. - 225328. i) q^{59} +(1789.71 - 1789.71i) q^{61} -1304.90i q^{63} -456895. q^{65} +(122582. + 122582. i) q^{67} +(-35680.9 - 35680.9i) q^{69} +213921. q^{71} +337380. i q^{73} +(84130.6 - 84130.6i) q^{75} +(262.868 - 262.868i) q^{77} +715537. i q^{79} -59049.0 q^{81} +(338143. + 338143. i) q^{83} +(418942. + 418942. i) q^{85} -674232. q^{87} -527375. i q^{89} +(-11376.0 + 11376.0i) q^{91} +(-595432. + 595432. i) q^{93} +1.26765e6i q^{95} -1.55143e6 q^{97} +(-11895.3 - 11895.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 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

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