LMFDB - Embedded newform 384.7.l.a.223.21

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			223.21
Character	$\chi$	$=$	384.223
Dual form			384.7.l.a.31.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(11.0227 - 11.0227i) q^{3} +(26.8357 - 26.8357i) q^{5} +81.4485 q^{7} -243.000i q^{9} +O(q^{10})$	\(q+(11.0227 - 11.0227i) q^{3} +(26.8357 - 26.8357i) q^{5} +81.4485 q^{7} -243.000i q^{9} +(-775.312 - 775.312i) q^{11} +(35.8378 + 35.8378i) q^{13} -591.604i q^{15} -3927.21 q^{17} +(-8023.59 + 8023.59i) q^{19} +(897.783 - 897.783i) q^{21} +12220.5 q^{23} +14184.7i q^{25} +(-2678.52 - 2678.52i) q^{27} +(4983.96 + 4983.96i) q^{29} +1910.12i q^{31} -17092.1 q^{33} +(2185.73 - 2185.73i) q^{35} +(2913.71 - 2913.71i) q^{37} +790.059 q^{39} +4731.95i q^{41} +(-9752.98 - 9752.98i) q^{43} +(-6521.08 - 6521.08i) q^{45} +190994. i q^{47} -111015. q^{49} +(-43288.4 + 43288.4i) q^{51} +(89261.5 - 89261.5i) q^{53} -41612.1 q^{55} +176883. i q^{57} +(-65576.0 - 65576.0i) q^{59} +(-46807.2 - 46807.2i) q^{61} -19792.0i q^{63} +1923.47 q^{65} +(156153. - 156153. i) q^{67} +(134703. - 134703. i) q^{69} -260179. q^{71} +239064. i q^{73} +(156354. + 156354. i) q^{75} +(-63148.0 - 63148.0i) q^{77} +845707. i q^{79} -59049.0 q^{81} +(124933. - 124933. i) q^{83} +(-105389. + 105389. i) q^{85} +109874. q^{87} +921193. i q^{89} +(2918.94 + 2918.94i) q^{91} +(21054.6 + 21054.6i) q^{93} +430637. i q^{95} +1.39151e6 q^{97} +(-188401. + 188401. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	11.0227	−	11.0227i	0.408248	−	0.408248i
$3$	11.0227	−	11.0227i	0.408248	−	0.408248i
$4$		0			0
$5$	26.8357	−	26.8357i	0.214686	−	0.214686i	−0.591569	−	0.806254i	$-0.701491\pi$
$5$	26.8357	−	26.8357i	0.214686	−	0.214686i	0.806254	+	0.591569i	$0.201491\pi$
$6$		0			0
$7$	81.4485			0.237459			0.118730	−	0.992927i	$-0.462118\pi$
$7$	81.4485			0.237459			0.118730	+	0.992927i	$0.462118\pi$
$8$		0			0
$9$		−	243.000i		−	0.333333i
$10$		0			0
$11$	−775.312	−	775.312i	−0.582503	−	0.582503i	0.353087	−	0.935590i	$-0.385132\pi$
$11$	−775.312	−	775.312i	−0.582503	−	0.582503i	−0.935590	+	0.353087i	$0.885132\pi$
$12$		0			0
$13$	35.8378	+	35.8378i	0.0163122	+	0.0163122i	0.715216	−	0.698904i	$-0.246328\pi$
$13$	35.8378	+	35.8378i	0.0163122	+	0.0163122i	−0.698904	+	0.715216i	$0.746328\pi$
$14$		0			0
$15$		−	591.604i		−	0.175290i
$16$		0			0
$17$	−3927.21			−0.799350			−0.399675	−	0.916657i	$-0.630877\pi$
$17$	−3927.21			−0.799350			−0.399675	+	0.916657i	$0.630877\pi$
$18$		0			0
$19$	−8023.59	+	8023.59i	−1.16979	+	1.16979i	−0.187531	+	0.982259i	$0.560048\pi$
$19$	−8023.59	+	8023.59i	−1.16979	+	1.16979i	−0.982259	+	0.187531i	$0.939952\pi$
$20$		0			0
$21$	897.783	−	897.783i	0.0969423	−	0.0969423i
$22$		0			0
$23$	12220.5			1.00440			0.502200	−	0.864751i	$-0.332524\pi$
$23$	12220.5			1.00440			0.502200	+	0.864751i	$0.332524\pi$
$24$		0			0
$25$			14184.7i			0.907820i
$26$		0			0
$27$	−2678.52	−	2678.52i	−0.136083	−	0.136083i
$28$		0			0
$29$	4983.96	+	4983.96i	0.204353	+	0.204353i	0.801862	−	0.597509i	$-0.203843\pi$
$29$	4983.96	+	4983.96i	0.204353	+	0.204353i	−0.597509	+	0.801862i	$0.703843\pi$
$30$		0			0
$31$			1910.12i			0.0641172i	0.999486	+	0.0320586i	$0.0102063\pi$
$31$			1910.12i			0.0641172i	−0.999486	+	0.0320586i	$0.989794\pi$
$32$		0			0
$33$	−17092.1			−0.475612
$34$		0			0
$35$	2185.73	−	2185.73i	0.0509791	−	0.0509791i
$36$		0			0
$37$	2913.71	−	2913.71i	0.0575229	−	0.0575229i	−0.677760	−	0.735283i	$-0.737049\pi$
$37$	2913.71	−	2913.71i	0.0575229	−	0.0575229i	0.735283	+	0.677760i	$0.237049\pi$
$38$		0			0
$39$	790.059			0.0133188
$40$		0			0
$41$			4731.95i			0.0686576i	0.999411	+	0.0343288i	$0.0109294\pi$
$41$			4731.95i			0.0686576i	−0.999411	+	0.0343288i	$0.989071\pi$
$42$		0			0
$43$	−9752.98	−	9752.98i	−0.122668	−	0.122668i	0.643108	−	0.765776i	$-0.277645\pi$
$43$	−9752.98	−	9752.98i	−0.122668	−	0.122668i	−0.765776	+	0.643108i	$0.777645\pi$
$44$		0			0
$45$	−6521.08	−	6521.08i	−0.0715619	−	0.0715619i
$46$		0			0
$47$			190994.i			1.83961i	0.392373	+	0.919806i	$0.371654\pi$
$47$			190994.i			1.83961i	−0.392373	+	0.919806i	$0.628346\pi$
$48$		0			0
$49$	−111015.			−0.943613
$50$		0			0
$51$	−43288.4	+	43288.4i	−0.326333	+	0.326333i
$52$		0			0
$53$	89261.5	−	89261.5i	0.599566	−	0.599566i	−0.340631	−	0.940197i	$-0.610641\pi$
$53$	89261.5	−	89261.5i	0.599566	−	0.599566i	0.940197	+	0.340631i	$0.110641\pi$
$54$		0			0
$55$	−41612.1			−0.250110
$56$		0			0
$57$			176883.i			0.955129i
$58$		0			0
$59$	−65576.0	−	65576.0i	−0.319293	−	0.319293i	0.529203	−	0.848495i	$-0.322491\pi$
$59$	−65576.0	−	65576.0i	−0.319293	−	0.319293i	−0.848495	+	0.529203i	$0.822491\pi$
$60$		0			0
$61$	−46807.2	−	46807.2i	−0.206216	−	0.206216i	0.596441	−	0.802657i	$-0.296581\pi$
$61$	−46807.2	−	46807.2i	−0.206216	−	0.206216i	−0.802657	+	0.596441i	$0.796581\pi$
$62$		0			0
$63$		−	19792.0i		−	0.0791531i
$64$		0			0
$65$	1923.47			0.00700397
$66$		0			0
$67$	156153.	−	156153.i	0.519190	−	0.519190i	−0.398136	−	0.917326i	$-0.630343\pi$
$67$	156153.	−	156153.i	0.519190	−	0.519190i	0.917326	+	0.398136i	$0.130343\pi$
$68$		0			0
$69$	134703.	−	134703.i	0.410045	−	0.410045i
$70$		0			0
$71$	−260179.			−0.726938			−0.363469	−	0.931606i	$-0.618408\pi$
$71$	−260179.			−0.726938			−0.363469	+	0.931606i	$0.618408\pi$
$72$		0			0
$73$			239064.i			0.614535i	0.951623	+	0.307267i	$0.0994146\pi$
$73$			239064.i			0.614535i	−0.951623	+	0.307267i	$0.900585\pi$
$74$		0			0
$75$	156354.	+	156354.i	0.370616	+	0.370616i
$76$		0			0
$77$	−63148.0	−	63148.0i	−0.138321	−	0.138321i
$78$		0			0
$79$			845707.i			1.71529i	0.514239	+	0.857647i	$0.328074\pi$
$79$			845707.i			1.71529i	−0.514239	+	0.857647i	$0.671926\pi$
$80$		0			0
$81$	−59049.0			−0.111111
$82$		0			0
$83$	124933.	−	124933.i	0.218496	−	0.218496i	−0.589368	−	0.807864i	$-0.700623\pi$
$83$	124933.	−	124933.i	0.218496	−	0.218496i	0.807864	+	0.589368i	$0.200623\pi$
$84$		0			0
$85$	−105389.	+	105389.i	−0.171609	+	0.171609i
$86$		0			0
$87$	109874.			0.166853
$88$		0			0
$89$			921193.i			1.30671i	0.757050	+	0.653357i	$0.226640\pi$
$89$			921193.i			1.30671i	−0.757050	+	0.653357i	$0.773360\pi$
$90$		0			0
$91$	2918.94	+	2918.94i	0.00387347	+	0.00387347i
$92$		0			0
$93$	21054.6	+	21054.6i	0.0261757	+	0.0261757i
$94$		0			0
$95$			430637.i			0.502274i
$96$		0			0
$97$	1.39151e6			1.52465			0.762326	−	0.647193i	$-0.224057\pi$
$97$	1.39151e6			1.52465			0.762326	+	0.647193i	$0.224057\pi$
$98$		0			0
$99$	−188401.	+	188401.i	−0.194168	+	0.194168i
$100$		0			0
$101$	373244.	−	373244.i	0.362267	−	0.362267i	−0.502380	−	0.864647i	$-0.667542\pi$
$101$	373244.	−	373244.i	0.362267	−	0.362267i	0.864647	+	0.502380i	$0.167542\pi$
$102$		0			0
$103$	−1.80911e6			−1.65559			−0.827795	−	0.561030i	$-0.810405\pi$
$103$	−1.80911e6			−1.65559			−0.827795	+	0.561030i	$0.810405\pi$
$104$		0			0
$105$		−	48185.3i		−	0.0416242i
$106$		0			0
$107$	−691978.	−	691978.i	−0.564860	−	0.564860i	0.365824	−	0.930684i	$-0.380787\pi$
$107$	−691978.	−	691978.i	−0.564860	−	0.564860i	−0.930684	+	0.365824i	$0.880787\pi$
$108$		0			0
$109$	822525.	+	822525.i	0.635140	+	0.635140i	0.949353	−	0.314213i	$-0.101740\pi$
$109$	822525.	+	822525.i	0.635140	+	0.635140i	−0.314213	+	0.949353i	$0.601740\pi$
$110$		0			0
$111$		−	64233.8i		−	0.0469672i
$112$		0			0
$113$	1.51173e6			1.04770			0.523852	−	0.851809i	$-0.324495\pi$
$113$	1.51173e6			1.04770			0.523852	+	0.851809i	$0.324495\pi$
$114$		0			0
$115$	327947.	−	327947.i	0.215630	−	0.215630i
$116$		0			0
$117$	8708.59	−	8708.59i	0.00543739	−	0.00543739i
$118$		0			0
$119$	−319865.			−0.189813
$120$		0			0
$121$		−	569345.i		−	0.321380i
$122$		0			0
$123$	52158.9	+	52158.9i	0.0280294	+	0.0280294i
$124$		0			0
$125$	799964.	+	799964.i	0.409582	+	0.409582i
$126$		0			0
$127$			1.28506e6i			0.627352i	0.949530	+	0.313676i	$0.101561\pi$
$127$			1.28506e6i			0.627352i	−0.949530	+	0.313676i	$0.898439\pi$
$128$		0			0
$129$	−215008.			−0.100158
$130$		0			0
$131$	−2.67757e6	+	2.67757e6i	−1.19104	+	1.19104i	−0.214268	+	0.976775i	$0.568737\pi$
$131$	−2.67757e6	+	2.67757e6i	−1.19104	+	1.19104i	−0.976775	+	0.214268i	$0.931263\pi$
$132$		0			0
$133$	−653509.	+	653509.i	−0.277777	+	0.277777i
$134$		0			0
$135$	−143760.			−0.0584300
$136$		0			0
$137$			4.39546e6i			1.70940i	0.519125	+	0.854698i	$0.326258\pi$
$137$			4.39546e6i			1.70940i	−0.519125	+	0.854698i	$0.673742\pi$
$138$		0			0
$139$	−297733.	−	297733.i	−0.110862	−	0.110862i	0.649500	−	0.760362i	$-0.274978\pi$
$139$	−297733.	−	297733.i	−0.110862	−	0.110862i	−0.760362	+	0.649500i	$0.774978\pi$
$140$		0			0
$141$	2.10527e6	+	2.10527e6i	0.751019	+	0.751019i
$142$		0			0
$143$		−	55570.9i		−	0.0190038i
$144$		0			0
$145$	267496.			0.0877433
$146$		0			0
$147$	−1.22369e6	+	1.22369e6i	−0.385228	+	0.385228i
$148$		0			0
$149$	3.12091e6	−	3.12091e6i	0.943457	−	0.943457i	−0.0550275	−	0.998485i	$-0.517525\pi$
$149$	3.12091e6	−	3.12091e6i	0.943457	−	0.943457i	0.998485	+	0.0550275i	$0.0175246\pi$
$150$		0			0
$151$	−802843.			−0.233185			−0.116592	−	0.993180i	$-0.537197\pi$
$151$	−802843.			−0.233185			−0.116592	+	0.993180i	$0.537197\pi$
$152$		0			0
$153$			954312.i			0.266450i
$154$		0			0
$155$	51259.3	+	51259.3i	0.0137650	+	0.0137650i
$156$		0			0
$157$	5.01290e6	+	5.01290e6i	1.29536	+	1.29536i	0.931425	+	0.363932i	$0.118566\pi$
$157$	5.01290e6	+	5.01290e6i	1.29536	+	1.29536i	0.363932	+	0.931425i	$0.381434\pi$
$158$		0			0
$159$		−	1.96781e6i		−	0.489543i
$160$		0			0
$161$	995345.			0.238504
$162$		0			0
$163$	−5.05411e6	+	5.05411e6i	−1.16703	+	1.16703i	−0.184127	+	0.982903i	$0.558946\pi$
$163$	−5.05411e6	+	5.05411e6i	−1.16703	+	1.16703i	−0.982903	+	0.184127i	$0.941054\pi$
$164$		0			0
$165$	−458677.	+	458677.i	−0.102107	+	0.102107i
$166$		0			0
$167$	3.16978e6			0.680581			0.340291	−	0.940320i	$-0.389475\pi$
$167$	3.16978e6			0.680581			0.340291	+	0.940320i	$0.389475\pi$
$168$		0			0
$169$		−	4.82424e6i		−	0.999468i
$170$		0			0
$171$	1.94973e6	+	1.94973e6i	0.389930	+	0.389930i
$172$		0			0
$173$	131325.	+	131325.i	0.0253635	+	0.0253635i	0.719675	−	0.694311i	$-0.244291\pi$
$173$	131325.	+	131325.i	0.0253635	+	0.0253635i	−0.694311	+	0.719675i	$0.744291\pi$
$174$		0			0
$175$			1.15532e6i			0.215570i
$176$		0			0
$177$	−1.44565e6			−0.260701
$178$		0			0
$179$	−3.48505e6	+	3.48505e6i	−0.607646	+	0.607646i	−0.942330	−	0.334685i	$-0.891370\pi$
$179$	−3.48505e6	+	3.48505e6i	−0.607646	+	0.607646i	0.334685	+	0.942330i	$0.391370\pi$
$180$		0			0
$181$	−3.29758e6	+	3.29758e6i	−0.556108	+	0.556108i	−0.928197	−	0.372089i	$-0.878642\pi$
$181$	−3.29758e6	+	3.29758e6i	−0.556108	+	0.556108i	0.372089	+	0.928197i	$0.378642\pi$
$182$		0			0
$183$	−1.03188e6			−0.168375
$184$		0			0
$185$		−	156383.i		−	0.0246987i
$186$		0			0
$187$	3.04481e6	+	3.04481e6i	0.465624	+	0.465624i
$188$		0			0
$189$	−218161.	−	218161.i	−0.0323141	−	0.0323141i
$190$		0			0
$191$			1.00627e7i			1.44415i	0.691815	+	0.722075i	$0.256812\pi$
$191$			1.00627e7i			1.44415i	−0.691815	+	0.722075i	$0.743188\pi$
$192$		0			0
$193$	7.50788e6			1.04435			0.522174	−	0.852839i	$-0.325121\pi$
$193$	7.50788e6			1.04435			0.522174	+	0.852839i	$0.325121\pi$
$194$		0			0
$195$	21201.8	−	21201.8i	0.00285936	−	0.00285936i
$196$		0			0
$197$	−9.83000e6	+	9.83000e6i	−1.28574	+	1.28574i	−0.348398	+	0.937347i	$0.613274\pi$
$197$	−9.83000e6	+	9.83000e6i	−1.28574	+	1.28574i	−0.937347	+	0.348398i	$0.886726\pi$
$198$		0			0
$199$	−1.08179e7			−1.37272			−0.686362	−	0.727260i	$-0.740793\pi$
$199$	−1.08179e7			−1.37272			−0.686362	+	0.727260i	$0.740793\pi$
$200$		0			0
$201$		−	3.44246e6i		−	0.423917i
$202$		0			0
$203$	405936.	+	405936.i	0.0485255	+	0.0485255i
$204$		0			0
$205$	126985.	+	126985.i	0.0147398	+	0.0147398i
$206$		0			0
$207$		−	2.96959e6i		−	0.334800i
$208$		0			0
$209$	1.24416e7			1.36281
$210$		0			0
$211$	−9.63203e6	+	9.63203e6i	−1.02535	+	1.02535i	−0.0256759	+	0.999670i	$0.508174\pi$
$211$	−9.63203e6	+	9.63203e6i	−1.02535	+	1.02535i	−0.999670	+	0.0256759i	$0.991826\pi$
$212$		0			0
$213$	−2.86788e6	+	2.86788e6i	−0.296771	+	0.296771i
$214$		0			0
$215$	−523456.			−0.0526702
$216$		0			0
$217$			155576.i			0.0152252i
$218$		0			0
$219$	2.63514e6	+	2.63514e6i	0.250883	+	0.250883i
$220$		0			0
$221$	−140743.	−	140743.i	−0.0130391	−	0.0130391i
$222$		0			0
$223$		−	1.26994e7i		−	1.14517i	−0.819847	−	0.572583i	$-0.805942\pi$
$223$		−	1.26994e7i		−	1.14517i	0.819847	−	0.572583i	$-0.194058\pi$
$224$		0			0
$225$	3.44688e6			0.302607
$226$		0			0
$227$	9.66433e6	−	9.66433e6i	0.826217	−	0.826217i	−0.160774	−	0.986991i	$-0.551399\pi$
$227$	9.66433e6	−	9.66433e6i	0.826217	−	0.826217i	0.986991	+	0.160774i	$0.0513990\pi$
$228$		0			0
$229$	7.46532e6	−	7.46532e6i	0.621644	−	0.621644i	−0.324308	−	0.945952i	$-0.605131\pi$
$229$	7.46532e6	−	7.46532e6i	0.621644	−	0.621644i	0.945952	+	0.324308i	$0.105131\pi$
$230$		0			0
$231$	−1.39212e6			−0.112938
$232$		0			0
$233$			1.57383e7i			1.24420i	0.782938	+	0.622100i	$0.213720\pi$
$233$			1.57383e7i			1.24420i	−0.782938	+	0.622100i	$0.786280\pi$
$234$		0			0
$235$	5.12546e6	+	5.12546e6i	0.394938	+	0.394938i
$236$		0			0
$237$	9.32198e6	+	9.32198e6i	0.700266	+	0.700266i
$238$		0			0
$239$			1.79587e7i			1.31547i	0.753249	+	0.657736i	$0.228486\pi$
$239$			1.79587e7i			1.31547i	−0.753249	+	0.657736i	$0.771514\pi$
$240$		0			0
$241$	−1.76960e7			−1.26423			−0.632113	−	0.774876i	$-0.717812\pi$
$241$	−1.76960e7			−1.26423			−0.632113	+	0.774876i	$0.717812\pi$
$242$		0			0
$243$	−650880.	+	650880.i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	−2.97917e6	+	2.97917e6i	−0.202580	+	0.202580i
$246$		0			0
$247$	−575096.			−0.0381636
$248$		0			0
$249$		−	2.75420e6i		−	0.178401i
$250$		0			0
$251$	−1.70291e7	−	1.70291e7i	−1.07689	−	1.07689i	−0.996786	−	0.0801047i	$-0.974475\pi$
$251$	−1.70291e7	−	1.70291e7i	−1.07689	−	1.07689i	−0.0801047	−	0.996786i	$-0.525525\pi$
$252$		0			0
$253$	−9.47473e6	−	9.47473e6i	−0.585066	−	0.585066i
$254$		0			0
$255$			2.32335e6i			0.140118i
$256$		0			0
$257$	−3.32789e6			−0.196051			−0.0980256	−	0.995184i	$-0.531253\pi$
$257$	−3.32789e6			−0.196051			−0.0980256	+	0.995184i	$0.531253\pi$
$258$		0			0
$259$	237317.	−	237317.i	0.0136593	−	0.0136593i
$260$		0			0
$261$	1.21110e6	−	1.21110e6i	0.0681176	−	0.0681176i
$262$		0			0
$263$	528417.			0.0290476			0.0145238	−	0.999895i	$-0.495377\pi$
$263$	528417.			0.0290476			0.0145238	+	0.999895i	$0.495377\pi$
$264$		0			0
$265$		−	4.79079e6i		−	0.257436i
$266$		0			0
$267$	1.01540e7	+	1.01540e7i	0.533464	+	0.533464i
$268$		0			0
$269$	−7.17633e6	−	7.17633e6i	−0.368677	−	0.368677i	0.498318	−	0.866994i	$-0.333951\pi$
$269$	−7.17633e6	−	7.17633e6i	−0.368677	−	0.368677i	−0.866994	+	0.498318i	$0.833951\pi$
$270$		0			0
$271$		−	4.41346e6i		−	0.221754i	−0.993834	−	0.110877i	$-0.964634\pi$
$271$		−	4.41346e6i		−	0.221754i	0.993834	−	0.110877i	$-0.0353660\pi$
$272$		0			0
$273$	64349.1			0.00316268
$274$		0			0
$275$	1.09976e7	−	1.09976e7i	0.528808	−	0.528808i
$276$		0			0
$277$	2.55357e7	−	2.55357e7i	1.20146	−	1.20146i	0.227732	−	0.973724i	$-0.426869\pi$
$277$	2.55357e7	−	2.55357e7i	1.20146	−	1.20146i	0.973724	−	0.227732i	$-0.0731309\pi$
$278$		0			0
$279$	464158.			0.0213724
$280$		0			0
$281$			1.23501e7i			0.556610i	0.960493	+	0.278305i	$0.0897725\pi$
$281$			1.23501e7i			0.556610i	−0.960493	+	0.278305i	$0.910227\pi$
$282$		0			0
$283$	−1.87645e7	−	1.87645e7i	−0.827901	−	0.827901i	0.159325	−	0.987226i	$-0.449068\pi$
$283$	−1.87645e7	−	1.87645e7i	−0.827901	−	0.827901i	−0.987226	+	0.159325i	$0.949068\pi$
$284$		0			0
$285$	4.74679e6	+	4.74679e6i	0.205053	+	0.205053i
$286$		0			0
$287$			385411.i			0.0163034i
$288$		0			0
$289$	−8.71461e6			−0.361039
$290$		0			0
$291$	1.53382e7	−	1.53382e7i	0.622437	−	0.622437i
$292$		0			0
$293$	2.33597e7	−	2.33597e7i	0.928675	−	0.928675i	−0.0689457	−	0.997620i	$-0.521964\pi$
$293$	2.33597e7	−	2.33597e7i	0.928675	−	0.928675i	0.997620	+	0.0689457i	$0.0219635\pi$
$294$		0			0
$295$	−3.51956e6			−0.137095
$296$		0			0
$297$			4.15337e6i			0.158537i
$298$		0			0
$299$	437957.	+	437957.i	0.0163839	+	0.0163839i
$300$		0			0
$301$	−794366.	−	794366.i	−0.0291287	−	0.0291287i
$302$		0			0
$303$		−	8.22831e6i		−	0.295790i
$304$		0			0
$305$	−2.51221e6			−0.0885434
$306$		0			0
$307$	4.10516e6	−	4.10516e6i	0.141878	−	0.141878i	−0.632600	−	0.774478i	$-0.718012\pi$
$307$	4.10516e6	−	4.10516e6i	0.141878	−	0.141878i	0.774478	+	0.632600i	$0.218012\pi$
$308$		0			0
$309$	−1.99413e7	+	1.99413e7i	−0.675892	+	0.675892i
$310$		0			0
$311$	4.81011e7			1.59909			0.799547	−	0.600604i	$-0.205073\pi$
$311$	4.81011e7			1.59909			0.799547	+	0.600604i	$0.205073\pi$
$312$		0			0
$313$		−	1.59905e7i		−	0.521469i	−0.965411	−	0.260734i	$-0.916035\pi$
$313$		−	1.59905e7i		−	0.521469i	0.965411	−	0.260734i	$-0.0839647\pi$
$314$		0			0
$315$	−531132.	−	531132.i	−0.0169930	−	0.0169930i
$316$		0			0
$317$	−2.98537e7	−	2.98537e7i	−0.937173	−	0.937173i	0.0609665	−	0.998140i	$-0.480582\pi$
$317$	−2.98537e7	−	2.98537e7i	−0.937173	−	0.937173i	−0.998140	+	0.0609665i	$0.980582\pi$
$318$		0			0
$319$		−	7.72825e6i		−	0.238072i
$320$		0			0
$321$	−1.52549e7			−0.461207
$322$		0			0
$323$	3.15103e7	−	3.15103e7i	0.935072	−	0.935072i
$324$		0			0
$325$	−508348.	+	508348.i	−0.0148085	+	0.0148085i
$326$		0			0
$327$	1.81329e7			0.518590
$328$		0			0
$329$			1.55562e7i			0.436833i
$330$		0			0
$331$	−1.52731e7	−	1.52731e7i	−0.421156	−	0.421156i	0.464446	−	0.885602i	$-0.346254\pi$
$331$	−1.52731e7	−	1.52731e7i	−0.421156	−	0.421156i	−0.885602	+	0.464446i	$0.846254\pi$
$332$		0			0
$333$	−708031.	−	708031.i	−0.0191743	−	0.0191743i
$334$		0			0
$335$		−	8.38096e6i		−	0.222925i
$336$		0			0
$337$	−3.20323e7			−0.836948			−0.418474	−	0.908229i	$-0.637435\pi$
$337$	−3.20323e7			−0.836948			−0.418474	+	0.908229i	$0.637435\pi$
$338$		0			0
$339$	1.66633e7	−	1.66633e7i	0.427723	−	0.427723i
$340$		0			0
$341$	1.48093e6	−	1.48093e6i	0.0373485	−	0.0373485i
$342$		0			0
$343$	−1.86244e7			−0.461529
$344$		0			0
$345$		−	7.22972e6i		−	0.176061i
$346$		0			0
$347$	4.52698e6	+	4.52698e6i	0.108348	+	0.108348i	0.759202	−	0.650855i	$-0.225589\pi$
$347$	4.52698e6	+	4.52698e6i	0.108348	+	0.108348i	−0.650855	+	0.759202i	$0.725589\pi$
$348$		0			0
$349$	−3.42959e7	−	3.42959e7i	−0.806801	−	0.806801i	0.177348	−	0.984148i	$-0.443248\pi$
$349$	−3.42959e7	−	3.42959e7i	−0.806801	−	0.806801i	−0.984148	+	0.177348i	$0.943248\pi$
$350$		0			0
$351$		−	191984.i		−	0.00443961i
$352$		0			0
$353$	−1.61140e6			−0.0366335			−0.0183168	−	0.999832i	$-0.505831\pi$
$353$	−1.61140e6			−0.0366335			−0.0183168	+	0.999832i	$0.505831\pi$
$354$		0			0
$355$	−6.98209e6	+	6.98209e6i	−0.156063	+	0.156063i
$356$		0			0
$357$	−3.52578e6	+	3.52578e6i	−0.0774909	+	0.0774909i
$358$		0			0
$359$	2.80317e7			0.605850			0.302925	−	0.953014i	$-0.402037\pi$
$359$	2.80317e7			0.605850			0.302925	+	0.953014i	$0.402037\pi$
$360$		0			0
$361$		−	8.17100e7i		−	1.73682i
$362$		0			0
$363$	−6.27572e6	−	6.27572e6i	−0.131203	−	0.131203i
$364$		0			0
$365$	6.41546e6	+	6.41546e6i	0.131932	+	0.131932i
$366$		0			0
$367$		−	1.29660e7i		−	0.262305i	−0.991362	−	0.131153i	$-0.958132\pi$
$367$		−	1.29660e7i		−	0.262305i	0.991362	−	0.131153i	$-0.0418678\pi$
$368$		0			0
$369$	1.14986e6			0.0228859
$370$		0			0
$371$	7.27022e6	−	7.27022e6i	0.142372	−	0.142372i
$372$		0			0
$373$	1.21108e7	−	1.21108e7i	0.233370	−	0.233370i	−0.580728	−	0.814098i	$-0.697232\pi$
$373$	1.21108e7	−	1.21108e7i	0.233370	−	0.233370i	0.814098	+	0.580728i	$0.197232\pi$
$374$		0			0
$375$	1.76355e7			0.334422
$376$		0			0
$377$			357229.i			0.00666687i
$378$		0			0
$379$	7.52090e6	+	7.52090e6i	0.138150	+	0.138150i	0.772800	−	0.634650i	$-0.218856\pi$
$379$	7.52090e6	+	7.52090e6i	0.138150	+	0.138150i	−0.634650	+	0.772800i	$0.718856\pi$
$380$		0			0
$381$	1.41648e7	+	1.41648e7i	0.256116	+	0.256116i
$382$		0			0
$383$		−	6.40799e7i		−	1.14058i	−0.821444	−	0.570290i	$-0.806831\pi$
$383$		−	6.40799e7i		−	1.14058i	0.821444	−	0.570290i	$-0.193169\pi$
$384$		0			0
$385$	−3.38924e6			−0.0593909
$386$		0			0
$387$	−2.36997e6	+	2.36997e6i	−0.0408894	+	0.0408894i
$388$		0			0
$389$	−2.83762e7	+	2.83762e7i	−0.482065	+	0.482065i	−0.905791	−	0.423725i	$-0.860722\pi$
$389$	−2.83762e7	+	2.83762e7i	−0.482065	+	0.482065i	0.423725	+	0.905791i	$0.360722\pi$
$390$		0			0
$391$	−4.79926e7			−0.802868
$392$		0			0
$393$			5.90282e7i			0.972483i
$394$		0			0
$395$	2.26951e7	+	2.26951e7i	0.368249	+	0.368249i
$396$		0			0
$397$	−8.65284e7	−	8.65284e7i	−1.38289	−	1.38289i	−0.839446	−	0.543443i	$-0.817120\pi$
$397$	−8.65284e7	−	8.65284e7i	−1.38289	−	1.38289i	−0.543443	−	0.839446i	$-0.682880\pi$
$398$		0			0
$399$			1.44069e7i			0.226804i
$400$		0			0
$401$	−5.90588e7			−0.915907			−0.457954	−	0.888976i	$-0.651417\pi$
$401$	−5.90588e7			−0.915907			−0.457954	+	0.888976i	$0.651417\pi$
$402$		0			0
$403$	−68454.4	+	68454.4i	−0.00104589	+	0.00104589i
$404$		0			0
$405$	−1.58462e6	+	1.58462e6i	−0.0238540	+	0.0238540i
$406$		0			0
$407$	−4.51806e6			−0.0670145
$408$		0			0
$409$		−	7.26547e7i		−	1.06192i	−0.847395	−	0.530962i	$-0.821831\pi$
$409$		−	7.26547e7i		−	1.06192i	0.847395	−	0.530962i	$-0.178169\pi$
$410$		0			0
$411$	4.84499e7	+	4.84499e7i	0.697858	+	0.697858i
$412$		0			0
$413$	−5.34107e6	−	5.34107e6i	−0.0758190	−	0.0758190i
$414$		0			0
$415$		−	6.70534e6i		−	0.0938160i
$416$		0			0
$417$	−6.56364e6			−0.0905183
$418$		0			0
$419$	1.95758e7	−	1.95758e7i	0.266120	−	0.266120i	−0.561415	−	0.827535i	$-0.689743\pi$
$419$	1.95758e7	−	1.95758e7i	0.266120	−	0.266120i	0.827535	+	0.561415i	$0.189743\pi$
$420$		0			0
$421$	−3.85272e7	+	3.85272e7i	−0.516323	+	0.516323i	−0.916457	−	0.400134i	$-0.868964\pi$
$421$	−3.85272e7	+	3.85272e7i	−0.516323	+	0.516323i	0.400134	+	0.916457i	$0.368964\pi$
$422$		0			0
$423$	4.64116e7			0.613204
$424$		0			0
$425$		−	5.57062e7i		−	0.725666i
$426$		0			0
$427$	−3.81238e6	−	3.81238e6i	−0.0489680	−	0.0489680i
$428$		0			0
$429$	−612542.	−	612542.i	−0.00775825	−	0.00775825i
$430$		0			0
$431$			7.68903e6i			0.0960373i	0.998846	+	0.0480186i	$0.0152907\pi$
$431$			7.68903e6i			0.0960373i	−0.998846	+	0.0480186i	$0.984709\pi$
$432$		0			0
$433$	6.11798e7			0.753607			0.376803	−	0.926293i	$-0.377023\pi$
$433$	6.11798e7			0.753607			0.376803	+	0.926293i	$0.377023\pi$
$434$		0			0
$435$	2.94853e6	−	2.94853e6i	0.0358210	−	0.0358210i
$436$		0			0
$437$	−9.80526e7	+	9.80526e7i	−1.17494	+	1.17494i
$438$		0			0
$439$	−2.46496e7			−0.291351			−0.145676	−	0.989332i	$-0.546536\pi$
$439$	−2.46496e7			−0.291351			−0.145676	+	0.989332i	$0.546536\pi$
$440$		0			0
$441$			2.69767e7i			0.314538i
$442$		0			0
$443$	4.36137e7	+	4.36137e7i	0.501662	+	0.501662i	0.911954	−	0.410292i	$-0.134573\pi$
$443$	4.36137e7	+	4.36137e7i	0.501662	+	0.501662i	−0.410292	+	0.911954i	$0.634573\pi$
$444$		0			0
$445$	2.47209e7	+	2.47209e7i	0.280533	+	0.280533i
$446$		0			0
$447$		−	6.88017e7i		−	0.770330i
$448$		0			0
$449$	1.69871e6			0.0187664			0.00938320	−	0.999956i	$-0.497013\pi$
$449$	1.69871e6			0.0187664			0.00938320	+	0.999956i	$0.497013\pi$
$450$		0			0
$451$	3.66874e6	−	3.66874e6i	0.0399933	−	0.0399933i
$452$		0			0
$453$	−8.84950e6	+	8.84950e6i	−0.0951972	+	0.0951972i
$454$		0			0
$455$	156663.			0.00166316
$456$		0			0
$457$		−	1.26874e8i		−	1.32931i	−0.747151	−	0.664654i	$-0.768579\pi$
$457$		−	1.26874e8i		−	1.32931i	0.747151	−	0.664654i	$-0.231421\pi$
$458$		0			0
$459$	1.05191e7	+	1.05191e7i	0.108778	+	0.108778i
$460$		0			0
$461$	9.90837e7	+	9.90837e7i	1.01135	+	1.01135i	0.999935	+	0.0114105i	$0.00363214\pi$
$461$	9.90837e7	+	9.90837e7i	1.01135	+	1.01135i	0.0114105	+	0.999935i	$0.496368\pi$
$462$		0			0
$463$			7.82203e7i			0.788091i	0.919091	+	0.394045i	$0.128925\pi$
$463$			7.82203e7i			0.788091i	−0.919091	+	0.394045i	$0.871075\pi$
$464$		0			0
$465$	1.13003e6			0.0112391
$466$		0			0
$467$	−4.15449e7	+	4.15449e7i	−0.407913	+	0.407913i	−0.881010	−	0.473097i	$-0.843136\pi$
$467$	−4.15449e7	+	4.15449e7i	−0.407913	+	0.407913i	0.473097	+	0.881010i	$0.343136\pi$
$468$		0			0
$469$	1.27184e7	−	1.27184e7i	0.123286	−	0.123286i
$470$		0			0
$471$	1.10511e8			1.05766
$472$		0			0
$473$			1.51232e7i			0.142909i
$474$		0			0
$475$	−1.13812e8	−	1.13812e8i	−1.06196	−	1.06196i
$476$		0			0
$477$	−2.16906e7	−	2.16906e7i	−0.199855	−	0.199855i
$478$		0			0
$479$		−	1.47963e8i		−	1.34631i	−0.739499	−	0.673157i	$-0.764938\pi$
$479$		−	1.47963e8i		−	1.34631i	0.739499	−	0.673157i	$-0.235062\pi$
$480$		0			0
$481$	208842.			0.00187664
$482$		0			0
$483$	1.09714e7	−	1.09714e7i	0.0973689	−	0.0973689i
$484$		0			0
$485$	3.73421e7	−	3.73421e7i	0.327321	−	0.327321i
$486$		0			0
$487$	−1.46672e8			−1.26988			−0.634938	−	0.772563i	$-0.718974\pi$
$487$	−1.46672e8			−1.26988			−0.634938	+	0.772563i	$0.718974\pi$
$488$		0			0
$489$			1.11420e8i			0.952875i
$490$		0			0
$491$	5.09913e7	+	5.09913e7i	0.430776	+	0.430776i	0.888892	−	0.458116i	$-0.151476\pi$
$491$	5.09913e7	+	5.09913e7i	0.430776	+	0.430776i	−0.458116	+	0.888892i	$0.651476\pi$
$492$		0			0
$493$	−1.95731e7	−	1.95731e7i	−0.163350	−	0.163350i
$494$		0			0
$495$			1.01117e7i			0.0833700i
$496$		0			0
$497$	−2.11912e7			−0.172618
$498$		0			0
$499$	−1.49891e8	+	1.49891e8i	−1.20635	+	1.20635i	−0.234152	+	0.972200i	$0.575231\pi$
$499$	−1.49891e8	+	1.49891e8i	−1.20635	+	1.20635i	−0.972200	+	0.234152i	$0.924769\pi$
$500$		0			0
$501$	3.49396e7	−	3.49396e7i	0.277846	−	0.277846i
$502$		0			0
$503$	1.74504e8			1.37120			0.685600	−	0.727979i	$-0.259540\pi$
$503$	1.74504e8			1.37120			0.685600	+	0.727979i	$0.259540\pi$
$504$		0			0
$505$		−	2.00325e7i		−	0.155547i
$506$		0			0
$507$	−5.31762e7	−	5.31762e7i	−0.408031	−	0.408031i
$508$		0			0
$509$	9.29471e7	+	9.29471e7i	0.704827	+	0.704827i	0.965443	−	0.260616i	$-0.0839256\pi$
$509$	9.29471e7	+	9.29471e7i	0.704827	+	0.704827i	−0.260616	+	0.965443i	$0.583926\pi$
$510$		0			0
$511$			1.94714e7i			0.145927i
$512$		0			0
$513$	4.29826e7			0.318376
$514$		0			0
$515$	−4.85487e7	+	4.85487e7i	−0.355432	+	0.355432i
$516$		0			0
$517$	1.48080e8	−	1.48080e8i	1.07158	−	1.07158i
$518$		0			0
$519$	2.89512e6			0.0207092
$520$		0			0
$521$		−	7.09637e7i		−	0.501791i	−0.968014	−	0.250895i	$-0.919275\pi$
$521$		−	7.09637e7i		−	0.501791i	0.968014	−	0.250895i	$-0.0807251\pi$
$522$		0			0
$523$	−5.50191e7	−	5.50191e7i	−0.384599	−	0.384599i	0.488157	−	0.872756i	$-0.337669\pi$
$523$	−5.50191e7	−	5.50191e7i	−0.384599	−	0.384599i	−0.872756	+	0.488157i	$0.837669\pi$
$524$		0			0
$525$	1.27348e7	+	1.27348e7i	0.0880062	+	0.0880062i
$526$		0			0
$527$		−	7.50142e6i		−	0.0512521i
$528$		0			0
$529$	1.30573e6			0.00882036
$530$		0			0
$531$	−1.59350e7	+	1.59350e7i	−0.106431	+	0.106431i
$532$		0			0
$533$	−169583.	+	169583.i	−0.00111995	+	0.00111995i
$534$		0			0
$535$	−3.71395e7			−0.242535
$536$		0			0
$537$			7.68294e7i			0.496141i
$538$		0			0
$539$	8.60713e7	+	8.60713e7i	0.549658	+	0.549658i
$540$		0			0
$541$	−9.74560e7	−	9.74560e7i	−0.615484	−	0.615484i	0.328886	−	0.944370i	$-0.393327\pi$
$541$	−9.74560e7	−	9.74560e7i	−0.615484	−	0.615484i	−0.944370	+	0.328886i	$0.893327\pi$
$542$		0			0
$543$			7.26965e7i			0.454061i
$544$		0			0
$545$	4.41461e7			0.272711
$546$		0			0
$547$	−6.39041e6	+	6.39041e6i	−0.0390451	+	0.0390451i	−0.726360	−	0.687315i	$-0.758789\pi$
$547$	−6.39041e6	+	6.39041e6i	−0.0390451	+	0.0390451i	0.687315	+	0.726360i	$0.258789\pi$
$548$		0			0
$549$	−1.13742e7	+	1.13742e7i	−0.0687388	+	0.0687388i
$550$		0			0
$551$	−7.99785e7			−0.478100
$552$		0			0
$553$			6.88816e7i			0.407312i
$554$		0			0
$555$	−1.72376e6	−	1.72376e6i	−0.0100832	−	0.0100832i
$556$		0			0
$557$	2.14251e8	+	2.14251e8i	1.23982	+	1.23982i	0.960075	+	0.279741i	$0.0902488\pi$
$557$	2.14251e8	+	2.14251e8i	1.23982	+	1.23982i	0.279741	+	0.960075i	$0.409751\pi$
$558$		0			0
$559$		−	699051.i		−	0.00400197i
$560$		0			0
$561$	6.71241e7			0.380180
$562$		0			0
$563$	3.29830e7	−	3.29830e7i	0.184827	−	0.184827i	−0.608628	−	0.793455i	$-0.708280\pi$
$563$	3.29830e7	−	3.29830e7i	0.184827	−	0.184827i	0.793455	+	0.608628i	$0.208280\pi$
$564$		0			0
$565$	4.05683e7	−	4.05683e7i	0.224927	−	0.224927i
$566$		0			0
$567$	−4.80945e6			−0.0263844
$568$		0			0
$569$			3.50326e8i			1.90167i	0.309694	+	0.950836i	$0.399773\pi$
$569$			3.50326e8i			1.90167i	−0.309694	+	0.950836i	$0.600227\pi$
$570$		0			0
$571$	−1.89558e8	−	1.89558e8i	−1.01820	−	1.01820i	−0.999831	−	0.0183727i	$-0.994151\pi$
$571$	−1.89558e8	−	1.89558e8i	−1.01820	−	1.01820i	−0.0183727	−	0.999831i	$-0.505849\pi$
$572$		0			0
$573$	1.10918e8	+	1.10918e8i	0.589572	+	0.589572i
$574$		0			0
$575$			1.73345e8i			0.911815i
$576$		0			0
$577$	2.39174e8			1.24505			0.622525	−	0.782600i	$-0.286107\pi$
$577$	2.39174e8			1.24505			0.622525	+	0.782600i	$0.286107\pi$
$578$		0			0
$579$	8.27572e7	−	8.27572e7i	0.426354	−	0.426354i
$580$		0			0
$581$	1.01756e7	−	1.01756e7i	0.0518839	−	0.0518839i
$582$		0			0
$583$	−1.38411e8			−0.698498
$584$		0			0
$585$		−	467402.i		−	0.00233466i
$586$		0			0
$587$	1.31381e8	+	1.31381e8i	0.649558	+	0.649558i	0.952886	−	0.303328i	$-0.0980979\pi$
$587$	1.31381e8	+	1.31381e8i	0.649558	+	0.649558i	−0.303328	+	0.952886i	$0.598098\pi$
$588$		0			0
$589$	−1.53260e7	−	1.53260e7i	−0.0750037	−	0.0750037i
$590$		0			0
$591$			2.16706e8i			1.04981i
$592$		0			0
$593$	3.40528e7			0.163301			0.0816504	−	0.996661i	$-0.473981\pi$
$593$	3.40528e7			0.163301			0.0816504	+	0.996661i	$0.473981\pi$
$594$		0			0
$595$	−8.58381e6	+	8.58381e6i	−0.0407501	+	0.0407501i
$596$		0			0
$597$	−1.19242e8	+	1.19242e8i	−0.560412	+	0.560412i
$598$		0			0
$599$	−3.20600e8			−1.49170			−0.745852	−	0.666112i	$-0.767957\pi$
$599$	−3.20600e8			−1.49170			−0.745852	+	0.666112i	$0.767957\pi$
$600$		0			0
$601$			1.29953e8i			0.598635i	0.954154	+	0.299318i	$0.0967590\pi$
$601$			1.29953e8i			0.598635i	−0.954154	+	0.299318i	$0.903241\pi$
$602$		0			0
$603$	−3.79452e7	−	3.79452e7i	−0.173063	−	0.173063i
$604$		0			0
$605$	−1.52788e7	−	1.52788e7i	−0.0689958	−	0.0689958i
$606$		0			0
$607$			2.92063e8i			1.30590i	0.757401	+	0.652950i	$0.226469\pi$
$607$			2.92063e8i			1.30590i	−0.757401	+	0.652950i	$0.773531\pi$
$608$		0			0
$609$	8.94903e6			0.0396209
$610$		0			0
$611$	−6.84481e6	+	6.84481e6i	−0.0300081	+	0.0300081i
$612$		0			0
$613$	1.14280e8	−	1.14280e8i	0.496123	−	0.496123i	−0.414106	−	0.910229i	$-0.635906\pi$
$613$	1.14280e8	−	1.14280e8i	0.496123	−	0.496123i	0.910229	+	0.414106i	$0.135906\pi$
$614$		0			0
$615$	2.79944e6			0.0120350
$616$		0			0
$617$		−	9.88451e6i		−	0.0420823i	−0.999779	−	0.0210412i	$-0.993302\pi$
$617$		−	9.88451e6i		−	0.0420823i	0.999779	−	0.0210412i	$-0.00669811\pi$
$618$		0			0
$619$	7.00948e7	+	7.00948e7i	0.295539	+	0.295539i	0.839263	−	0.543725i	$-0.182987\pi$
$619$	7.00948e7	+	7.00948e7i	0.295539	+	0.295539i	−0.543725	+	0.839263i	$0.682987\pi$
$620$		0			0
$621$	−3.27329e7	−	3.27329e7i	−0.136682	−	0.136682i
$622$		0			0
$623$			7.50298e7i			0.310291i
$624$		0			0
$625$	−1.78701e8			−0.731958
$626$		0			0
$627$	1.37140e8	−	1.37140e8i	0.556366	−	0.556366i
$628$		0			0
$629$	−1.14427e7	+	1.14427e7i	−0.0459809	+	0.0459809i
$630$		0			0
$631$	−3.77054e8			−1.50078			−0.750388	−	0.660998i	$-0.770133\pi$
$631$	−3.77054e8			−1.50078			−0.750388	+	0.660998i	$0.770133\pi$
$632$		0			0
$633$			2.12342e8i			0.837192i
$634$		0			0
$635$	3.44854e7	+	3.44854e7i	0.134684	+	0.134684i
$636$		0			0
$637$	−3.97854e6	−	3.97854e6i	−0.0153924	−	0.0153924i
$638$		0			0
$639$			6.32235e7i			0.242313i
$640$		0			0
$641$	9.95731e7			0.378066			0.189033	−	0.981971i	$-0.439465\pi$
$641$	9.95731e7			0.378066			0.189033	+	0.981971i	$0.439465\pi$
$642$		0			0
$643$	−1.77761e8	+	1.77761e8i	−0.668659	+	0.668659i	−0.957406	−	0.288747i	$-0.906761\pi$
$643$	−1.77761e8	+	1.77761e8i	−0.668659	+	0.668659i	0.288747	+	0.957406i	$0.406761\pi$
$644$		0			0
$645$	−5.76990e6	+	5.76990e6i	−0.0215025	+	0.0215025i
$646$		0			0
$647$	−3.33059e7			−0.122973			−0.0614864	−	0.998108i	$-0.519584\pi$
$647$	−3.33059e7			−0.122973			−0.0614864	+	0.998108i	$0.519584\pi$
$648$		0			0
$649$			1.01684e8i			0.371978i
$650$		0			0
$651$	1.71487e6	+	1.71487e6i	0.00621567	+	0.00621567i
$652$		0			0
$653$	−6.98414e7	−	6.98414e7i	−0.250826	−	0.250826i	0.570483	−	0.821309i	$-0.306756\pi$
$653$	−6.98414e7	−	6.98414e7i	−0.250826	−	0.250826i	−0.821309	+	0.570483i	$0.806756\pi$
$654$		0			0
$655$			1.43709e8i			0.511400i
$656$		0			0
$657$	5.80926e7			0.204845
$658$		0			0
$659$	−1.42365e7	+	1.42365e7i	−0.0497448	+	0.0497448i	−0.731542	−	0.681797i	$-0.761199\pi$
$659$	−1.42365e7	+	1.42365e7i	−0.0497448	+	0.0497448i	0.681797	+	0.731542i	$0.261199\pi$
$660$		0			0
$661$	−3.36860e7	+	3.36860e7i	−0.116639	+	0.116639i	−0.763017	−	0.646378i	$-0.776283\pi$
$661$	−3.36860e7	+	3.36860e7i	−0.116639	+	0.116639i	0.646378	+	0.763017i	$0.276283\pi$
$662$		0			0
$663$	−3.10273e6			−0.0106464
$664$		0			0
$665$			3.50748e7i			0.119270i
$666$		0			0
$667$	6.09067e7	+	6.09067e7i	0.205252	+	0.205252i
$668$		0			0
$669$	−1.39982e8	−	1.39982e8i	−0.467512	−	0.467512i
$670$		0			0
$671$			7.25803e7i			0.240243i
$672$		0			0
$673$	1.32491e8			0.434651			0.217325	−	0.976099i	$-0.430267\pi$
$673$	1.32491e8			0.434651			0.217325	+	0.976099i	$0.430267\pi$
$674$		0			0
$675$	3.79939e7	−	3.79939e7i	0.123539	−	0.123539i
$676$		0			0
$677$	−1.24130e8	+	1.24130e8i	−0.400048	+	0.400048i	−0.878250	−	0.478202i	$-0.841289\pi$
$677$	−1.24130e8	+	1.24130e8i	−0.400048	+	0.400048i	0.478202	+	0.878250i	$0.341289\pi$
$678$		0			0
$679$	1.13336e8			0.362043
$680$		0			0
$681$		−	2.13054e8i		−	0.674604i
$682$		0			0
$683$	−2.13536e8	−	2.13536e8i	−0.670207	−	0.670207i	0.287557	−	0.957764i	$-0.407157\pi$
$683$	−2.13536e8	−	2.13536e8i	−0.670207	−	0.670207i	−0.957764	+	0.287557i	$0.907157\pi$
$684$		0			0
$685$	1.17955e8	+	1.17955e8i	0.366983	+	0.366983i
$686$		0			0
$687$		−	1.64576e8i		−	0.507570i
$688$		0			0
$689$	6.39788e6			0.0195604
$690$		0			0
$691$	−2.45627e8	+	2.45627e8i	−0.744460	+	0.744460i	−0.973433	−	0.228973i	$-0.926463\pi$
$691$	−2.45627e8	+	2.45627e8i	−0.744460	+	0.744460i	0.228973	+	0.973433i	$0.426463\pi$
$692$		0			0
$693$	−1.53450e7	+	1.53450e7i	−0.0461069	+	0.0461069i
$694$		0			0
$695$	−1.59797e7			−0.0476009
$696$		0			0
$697$		−	1.85834e7i		−	0.0548815i
$698$		0			0
$699$	1.73479e8	+	1.73479e8i	0.507942	+	0.507942i
$700$		0			0
$701$	1.47613e8	+	1.47613e8i	0.428519	+	0.428519i	0.888124	−	0.459605i	$-0.152009\pi$
$701$	1.47613e8	+	1.47613e8i	0.428519	+	0.428519i	−0.459605	+	0.888124i	$0.652009\pi$
$702$		0			0
$703$			4.67567e7i			0.134579i
$704$		0			0
$705$	1.12993e8			0.322466
$706$		0			0
$707$	3.04001e7	−	3.04001e7i	0.0860236	−	0.0860236i
$708$		0			0
$709$	3.51942e8	−	3.51942e8i	0.987490	−	0.987490i	−0.0124323	−	0.999923i	$-0.503957\pi$
$709$	3.51942e8	−	3.51942e8i	0.987490	−	0.987490i	0.999923	+	0.0124323i	$0.00395742\pi$
$710$		0			0
$711$	2.05507e8			0.571765
$712$		0			0
$713$			2.33426e7i			0.0643994i
$714$		0			0
$715$	−1.49129e6	−	1.49129e6i	−0.00407983	−	0.00407983i
$716$		0			0
$717$	1.97954e8	+	1.97954e8i	0.537039	+	0.537039i
$718$		0			0
$719$		−	1.45173e8i		−	0.390571i	−0.980746	−	0.195286i	$-0.937437\pi$
$719$		−	1.45173e8i		−	0.390571i	0.980746	−	0.195286i	$-0.0625634\pi$
$720$		0			0
$721$	−1.47349e8			−0.393135
$722$		0			0
$723$	−1.95058e8	+	1.95058e8i	−0.516118	+	0.516118i
$724$		0			0
$725$	−7.06960e7	+	7.06960e7i	−0.185516	+	0.185516i
$726$		0			0
$727$	6.00279e8			1.56225			0.781124	−	0.624375i	$-0.214646\pi$
$727$	6.00279e8			1.56225			0.781124	+	0.624375i	$0.214646\pi$
$728$		0			0
$729$			1.43489e7i			0.0370370i
$730$		0			0
$731$	3.83020e7	+	3.83020e7i	0.0980549	+	0.0980549i
$732$		0			0
$733$	−2.06518e8	−	2.06518e8i	−0.524381	−	0.524381i	0.394511	−	0.918891i	$-0.370914\pi$
$733$	−2.06518e8	−	2.06518e8i	−0.524381	−	0.524381i	−0.918891	+	0.394511i	$0.870914\pi$
$734$		0			0
$735$			6.56770e7i			0.165406i
$736$		0			0
$737$	−2.42135e8			−0.604859
$738$		0			0
$739$	−2.55773e8	+	2.55773e8i	−0.633755	+	0.633755i	−0.949008	−	0.315252i	$-0.897911\pi$
$739$	−2.55773e8	+	2.55773e8i	−0.633755	+	0.633755i	0.315252	+	0.949008i	$0.397911\pi$
$740$		0			0
$741$	−6.33911e6	+	6.33911e6i	−0.0155802	+	0.0155802i
$742$		0			0
$743$	3.84449e8			0.937285			0.468643	−	0.883388i	$-0.344743\pi$
$743$	3.84449e8			0.937285			0.468643	+	0.883388i	$0.344743\pi$
$744$		0			0
$745$		−	1.67504e8i		−	0.405094i
$746$		0			0
$747$	−3.03588e7	−	3.03588e7i	−0.0728320	−	0.0728320i
$748$		0			0
$749$	−5.63606e7	−	5.63606e7i	−0.134131	−	0.134131i
$750$		0			0
$751$		−	5.91852e8i		−	1.39731i	−0.715458	−	0.698656i	$-0.753782\pi$
$751$		−	5.91852e8i		−	1.39731i	0.715458	−	0.698656i	$-0.246218\pi$
$752$		0			0
$753$	−3.75415e8			−0.879278
$754$		0			0
$755$	−2.15449e7	+	2.15449e7i	−0.0500614	+	0.0500614i
$756$		0			0
$757$	−2.68713e8	+	2.68713e8i	−0.619442	+	0.619442i	−0.945388	−	0.325946i	$-0.894317\pi$
$757$	−2.68713e8	+	2.68713e8i	−0.619442	+	0.619442i	0.325946	+	0.945388i	$0.394317\pi$
$758$		0			0
$759$	−2.08874e8			−0.477705
$760$		0			0
$761$		−	4.52025e8i		−	1.02567i	−0.858487	−	0.512836i	$-0.828595\pi$
$761$		−	4.52025e8i		−	1.02567i	0.858487	−	0.512836i	$-0.171405\pi$
$762$		0			0
$763$	6.69934e7	+	6.69934e7i	0.150820	+	0.150820i
$764$		0			0
$765$	2.56096e7	+	2.56096e7i	0.0572030	+	0.0572030i
$766$		0			0
$767$		−	4.70020e6i		−	0.0104167i
$768$		0			0
$769$	−3.89939e8			−0.857466			−0.428733	−	0.903431i	$-0.641040\pi$
$769$	−3.89939e8			−0.857466			−0.428733	+	0.903431i	$0.641040\pi$
$770$		0			0
$771$	−3.66823e7	+	3.66823e7i	−0.0800376	+	0.0800376i
$772$		0			0
$773$	−1.43202e8	+	1.43202e8i	−0.310035	+	0.310035i	−0.844923	−	0.534888i	$-0.820354\pi$
$773$	−1.43202e8	+	1.43202e8i	−0.310035	+	0.310035i	0.534888	+	0.844923i	$0.320354\pi$
$774$		0			0
$775$	−2.70944e7			−0.0582069
$776$		0			0
$777$		−	5.23175e6i		−	0.0111528i
$778$		0			0
$779$	−3.79672e7	−	3.79672e7i	−0.0803150	−	0.0803150i
$780$		0			0
$781$	2.01720e8	+	2.01720e8i	0.423444	+	0.423444i
$782$		0			0
$783$		−	2.66993e7i		−	0.0556178i
$784$		0			0
$785$	2.69049e8			0.556189
$786$		0			0
$787$	6.07213e8	−	6.07213e8i	1.24571	−	1.24571i	0.288114	−	0.957596i	$-0.406972\pi$
$787$	6.07213e8	−	6.07213e8i	1.24571	−	1.24571i	0.957596	−	0.288114i	$-0.0930281\pi$
$788$		0			0
$789$	5.82459e6	−	5.82459e6i	0.0118586	−	0.0118586i
$790$		0			0
$791$	1.23128e8			0.248787
$792$		0			0
$793$		−	3.35494e6i		−	0.00672767i
$794$		0			0
$795$	−5.28075e7	−	5.28075e7i	−0.105098	−	0.105098i
$796$		0			0
$797$	−5.04366e7	−	5.04366e7i	−0.0996255	−	0.0996255i	0.655537	−	0.755163i	$-0.272442\pi$
$797$	−5.04366e7	−	5.04366e7i	−0.0996255	−	0.0996255i	−0.755163	+	0.655537i	$0.772442\pi$
$798$		0			0
$799$		−	7.50074e8i		−	1.47049i
$800$		0			0
$801$	2.23850e8			0.435571
$802$		0			0
$803$	1.85349e8	−	1.85349e8i	0.357968	−	0.357968i
$804$		0			0
$805$	2.67108e7	−	2.67108e7i	0.0512034	−	0.0512034i
$806$		0			0
$807$	−1.58205e8			−0.301023
$808$		0			0
$809$		−	4.00282e8i		−	0.755997i	−0.925806	−	0.377999i	$-0.876612\pi$
$809$		−	4.00282e8i		−	0.755997i	0.925806	−	0.377999i	$-0.123388\pi$
$810$		0			0
$811$	8.86243e7	+	8.86243e7i	0.166146	+	0.166146i	0.785283	−	0.619137i	$-0.212517\pi$
$811$	8.86243e7	+	8.86243e7i	0.166146	+	0.166146i	−0.619137	+	0.785283i	$0.712517\pi$
$812$		0			0
$813$	−4.86483e7	−	4.86483e7i	−0.0905308	−	0.0905308i
$814$		0			0
$815$			2.71261e8i			0.501089i
$816$		0			0
$817$	1.56508e8			0.286992
$818$		0			0
$819$	709301.	−	709301.i	0.00129116	−	0.00129116i
$820$		0			0
$821$	2.23870e8	−	2.23870e8i	0.404545	−	0.404545i	−0.475286	−	0.879831i	$-0.657656\pi$
$821$	2.23870e8	−	2.23870e8i	0.404545	−	0.404545i	0.879831	+	0.475286i	$0.157656\pi$
$822$		0			0
$823$	−1.27752e8			−0.229175			−0.114587	−	0.993413i	$-0.536555\pi$
$823$	−1.27752e8			−0.229175			−0.114587	+	0.993413i	$0.536555\pi$
$824$		0			0
$825$		−	2.42446e8i		−	0.431770i
$826$		0			0
$827$	−4.55767e8	−	4.55767e8i	−0.805798	−	0.805798i	0.178197	−	0.983995i	$-0.442974\pi$
$827$	−4.55767e8	−	4.55767e8i	−0.805798	−	0.805798i	−0.983995	+	0.178197i	$0.942974\pi$
$828$		0			0
$829$	−3.03952e8	−	3.03952e8i	−0.533509	−	0.533509i	0.388106	−	0.921615i	$-0.373130\pi$
$829$	−3.03952e8	−	3.03952e8i	−0.533509	−	0.533509i	−0.921615	+	0.388106i	$0.873130\pi$
$830$		0			0
$831$		−	5.62944e8i		−	0.980984i
$832$		0			0
$833$	4.35980e8			0.754277
$834$		0			0
$835$	8.50633e7	−	8.50633e7i	0.146111	−	0.146111i
$836$		0			0
$837$	5.11628e6	−	5.11628e6i	0.00872525	−	0.00872525i
$838$		0			0
$839$	−2.05872e8			−0.348588			−0.174294	−	0.984694i	$-0.555764\pi$
$839$	−2.05872e8			−0.348588			−0.174294	+	0.984694i	$0.555764\pi$
$840$		0			0
$841$		−	5.45144e8i		−	0.916480i
$842$		0			0
$843$	1.36131e8	+	1.36131e8i	0.227235	+	0.227235i
$844$		0			0
$845$	−1.29462e8	−	1.29462e8i	−0.214571	−	0.214571i
$846$		0			0
$847$		−	4.63723e7i		−	0.0763147i
$848$		0			0
$849$	−4.13672e8			−0.675979
$850$		0			0
$851$	3.56071e7	−	3.56071e7i	0.0577760	−	0.0577760i
$852$		0			0
$853$	−8.70314e8	+	8.70314e8i	−1.40226	+	1.40226i	−0.609391	+	0.792870i	$0.708586\pi$
$853$	−8.70314e8	+	8.70314e8i	−1.40226	+	1.40226i	−0.792870	+	0.609391i	$0.791414\pi$
$854$		0			0
$855$	1.04645e8			0.167425
$856$		0			0
$857$			3.02830e8i			0.481124i	0.970634	+	0.240562i	$0.0773318\pi$
$857$			3.02830e8i			0.481124i	−0.970634	+	0.240562i	$0.922668\pi$
$858$		0			0
$859$	4.31496e8	+	4.31496e8i	0.680765	+	0.680765i	0.960173	−	0.279408i	$-0.0901381\pi$
$859$	4.31496e8	+	4.31496e8i	0.680765	+	0.680765i	−0.279408	+	0.960173i	$0.590138\pi$
$860$		0			0
$861$	4.24827e6	+	4.24827e6i	0.00665583	+	0.00665583i
$862$		0			0
$863$		−	3.92538e8i		−	0.610729i	−0.952235	−	0.305365i	$-0.901222\pi$
$863$		−	3.92538e8i		−	0.610729i	0.952235	−	0.305365i	$-0.0987784\pi$
$864$		0			0
$865$	7.04841e6			0.0108904
$866$		0			0
$867$	−9.60585e7	+	9.60585e7i	−0.147394	+	0.147394i
$868$		0			0
$869$	6.55686e8	−	6.55686e8i	0.999164	−	0.999164i
$870$		0			0
$871$	1.11924e7			0.0169382
$872$		0			0
$873$		−	3.38137e8i		−	0.508218i
$874$		0			0
$875$	6.51559e7	+	6.51559e7i	0.0972589	+	0.0972589i
$876$		0			0
$877$	7.63567e8	+	7.63567e8i	1.13201	+	1.13201i	0.989843	+	0.142162i	$0.0454052\pi$
$877$	7.63567e8	+	7.63567e8i	1.13201	+	1.13201i	0.142162	+	0.989843i	$0.454595\pi$
$878$		0			0
$879$		−	5.14973e8i		−	0.758260i
$880$		0			0
$881$	−8.54724e8			−1.24997			−0.624983	−	0.780638i	$-0.714894\pi$
$881$	−8.54724e8			−1.24997			−0.624983	+	0.780638i	$0.714894\pi$
$882$		0			0
$883$	4.53290e8	−	4.53290e8i	0.658406	−	0.658406i	−0.296596	−	0.955003i	$-0.595852\pi$
$883$	4.53290e8	−	4.53290e8i	0.658406	−	0.658406i	0.955003	+	0.296596i	$0.0958516\pi$
$884$		0			0
$885$	−3.87950e7	+	3.87950e7i	−0.0559689	+	0.0559689i
$886$		0			0
$887$	9.71858e8			1.39262			0.696309	−	0.717742i	$-0.254824\pi$
$887$	9.71858e8			1.39262			0.696309	+	0.717742i	$0.254824\pi$
$888$		0			0
$889$			1.04666e8i			0.148971i
$890$		0			0
$891$	4.57814e7	+	4.57814e7i	0.0647226	+	0.0647226i
$892$		0			0
$893$	−1.53246e9	−	1.53246e9i	−2.15196	−	2.15196i
$894$		0			0
$895$			1.87048e8i			0.260906i
$896$		0			0
$897$	9.65495e6			0.0133774
$898$		0			0
$899$	−9.51995e6	+	9.51995e6i	−0.0131025	+	0.0131025i
$900$		0			0
$901$	−3.50549e8	+	3.50549e8i	−0.479263	+	0.479263i
$902$		0			0
$903$	−1.75121e7			−0.0237835
$904$		0			0
$905$			1.76986e8i			0.238777i
$906$		0			0
$907$	−1.75732e8	−	1.75732e8i	−0.235521	−	0.235521i	0.579472	−	0.814992i	$-0.303259\pi$
$907$	−1.75732e8	−	1.75732e8i	−0.235521	−	0.235521i	−0.814992	+	0.579472i	$0.803259\pi$
$908$		0			0
$909$	−9.06982e7	−	9.06982e7i	−0.120756	−	0.120756i
$910$		0			0
$911$		−	6.20037e8i		−	0.820091i	−0.912065	−	0.410046i	$-0.865513\pi$
$911$		−	6.20037e8i		−	0.820091i	0.912065	−	0.410046i	$-0.134487\pi$
$912$		0			0
$913$	−1.93724e8			−0.254549
$914$		0			0
$915$	−2.76913e7	+	2.76913e7i	−0.0361477	+	0.0361477i
$916$		0			0
$917$	−2.18084e8	+	2.18084e8i	−0.282824	+	0.282824i
$918$		0			0
$919$	6.45209e8			0.831292			0.415646	−	0.909526i	$-0.363555\pi$
$919$	6.45209e8			0.831292			0.415646	+	0.909526i	$0.363555\pi$
$920$		0			0
$921$		−	9.04999e7i		−	0.115843i
$922$		0			0
$923$	−9.32425e6	−	9.32425e6i	−0.0118579	−	0.0118579i
$924$		0			0
$925$	4.13300e7	+	4.13300e7i	0.0522204	+	0.0522204i
$926$		0			0
$927$			4.39613e8i			0.551864i
$928$		0			0
$929$	8.35063e8			1.04153			0.520765	−	0.853700i	$-0.325647\pi$
$929$	8.35063e8			1.04153			0.520765	+	0.853700i	$0.325647\pi$
$930$		0			0
$931$	8.90740e8	−	8.90740e8i	1.10383	−	1.10383i
$932$		0			0
$933$	5.30204e8	−	5.30204e8i	0.652827	−	0.652827i
$934$		0			0
$935$	1.63419e8			0.199926
$936$		0			0
$937$		−	9.19162e8i		−	1.11731i	−0.829401	−	0.558654i	$-0.811318\pi$
$937$		−	9.19162e8i		−	1.11731i	0.829401	−	0.558654i	$-0.188682\pi$
$938$		0			0
$939$	−1.76258e8	−	1.76258e8i	−0.212889	−	0.212889i
$940$		0			0
$941$	−4.64558e8	−	4.64558e8i	−0.557534	−	0.557534i	0.371071	−	0.928605i	$-0.378991\pi$
$941$	−4.64558e8	−	4.64558e8i	−0.557534	−	0.557534i	−0.928605	+	0.371071i	$0.878991\pi$
$942$		0			0
$943$			5.78270e7i			0.0689598i
$944$		0			0
$945$	−1.17090e7			−0.0138747
$946$		0			0
$947$	2.95450e8	−	2.95450e8i	0.347884	−	0.347884i	−0.511437	−	0.859321i	$-0.670887\pi$
$947$	2.95450e8	−	2.95450e8i	0.347884	−	0.347884i	0.859321	+	0.511437i	$0.170887\pi$
$948$		0			0
$949$	−8.56754e6	+	8.56754e6i	−0.0100244	+	0.0100244i
$950$		0			0
$951$	−6.58136e8			−0.765199
$952$		0			0
$953$			9.92140e8i			1.14629i	0.819454	+	0.573145i	$0.194277\pi$
$953$			9.92140e8i			1.14629i	−0.819454	+	0.573145i	$0.805723\pi$
$954$		0			0
$955$	2.70038e8	+	2.70038e8i	0.310038	+	0.310038i
$956$		0			0
$957$	−8.51862e7	−	8.51862e7i	−0.0971927	−	0.0971927i
$958$		0			0
$959$			3.58004e8i			0.405912i
$960$		0			0
$961$	8.83855e8			0.995889
$962$		0			0
$963$	−1.68151e8	+	1.68151e8i	−0.188287	+	0.188287i
$964$		0			0
$965$	2.01479e8	−	2.01479e8i	0.224207	−	0.224207i
$966$		0			0
$967$	4.13366e8			0.457147			0.228573	−	0.973527i	$-0.426594\pi$
$967$	4.13366e8			0.457147			0.228573	+	0.973527i	$0.426594\pi$
$968$		0			0
$969$		−	6.94657e8i		−	0.763483i
$970$		0			0
$971$	−8.79406e8	−	8.79406e8i	−0.960576	−	0.960576i	0.0386761	−	0.999252i	$-0.487686\pi$
$971$	−8.79406e8	−	8.79406e8i	−0.960576	−	0.960576i	−0.999252	+	0.0386761i	$0.987686\pi$
$972$		0			0
$973$	−2.42499e7	−	2.42499e7i	−0.0263252	−	0.0263252i
$974$		0			0
$975$			1.12067e7i			0.0120911i
$976$		0			0
$977$	−1.52615e9			−1.63649			−0.818243	−	0.574873i	$-0.805052\pi$
$977$	−1.52615e9			−1.63649			−0.818243	+	0.574873i	$0.805052\pi$
$978$		0			0
$979$	7.14211e8	−	7.14211e8i	0.761165	−	0.761165i
$980$		0			0
$981$	1.99873e8	−	1.99873e8i	0.211713	−	0.211713i
$982$		0			0
$983$	−1.39922e9			−1.47308			−0.736538	−	0.676396i	$-0.763541\pi$
$983$	−1.39922e9			−1.47308			−0.736538	+	0.676396i	$0.763541\pi$
$984$		0			0
$985$			5.27590e8i			0.552062i
$986$		0			0
$987$	1.71471e8	+	1.71471e8i	0.178336	+	0.178336i
$988$		0			0
$989$	−1.19187e8	−	1.19187e8i	−0.123208	−	0.123208i
$990$		0			0
$991$			5.93840e8i			0.610167i	0.952326	+	0.305083i	$0.0986843\pi$
$991$			5.93840e8i			0.610167i	−0.952326	+	0.305083i	$0.901316\pi$
$992$		0			0
$993$	−3.36701e8			−0.343872
$994$		0			0
$995$	−2.90306e8	+	2.90306e8i	−0.294704	+	0.294704i
$996$		0			0
$997$	−3.37349e8	+	3.37349e8i	−0.340403	+	0.340403i	−0.856519	−	0.516116i	$-0.827377\pi$
$997$	−3.37349e8	+	3.37349e8i	−0.340403	+	0.340403i	0.516116	+	0.856519i	$0.327377\pi$
$998$		0			0
$999$	−1.56088e7			−0.0156557

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.7.l.a.223.21		48
4.3	odd	2		384.7.l.b.223.4		48
8.3	odd	2		48.7.l.a.19.5	✓	48
8.5	even	2		192.7.l.a.175.4		48
16.3	odd	4		192.7.l.a.79.4		48
16.5	even	4		384.7.l.b.31.4		48
16.11	odd	4	inner	384.7.l.a.31.21		48
16.13	even	4		48.7.l.a.43.5	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.l.a.19.5	✓	48	8.3	odd	2
48.7.l.a.43.5	yes	48	16.13	even	4
192.7.l.a.79.4		48	16.3	odd	4
192.7.l.a.175.4		48	8.5	even	2
384.7.l.a.31.21		48	16.11	odd	4	inner
384.7.l.a.223.21		48	1.1	even	1	trivial
384.7.l.b.31.4		48	16.5	even	4
384.7.l.b.223.4		48	4.3	odd	2

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)

\(f(q)\)	\(=\)	\(q+(11.0227 - 11.0227i) q^{3} +(26.8357 - 26.8357i) q^{5} +81.4485 q^{7} -243.000i q^{9} +O(q^{10})\)	\(q+(11.0227 - 11.0227i) q^{3} +(26.8357 - 26.8357i) q^{5} +81.4485 q^{7} -243.000i q^{9} +(-775.312 - 775.312i) q^{11} +(35.8378 + 35.8378i) q^{13} -591.604i q^{15} -3927.21 q^{17} +(-8023.59 + 8023.59i) q^{19} +(897.783 - 897.783i) q^{21} +12220.5 q^{23} +14184.7i q^{25} +(-2678.52 - 2678.52i) q^{27} +(4983.96 + 4983.96i) q^{29} +1910.12i q^{31} -17092.1 q^{33} +(2185.73 - 2185.73i) q^{35} +(2913.71 - 2913.71i) q^{37} +790.059 q^{39} +4731.95i q^{41} +(-9752.98 - 9752.98i) q^{43} +(-6521.08 - 6521.08i) q^{45} +190994. i q^{47} -111015. q^{49} +(-43288.4 + 43288.4i) q^{51} +(89261.5 - 89261.5i) q^{53} -41612.1 q^{55} +176883. i q^{57} +(-65576.0 - 65576.0i) q^{59} +(-46807.2 - 46807.2i) q^{61} -19792.0i q^{63} +1923.47 q^{65} +(156153. - 156153. i) q^{67} +(134703. - 134703. i) q^{69} -260179. q^{71} +239064. i q^{73} +(156354. + 156354. i) q^{75} +(-63148.0 - 63148.0i) q^{77} +845707. i q^{79} -59049.0 q^{81} +(124933. - 124933. i) q^{83} +(-105389. + 105389. i) q^{85} +109874. q^{87} +921193. i q^{89} +(2918.94 + 2918.94i) q^{91} +(21054.6 + 21054.6i) q^{93} +430637. i q^{95} +1.39151e6 q^{97} +(-188401. + 188401. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 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

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