LMFDB - Embedded newform 384.7.l.b.31.5

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			31.5
Character	$\chi$	$=$	384.31
Dual form			384.7.l.b.223.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.0227 - 11.0227i) q^{3} +(26.6395 + 26.6395i) q^{5} -403.840 q^{7} +243.000i q^{9} +O(q^{10})$	\(q+(-11.0227 - 11.0227i) q^{3} +(26.6395 + 26.6395i) q^{5} -403.840 q^{7} +243.000i q^{9} +(-152.675 + 152.675i) q^{11} +(1728.86 - 1728.86i) q^{13} -587.279i q^{15} +110.784 q^{17} +(-3293.87 - 3293.87i) q^{19} +(4451.41 + 4451.41i) q^{21} -4142.48 q^{23} -14205.7i q^{25} +(2678.52 - 2678.52i) q^{27} +(26256.6 - 26256.6i) q^{29} +15500.0i q^{31} +3365.79 q^{33} +(-10758.1 - 10758.1i) q^{35} +(-41837.5 - 41837.5i) q^{37} -38113.5 q^{39} +135328. i q^{41} +(-25578.8 + 25578.8i) q^{43} +(-6473.40 + 6473.40i) q^{45} +36531.8i q^{47} +45437.8 q^{49} +(-1221.13 - 1221.13i) q^{51} +(-115323. - 115323. i) q^{53} -8134.39 q^{55} +72614.7i q^{57} +(-71056.8 + 71056.8i) q^{59} +(96379.6 - 96379.6i) q^{61} -98133.1i q^{63} +92112.0 q^{65} +(266382. + 266382. i) q^{67} +(45661.3 + 45661.3i) q^{69} -416772. q^{71} -202516. i q^{73} +(-156585. + 156585. i) q^{75} +(61656.4 - 61656.4i) q^{77} -832723. i q^{79} -59049.0 q^{81} +(157114. + 157114. i) q^{83} +(2951.22 + 2951.22i) q^{85} -578837. q^{87} +985026. i q^{89} +(-698184. + 698184. i) q^{91} +(170852. - 170852. i) q^{93} -175494. i q^{95} +1.46802e6 q^{97} +(-37100.1 - 37100.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	26.6395	+	26.6395i	0.213116	+	0.213116i	0.805590	−	0.592474i	$-0.201849\pi$
$5$	26.6395	+	26.6395i	0.213116	+	0.213116i	−0.592474	+	0.805590i	$0.701849\pi$
$6$		0			0
$7$	−403.840			−1.17738			−0.588688	−	0.808360i	$-0.700355\pi$
$7$	−403.840			−1.17738			−0.588688	+	0.808360i	$0.700355\pi$
$8$		0			0
$9$			243.000i			0.333333i
$10$		0			0
$11$	−152.675	+	152.675i	−0.114707	+	0.114707i	−0.762131	−	0.647423i	$-0.775847\pi$
$11$	−152.675	+	152.675i	−0.114707	+	0.114707i	0.647423	+	0.762131i	$0.275847\pi$
$12$		0			0
$13$	1728.86	−	1728.86i	0.786919	−	0.786919i	−0.194069	−	0.980988i	$-0.562168\pi$
$13$	1728.86	−	1728.86i	0.786919	−	0.786919i	0.980988	+	0.194069i	$0.0621685\pi$
$14$		0			0
$15$		−	587.279i		−	0.174008i
$16$		0			0
$17$	110.784			0.0225491			0.0112745	−	0.999936i	$-0.496411\pi$
$17$	110.784			0.0225491			0.0112745	+	0.999936i	$0.496411\pi$
$18$		0			0
$19$	−3293.87	−	3293.87i	−0.480226	−	0.480226i	0.424978	−	0.905204i	$-0.360282\pi$
$19$	−3293.87	−	3293.87i	−0.480226	−	0.480226i	−0.905204	+	0.424978i	$0.860282\pi$
$20$		0			0
$21$	4451.41	+	4451.41i	0.480662	+	0.480662i
$22$		0			0
$23$	−4142.48			−0.340468			−0.170234	−	0.985404i	$-0.554452\pi$
$23$	−4142.48			−0.340468			−0.170234	+	0.985404i	$0.554452\pi$
$24$		0			0
$25$		−	14205.7i		−	0.909163i
$26$		0			0
$27$	2678.52	−	2678.52i	0.136083	−	0.136083i
$28$		0			0
$29$	26256.6	−	26256.6i	1.07658	−	1.07658i	0.0797613	−	0.996814i	$-0.474584\pi$
$29$	26256.6	−	26256.6i	1.07658	−	1.07658i	0.996814	−	0.0797613i	$-0.0254158\pi$
$30$		0			0
$31$			15500.0i			0.520293i	0.965569	+	0.260146i	$0.0837708\pi$
$31$			15500.0i			0.520293i	−0.965569	+	0.260146i	$0.916229\pi$
$32$		0			0
$33$	3365.79			0.0936580
$34$		0			0
$35$	−10758.1	−	10758.1i	−0.250918	−	0.250918i
$36$		0			0
$37$	−41837.5	−	41837.5i	−0.825963	−	0.825963i	0.160993	−	0.986956i	$-0.448530\pi$
$37$	−41837.5	−	41837.5i	−0.825963	−	0.825963i	−0.986956	+	0.160993i	$0.948530\pi$
$38$		0			0
$39$	−38113.5			−0.642517
$40$		0			0
$41$			135328.i			1.96352i	0.190121	+	0.981761i	$0.439112\pi$
$41$			135328.i			1.96352i	−0.190121	+	0.981761i	$0.560888\pi$
$42$		0			0
$43$	−25578.8	+	25578.8i	−0.321717	+	0.321717i	−0.849426	−	0.527708i	$-0.823051\pi$
$43$	−25578.8	+	25578.8i	−0.321717	+	0.321717i	0.527708	+	0.849426i	$0.323051\pi$
$44$		0			0
$45$	−6473.40	+	6473.40i	−0.0710387	+	0.0710387i
$46$		0			0
$47$			36531.8i			0.351866i	0.984402	+	0.175933i	$0.0562942\pi$
$47$			36531.8i			0.351866i	−0.984402	+	0.175933i	$0.943706\pi$
$48$		0			0
$49$	45437.8			0.386215
$50$		0			0
$51$	−1221.13	−	1221.13i	−0.00920562	−	0.00920562i
$52$		0			0
$53$	−115323.	−	115323.i	−0.774619	−	0.774619i	0.204291	−	0.978910i	$-0.434511\pi$
$53$	−115323.	−	115323.i	−0.774619	−	0.774619i	−0.978910	+	0.204291i	$0.934511\pi$
$54$		0			0
$55$	−8134.39			−0.0488919
$56$		0			0
$57$			72614.7i			0.392103i
$58$		0			0
$59$	−71056.8	+	71056.8i	−0.345979	+	0.345979i	−0.858609	−	0.512630i	$-0.828671\pi$
$59$	−71056.8	+	71056.8i	−0.345979	+	0.345979i	0.512630	+	0.858609i	$0.328671\pi$
$60$		0			0
$61$	96379.6	−	96379.6i	0.424615	−	0.424615i	−0.462174	−	0.886789i	$-0.652930\pi$
$61$	96379.6	−	96379.6i	0.424615	−	0.424615i	0.886789	+	0.462174i	$0.152930\pi$
$62$		0			0
$63$		−	98133.1i		−	0.392459i
$64$		0			0
$65$	92112.0			0.335410
$66$		0			0
$67$	266382.	+	266382.i	0.885688	+	0.885688i	0.994105	−	0.108417i	$-0.0345783\pi$
$67$	266382.	+	266382.i	0.885688	+	0.885688i	−0.108417	+	0.994105i	$0.534578\pi$
$68$		0			0
$69$	45661.3	+	45661.3i	0.138996	+	0.138996i
$70$		0			0
$71$	−416772.			−1.16446			−0.582229	−	0.813025i	$-0.697819\pi$
$71$	−416772.			−1.16446			−0.582229	+	0.813025i	$0.697819\pi$
$72$		0			0
$73$		−	202516.i		−	0.520584i	−0.965530	−	0.260292i	$-0.916181\pi$
$73$		−	202516.i		−	0.520584i	0.965530	−	0.260292i	$-0.0838189\pi$
$74$		0			0
$75$	−156585.	+	156585.i	−0.371164	+	0.371164i
$76$		0			0
$77$	61656.4	−	61656.4i	0.135054	−	0.135054i
$78$		0			0
$79$		−	832723.i		−	1.68896i	−0.535588	−	0.844479i	$-0.679910\pi$
$79$		−	832723.i		−	1.68896i	0.535588	−	0.844479i	$-0.320090\pi$
$80$		0			0
$81$	−59049.0			−0.111111
$82$		0			0
$83$	157114.	+	157114.i	0.274777	+	0.274777i	0.831020	−	0.556243i	$-0.187757\pi$
$83$	157114.	+	157114.i	0.274777	+	0.274777i	−0.556243	+	0.831020i	$0.687757\pi$
$84$		0			0
$85$	2951.22	+	2951.22i	0.00480557	+	0.00480557i
$86$		0			0
$87$	−578837.			−0.879020
$88$		0			0
$89$			985026.i			1.39726i	0.715483	+	0.698631i	$0.246207\pi$
$89$			985026.i			1.39726i	−0.715483	+	0.698631i	$0.753793\pi$
$90$		0			0
$91$	−698184.	+	698184.i	−0.926500	+	0.926500i
$92$		0			0
$93$	170852.	−	170852.i	0.212409	−	0.212409i
$94$		0			0
$95$		−	175494.i		−	0.204688i
$96$		0			0
$97$	1.46802e6			1.60848			0.804239	−	0.594305i	$-0.202573\pi$
$97$	1.46802e6			1.60848			0.804239	+	0.594305i	$0.202573\pi$
$98$		0			0
$99$	−37100.1	−	37100.1i	−0.0382357	−	0.0382357i
$100$		0			0
$101$	653326.	+	653326.i	0.634112	+	0.634112i	0.949097	−	0.314985i	$-0.101999\pi$
$101$	653326.	+	653326.i	0.634112	+	0.634112i	−0.314985	+	0.949097i	$0.601999\pi$
$102$		0			0
$103$	697466.			0.638280			0.319140	−	0.947708i	$-0.396606\pi$
$103$	697466.			0.638280			0.319140	+	0.947708i	$0.396606\pi$
$104$		0			0
$105$			237167.i			0.204873i
$106$		0			0
$107$	−1.08466e6	+	1.08466e6i	−0.885408	+	0.885408i	−0.994078	−	0.108670i	$-0.965341\pi$
$107$	−1.08466e6	+	1.08466e6i	−0.885408	+	0.885408i	0.108670	+	0.994078i	$0.465341\pi$
$108$		0			0
$109$	−1.10911e6	+	1.10911e6i	−0.856434	+	0.856434i	−0.990916	−	0.134482i	$-0.957063\pi$
$109$	−1.10911e6	+	1.10911e6i	−0.856434	+	0.856434i	0.134482	+	0.990916i	$0.457063\pi$
$110$		0			0
$111$			922325.i			0.674396i
$112$		0			0
$113$	−383617.			−0.265866			−0.132933	−	0.991125i	$-0.542439\pi$
$113$	−383617.			−0.265866			−0.132933	+	0.991125i	$0.542439\pi$
$114$		0			0
$115$	−110354.	−	110354.i	−0.0725592	−	0.0725592i
$116$		0			0
$117$	420113.	+	420113.i	0.262306	+	0.262306i
$118$		0			0
$119$	−44738.8			−0.0265487
$120$		0			0
$121$			1.72494e6i			0.973685i
$122$		0			0
$123$	1.49168e6	−	1.49168e6i	0.801604	−	0.801604i
$124$		0			0
$125$	794674.	−	794674.i	0.406873	−	0.406873i
$126$		0			0
$127$			3.40598e6i			1.66277i	0.555699	+	0.831383i	$0.312451\pi$
$127$			3.40598e6i			1.66277i	−0.555699	+	0.831383i	$0.687549\pi$
$128$		0			0
$129$	563894.			0.262681
$130$		0			0
$131$	1.96163e6	+	1.96163e6i	0.872577	+	0.872577i	0.992753	−	0.120176i	$-0.0383458\pi$
$131$	1.96163e6	+	1.96163e6i	0.872577	+	0.872577i	−0.120176	+	0.992753i	$0.538346\pi$
$132$		0			0
$133$	1.33020e6	+	1.33020e6i	0.565406	+	0.565406i
$134$		0			0
$135$	142709.			0.0580028
$136$		0			0
$137$			3.22491e6i			1.25417i	0.778952	+	0.627084i	$0.215752\pi$
$137$			3.22491e6i			1.25417i	−0.778952	+	0.627084i	$0.784248\pi$
$138$		0			0
$139$	−2.53730e6	+	2.53730e6i	−0.944774	+	0.944774i	−0.998553	−	0.0537786i	$-0.982873\pi$
$139$	−2.53730e6	+	2.53730e6i	−0.944774	+	0.944774i	0.0537786	+	0.998553i	$0.482873\pi$
$140$		0			0
$141$	402679.	−	402679.i	0.143649	−	0.143649i
$142$		0			0
$143$			527909.i			0.180531i
$144$		0			0
$145$	1.39893e6			0.458871
$146$		0			0
$147$	−500848.	−	500848.i	−0.157672	−	0.157672i
$148$		0			0
$149$	2.49552e6	+	2.49552e6i	0.754400	+	0.754400i	0.975297	−	0.220897i	$-0.0708986\pi$
$149$	2.49552e6	+	2.49552e6i	0.754400	+	0.754400i	−0.220897	+	0.975297i	$0.570899\pi$
$150$		0			0
$151$	−6.26921e6			−1.82088			−0.910441	−	0.413640i	$-0.864257\pi$
$151$	−6.26921e6			−1.82088			−0.910441	+	0.413640i	$0.864257\pi$
$152$		0			0
$153$			26920.4i			0.00751635i
$154$		0			0
$155$	−412913.	+	412913.i	−0.110883	+	0.110883i
$156$		0			0
$157$	−2.79743e6	+	2.79743e6i	−0.722871	+	0.722871i	−0.969189	−	0.246318i	$-0.920779\pi$
$157$	−2.79743e6	+	2.79743e6i	−0.722871	+	0.722871i	0.246318	+	0.969189i	$0.420779\pi$
$158$		0			0
$159$			2.54234e6i			0.632474i
$160$		0			0
$161$	1.67290e6			0.400859
$162$		0			0
$163$	−4.03319e6	−	4.03319e6i	−0.931291	−	0.931291i	0.0664955	−	0.997787i	$-0.478818\pi$
$163$	−4.03319e6	−	4.03319e6i	−0.931291	−	0.931291i	−0.997787	+	0.0664955i	$0.978818\pi$
$164$		0			0
$165$	89662.9	+	89662.9i	0.0199600	+	0.0199600i
$166$		0			0
$167$	−1.19127e6			−0.255777			−0.127889	−	0.991789i	$-0.540820\pi$
$167$	−1.19127e6			−0.255777			−0.127889	+	0.991789i	$0.540820\pi$
$168$		0			0
$169$		−	1.15112e6i		−	0.238484i
$170$		0			0
$171$	800410.	−	800410.i	0.160075	−	0.160075i
$172$		0			0
$173$	4.28834e6	−	4.28834e6i	0.828230	−	0.828230i	−0.159042	−	0.987272i	$-0.550840\pi$
$173$	4.28834e6	−	4.28834e6i	0.828230	−	0.828230i	0.987272	+	0.159042i	$0.0508405\pi$
$174$		0			0
$175$			5.73682e6i			1.07043i
$176$		0			0
$177$	1.56648e6			0.282491
$178$		0			0
$179$	−6.40473e6	−	6.40473e6i	−1.11671	−	1.11671i	−0.992220	−	0.124494i	$-0.960269\pi$
$179$	−6.40473e6	−	6.40473e6i	−1.11671	−	1.11671i	−0.124494	−	0.992220i	$-0.539731\pi$
$180$		0			0
$181$	6.09230e6	+	6.09230e6i	1.02741	+	1.02741i	0.999613	+	0.0278011i	$0.00885050\pi$
$181$	6.09230e6	+	6.09230e6i	1.02741	+	1.02741i	0.0278011	+	0.999613i	$0.491150\pi$
$182$		0			0
$183$	−2.12473e6			−0.346697
$184$		0			0
$185$		−	2.22906e6i		−	0.352052i
$186$		0			0
$187$	−16913.9	+	16913.9i	−0.00258654	+	0.00258654i
$188$		0			0
$189$	−1.08169e6	+	1.08169e6i	−0.160221	+	0.160221i
$190$		0			0
$191$			2.73988e6i			0.393216i	0.980482	+	0.196608i	$0.0629927\pi$
$191$			2.73988e6i			0.393216i	−0.980482	+	0.196608i	$0.937007\pi$
$192$		0			0
$193$	−234810.			−0.0326622			−0.0163311	−	0.999867i	$-0.505199\pi$
$193$	−234810.			−0.0326622			−0.0163311	+	0.999867i	$0.505199\pi$
$194$		0			0
$195$	−1.01532e6	−	1.01532e6i	−0.136931	−	0.136931i
$196$		0			0
$197$	1.24528e6	+	1.24528e6i	0.162881	+	0.162881i	0.783842	−	0.620961i	$-0.213257\pi$
$197$	1.24528e6	+	1.24528e6i	0.162881	+	0.162881i	−0.620961	+	0.783842i	$0.713257\pi$
$198$		0			0
$199$	3.73945e6			0.474513			0.237257	−	0.971447i	$-0.423752\pi$
$199$	3.73945e6			0.474513			0.237257	+	0.971447i	$0.423752\pi$
$200$		0			0
$201$		−	5.87250e6i		−	0.723161i
$202$		0			0
$203$	−1.06035e7	+	1.06035e7i	−1.26753	+	1.26753i
$204$		0			0
$205$	−3.60507e6	+	3.60507e6i	−0.418458	+	0.418458i
$206$		0			0
$207$		−	1.00662e6i		−	0.113489i
$208$		0			0
$209$	1.00578e6			0.110171
$210$		0			0
$211$	3.39522e6	+	3.39522e6i	0.361427	+	0.361427i	0.864338	−	0.502911i	$-0.167738\pi$
$211$	3.39522e6	+	3.39522e6i	0.361427	+	0.361427i	−0.502911	+	0.864338i	$0.667738\pi$
$212$		0			0
$213$	4.59396e6	+	4.59396e6i	0.475388	+	0.475388i
$214$		0			0
$215$	−1.36281e6			−0.137126
$216$		0			0
$217$		−	6.25954e6i		−	0.612580i
$218$		0			0
$219$	−2.23228e6	+	2.23228e6i	−0.212528	+	0.212528i
$220$		0			0
$221$	191529.	−	191529.i	0.0177443	−	0.0177443i
$222$		0			0
$223$			1.00504e7i			0.906295i	0.891435	+	0.453148i	$0.149699\pi$
$223$			1.00504e7i			0.906295i	−0.891435	+	0.453148i	$0.850301\pi$
$224$		0			0
$225$	3.45198e6			0.303054
$226$		0			0
$227$	3.03181e6	+	3.03181e6i	0.259194	+	0.259194i	0.824726	−	0.565532i	$-0.191329\pi$
$227$	3.03181e6	+	3.03181e6i	0.259194	+	0.259194i	−0.565532	+	0.824726i	$0.691329\pi$
$228$		0			0
$229$	−449030.	−	449030.i	−0.0373911	−	0.0373911i	0.688164	−	0.725555i	$-0.258417\pi$
$229$	−449030.	−	449030.i	−0.0373911	−	0.0373911i	−0.725555	+	0.688164i	$0.758417\pi$
$230$		0			0
$231$	−1.35924e6			−0.110271
$232$		0			0
$233$			1.61678e7i			1.27816i	0.769142	+	0.639078i	$0.220684\pi$
$233$			1.61678e7i			1.27816i	−0.769142	+	0.639078i	$0.779316\pi$
$234$		0			0
$235$	−973188.	+	973188.i	−0.0749882	+	0.0749882i
$236$		0			0
$237$	−9.17885e6	+	9.17885e6i	−0.689515	+	0.689515i
$238$		0			0
$239$		−	1.69324e7i		−	1.24029i	−0.784486	−	0.620146i	$-0.787073\pi$
$239$		−	1.69324e7i		−	1.24029i	0.784486	−	0.620146i	$-0.212927\pi$
$240$		0			0
$241$	−6.23137e6			−0.445177			−0.222588	−	0.974913i	$-0.571451\pi$
$241$	−6.23137e6			−0.445177			−0.222588	+	0.974913i	$0.571451\pi$
$242$		0			0
$243$	650880.	+	650880.i	0.0453609	+	0.0453609i
$244$		0			0
$245$	1.21044e6	+	1.21044e6i	0.0823086	+	0.0823086i
$246$		0			0
$247$	−1.13893e7			−0.755798
$248$		0			0
$249$		−	3.46364e6i		−	0.224355i
$250$		0			0
$251$	−2.89165e6	+	2.89165e6i	−0.182863	+	0.182863i	−0.792602	−	0.609739i	$-0.791274\pi$
$251$	−2.89165e6	+	2.89165e6i	−0.182863	+	0.182863i	0.609739	+	0.792602i	$0.291274\pi$
$252$		0			0
$253$	632454.	−	632454.i	0.0390542	−	0.0390542i
$254$		0			0
$255$		−	65060.8i		−	0.00392373i
$256$		0			0
$257$	3.03086e6			0.178552			0.0892762	−	0.996007i	$-0.471545\pi$
$257$	3.03086e6			0.178552			0.0892762	+	0.996007i	$0.471545\pi$
$258$		0			0
$259$	1.68957e7	+	1.68957e7i	0.972469	+	0.972469i
$260$		0			0
$261$	6.38035e6	+	6.38035e6i	0.358858	+	0.358858i
$262$		0			0
$263$	1.28970e7			0.708958			0.354479	−	0.935064i	$-0.384658\pi$
$263$	1.28970e7			0.708958			0.354479	+	0.935064i	$0.384658\pi$
$264$		0			0
$265$		−	6.14430e6i		−	0.330168i
$266$		0			0
$267$	1.08576e7	−	1.08576e7i	0.570430	−	0.570430i
$268$		0			0
$269$	1.99946e7	−	1.99946e7i	1.02720	−	1.02720i	0.0275804	−	0.999620i	$-0.491220\pi$
$269$	1.99946e7	−	1.99946e7i	1.02720	−	1.02720i	0.999620	−	0.0275804i	$-0.00878022\pi$
$270$		0			0
$271$			1.61595e7i			0.811935i	0.913887	+	0.405968i	$0.133065\pi$
$271$			1.61595e7i			0.811935i	−0.913887	+	0.405968i	$0.866935\pi$
$272$		0			0
$273$	1.53917e7			0.756484
$274$		0			0
$275$	2.16886e6	+	2.16886e6i	0.104288	+	0.104288i
$276$		0			0
$277$	−2.71035e7	−	2.71035e7i	−1.27522	−	1.27522i	−0.943311	−	0.331911i	$-0.892307\pi$
$277$	−2.71035e7	−	2.71035e7i	−1.27522	−	1.27522i	−0.331911	−	0.943311i	$-0.607693\pi$
$278$		0			0
$279$	−3.76651e6			−0.173431
$280$		0			0
$281$			2.50197e7i			1.12762i	0.825905	+	0.563810i	$0.190665\pi$
$281$			2.50197e7i			1.12762i	−0.825905	+	0.563810i	$0.809335\pi$
$282$		0			0
$283$	1.99085e7	−	1.99085e7i	0.878376	−	0.878376i	−0.114991	−	0.993367i	$-0.536684\pi$
$283$	1.99085e7	−	1.99085e7i	0.878376	−	0.878376i	0.993367	+	0.114991i	$0.0366839\pi$
$284$		0			0
$285$	−1.93442e6	+	1.93442e6i	−0.0835633	+	0.0835633i
$286$		0			0
$287$		−	5.46508e7i		−	2.31180i
$288$		0			0
$289$	−2.41253e7			−0.999492
$290$		0			0
$291$	−1.61815e7	−	1.61815e7i	−0.656659	−	0.656659i
$292$		0			0
$293$	−1.84063e7	−	1.84063e7i	−0.731750	−	0.731750i	0.239216	−	0.970966i	$-0.423110\pi$
$293$	−1.84063e7	−	1.84063e7i	−0.731750	−	0.731750i	−0.970966	+	0.239216i	$0.923110\pi$
$294$		0			0
$295$	−3.78583e6			−0.147467
$296$		0			0
$297$			817887.i			0.0312193i
$298$		0			0
$299$	−7.16177e6	+	7.16177e6i	−0.267921	+	0.267921i
$300$		0			0
$301$	1.03297e7	−	1.03297e7i	0.378782	−	0.378782i
$302$		0			0
$303$		−	1.44028e7i		−	0.517750i
$304$		0			0
$305$	5.13501e6			0.180985
$306$		0			0
$307$	8.59455e6	+	8.59455e6i	0.297035	+	0.297035i	0.839852	−	0.542816i	$-0.182642\pi$
$307$	8.59455e6	+	8.59455e6i	0.297035	+	0.297035i	−0.542816	+	0.839852i	$0.682642\pi$
$308$		0			0
$309$	−7.68796e6	−	7.68796e6i	−0.260577	−	0.260577i
$310$		0			0
$311$	2.28440e7			0.759436			0.379718	−	0.925102i	$-0.376021\pi$
$311$	2.28440e7			0.759436			0.379718	+	0.925102i	$0.376021\pi$
$312$		0			0
$313$			3.00742e7i			0.980755i	0.871510	+	0.490377i	$0.163141\pi$
$313$			3.00742e7i			0.980755i	−0.871510	+	0.490377i	$0.836859\pi$
$314$		0			0
$315$	2.61422e6	−	2.61422e6i	0.0836393	−	0.0836393i
$316$		0			0
$317$	−6.07210e6	+	6.07210e6i	−0.190617	+	0.190617i	−0.795963	−	0.605346i	$-0.793035\pi$
$317$	−6.07210e6	+	6.07210e6i	−0.190617	+	0.190617i	0.605346	+	0.795963i	$0.293035\pi$
$318$		0			0
$319$			8.01747e6i			0.246982i
$320$		0			0
$321$	2.39118e7			0.722933
$322$		0			0
$323$	−364906.	−	364906.i	−0.0108286	−	0.0108286i
$324$		0			0
$325$	−2.45596e7	−	2.45596e7i	−0.715438	−	0.715438i
$326$		0			0
$327$	2.44507e7			0.699275
$328$		0			0
$329$		−	1.47530e7i		−	0.414278i
$330$		0			0
$331$	9.24350e6	−	9.24350e6i	0.254890	−	0.254890i	−0.568082	−	0.822972i	$-0.692314\pi$
$331$	9.24350e6	−	9.24350e6i	0.254890	−	0.254890i	0.822972	+	0.568082i	$0.192314\pi$
$332$		0			0
$333$	1.01665e7	−	1.01665e7i	0.275321	−	0.275321i
$334$		0			0
$335$			1.41926e7i			0.377509i
$336$		0			0
$337$	−6.00061e7			−1.56785			−0.783927	−	0.620853i	$-0.786786\pi$
$337$	−6.00061e7			−1.56785			−0.783927	+	0.620853i	$0.786786\pi$
$338$		0			0
$339$	4.22850e6	+	4.22850e6i	0.108539	+	0.108539i
$340$		0			0
$341$	−2.36647e6	−	2.36647e6i	−0.0596813	−	0.0596813i
$342$		0			0
$343$	2.91618e7			0.722656
$344$		0			0
$345$			2.43279e6i			0.0592444i
$346$		0			0
$347$	4.30217e7	−	4.30217e7i	1.02967	−	1.02967i	0.0301258	−	0.999546i	$-0.490409\pi$
$347$	4.30217e7	−	4.30217e7i	1.02967	−	1.02967i	0.999546	−	0.0301258i	$-0.00959080\pi$
$348$		0			0
$349$	−2.63834e7	+	2.63834e7i	−0.620662	+	0.620662i	−0.945701	−	0.325039i	$-0.894623\pi$
$349$	−2.63834e7	+	2.63834e7i	−0.620662	+	0.620662i	0.325039	+	0.945701i	$0.394623\pi$
$350$		0			0
$351$		−	9.26157e6i		−	0.214172i
$352$		0			0
$353$	−2.69154e7			−0.611894			−0.305947	−	0.952049i	$-0.598973\pi$
$353$	−2.69154e7			−0.611894			−0.305947	+	0.952049i	$0.598973\pi$
$354$		0			0
$355$	−1.11026e7	−	1.11026e7i	−0.248165	−	0.248165i
$356$		0			0
$357$	493143.	+	493143.i	0.0108385	+	0.0108385i
$358$		0			0
$359$	1.32413e7			0.286185			0.143092	−	0.989709i	$-0.454295\pi$
$359$	1.32413e7			0.286185			0.143092	+	0.989709i	$0.454295\pi$
$360$		0			0
$361$		−	2.53468e7i		−	0.538767i
$362$		0			0
$363$	1.90135e7	−	1.90135e7i	0.397505	−	0.397505i
$364$		0			0
$365$	5.39493e6	−	5.39493e6i	0.110945	−	0.110945i
$366$		0			0
$367$			1.01398e7i			0.205131i	0.994726	+	0.102566i	$0.0327052\pi$
$367$			1.01398e7i			0.205131i	−0.994726	+	0.102566i	$0.967295\pi$
$368$		0			0
$369$	−3.28847e7			−0.654507
$370$		0			0
$371$	4.65721e7	+	4.65721e7i	0.912019	+	0.912019i
$372$		0			0
$373$	−2.01133e7	−	2.01133e7i	−0.387577	−	0.387577i	0.486245	−	0.873822i	$-0.338366\pi$
$373$	−2.01133e7	−	2.01133e7i	−0.387577	−	0.387577i	−0.873822	+	0.486245i	$0.838366\pi$
$374$		0			0
$375$	−1.75189e7			−0.332211
$376$		0			0
$377$		−	9.07880e7i		−	1.69436i
$378$		0			0
$379$	−5.39896e7	+	5.39896e7i	−0.991728	+	0.991728i	−0.999966	−	0.00823775i	$-0.997378\pi$
$379$	−5.39896e7	+	5.39896e7i	−0.991728	+	0.991728i	0.00823775	+	0.999966i	$0.497378\pi$
$380$		0			0
$381$	3.75431e7	−	3.75431e7i	0.678822	−	0.678822i
$382$		0			0
$383$		−	1.00149e8i		−	1.78258i	−0.453436	−	0.891289i	$-0.649802\pi$
$383$		−	1.00149e8i		−	1.78258i	0.453436	−	0.891289i	$-0.350198\pi$
$384$		0			0
$385$	3.28499e6			0.0575642
$386$		0			0
$387$	−6.21564e6	−	6.21564e6i	−0.107239	−	0.107239i
$388$		0			0
$389$	−513308.	−	513308.i	−0.00872025	−	0.00872025i	0.702733	−	0.711453i	$-0.251963\pi$
$389$	−513308.	−	513308.i	−0.00872025	−	0.00872025i	−0.711453	+	0.702733i	$0.751963\pi$
$390$		0			0
$391$	−458918.			−0.00767724
$392$		0			0
$393$		−	4.32450e7i		−	0.712456i
$394$		0			0
$395$	2.21833e7	−	2.21833e7i	0.359944	−	0.359944i
$396$		0			0
$397$	−7.43291e7	+	7.43291e7i	−1.18792	+	1.18792i	−0.210280	+	0.977641i	$0.567437\pi$
$397$	−7.43291e7	+	7.43291e7i	−1.18792	+	1.18792i	−0.977641	+	0.210280i	$0.932563\pi$
$398$		0			0
$399$		−	2.93247e7i		−	0.461652i
$400$		0			0
$401$	4.28921e6			0.0665187			0.0332594	−	0.999447i	$-0.489411\pi$
$401$	4.28921e6			0.0665187			0.0332594	+	0.999447i	$0.489411\pi$
$402$		0			0
$403$	2.67974e7	+	2.67974e7i	0.409428	+	0.409428i
$404$		0			0
$405$	−1.57304e6	−	1.57304e6i	−0.0236796	−	0.0236796i
$406$		0			0
$407$	1.27751e7			0.189488
$408$		0			0
$409$		−	7.90997e7i		−	1.15613i	−0.815992	−	0.578063i	$-0.803809\pi$
$409$		−	7.90997e7i		−	1.15613i	0.815992	−	0.578063i	$-0.196191\pi$
$410$		0			0
$411$	3.55472e7	−	3.55472e7i	0.512012	−	0.512012i
$412$		0			0
$413$	2.86956e7	−	2.86956e7i	0.407347	−	0.407347i
$414$		0			0
$415$			8.37088e6i			0.117119i
$416$		0			0
$417$	5.59359e7			0.771405
$418$		0			0
$419$	−9.85115e7	−	9.85115e7i	−1.33920	−	1.33920i	−0.896837	−	0.442361i	$-0.854141\pi$
$419$	−9.85115e7	−	9.85115e7i	−1.33920	−	1.33920i	−0.442361	−	0.896837i	$-0.645859\pi$
$420$		0			0
$421$	8.68766e6	+	8.68766e6i	0.116428	+	0.116428i	0.762920	−	0.646493i	$-0.223765\pi$
$421$	8.68766e6	+	8.68766e6i	0.116428	+	0.116428i	−0.646493	+	0.762920i	$0.723765\pi$
$422$		0			0
$423$	−8.87722e6			−0.117289
$424$		0			0
$425$		−	1.57375e6i		−	0.0205008i
$426$		0			0
$427$	−3.89219e7	+	3.89219e7i	−0.499932	+	0.499932i
$428$		0			0
$429$	5.81898e6	−	5.81898e6i	0.0737013	−	0.0737013i
$430$		0			0
$431$			9.13408e7i			1.14086i	0.821346	+	0.570431i	$0.193224\pi$
$431$			9.13408e7i			1.14086i	−0.821346	+	0.570431i	$0.806776\pi$
$432$		0			0
$433$	−5.70687e7			−0.702965			−0.351483	−	0.936194i	$-0.614322\pi$
$433$	−5.70687e7			−0.702965			−0.351483	+	0.936194i	$0.614322\pi$
$434$		0			0
$435$	−1.54199e7	−	1.54199e7i	−0.187333	−	0.187333i
$436$		0			0
$437$	1.36448e7	+	1.36448e7i	0.163502	+	0.163502i
$438$		0			0
$439$	−1.29673e7			−0.153269			−0.0766347	−	0.997059i	$-0.524418\pi$
$439$	−1.29673e7			−0.153269			−0.0766347	+	0.997059i	$0.524418\pi$
$440$		0			0
$441$			1.10414e7i			0.128738i
$442$		0			0
$443$	4.74461e7	−	4.74461e7i	0.545745	−	0.545745i	−0.379462	−	0.925207i	$-0.623891\pi$
$443$	4.74461e7	−	4.74461e7i	0.545745	−	0.545745i	0.925207	+	0.379462i	$0.123891\pi$
$444$		0			0
$445$	−2.62406e7	+	2.62406e7i	−0.297779	+	0.297779i
$446$		0			0
$447$		−	5.50147e7i		−	0.615965i
$448$		0			0
$449$	3.70427e7			0.409226			0.204613	−	0.978843i	$-0.434406\pi$
$449$	3.70427e7			0.409226			0.204613	+	0.978843i	$0.434406\pi$
$450$		0			0
$451$	−2.06612e7	−	2.06612e7i	−0.225230	−	0.225230i
$452$		0			0
$453$	6.91036e7	+	6.91036e7i	0.743372	+	0.743372i
$454$		0			0
$455$	−3.71985e7			−0.394904
$456$		0			0
$457$		−	7.63145e7i		−	0.799573i	−0.916608	−	0.399787i	$-0.869084\pi$
$457$		−	7.63145e7i		−	0.799573i	0.916608	−	0.399787i	$-0.130916\pi$
$458$		0			0
$459$	296736.	−	296736.i	0.00306854	−	0.00306854i
$460$		0			0
$461$	2.82948e7	−	2.82948e7i	0.288804	−	0.288804i	−0.547803	−	0.836607i	$-0.684536\pi$
$461$	2.82948e7	−	2.82948e7i	0.288804	−	0.288804i	0.836607	+	0.547803i	$0.184536\pi$
$462$		0			0
$463$			1.01789e8i			1.02555i	0.858523	+	0.512776i	$0.171383\pi$
$463$			1.01789e8i			1.02555i	−0.858523	+	0.512776i	$0.828617\pi$
$464$		0			0
$465$	9.10284e6			0.0905353
$466$		0			0
$467$	−9.43637e7	−	9.43637e7i	−0.926519	−	0.926519i	0.0709599	−	0.997479i	$-0.477394\pi$
$467$	−9.43637e7	−	9.43637e7i	−0.926519	−	0.926519i	−0.997479	+	0.0709599i	$0.977394\pi$
$468$		0			0
$469$	−1.07576e8	−	1.07576e8i	−1.04279	−	1.04279i
$470$		0			0
$471$	6.16705e7			0.590221
$472$		0			0
$473$		−	7.81049e6i		−	0.0738066i
$474$		0			0
$475$	−4.67916e7	+	4.67916e7i	−0.436603	+	0.436603i
$476$		0			0
$477$	2.80235e7	−	2.80235e7i	0.258206	−	0.258206i
$478$		0			0
$479$			1.11086e8i			1.01077i	0.862893	+	0.505387i	$0.168650\pi$
$479$			1.11086e8i			1.01077i	−0.862893	+	0.505387i	$0.831350\pi$
$480$		0			0
$481$	−1.44662e8			−1.29993
$482$		0			0
$483$	−1.84399e7	−	1.84399e7i	−0.163650	−	0.163650i
$484$		0			0
$485$	3.91072e7	+	3.91072e7i	0.342793	+	0.342793i
$486$		0			0
$487$	1.62475e8			1.40669			0.703347	−	0.710846i	$-0.251688\pi$
$487$	1.62475e8			1.40669			0.703347	+	0.710846i	$0.251688\pi$
$488$		0			0
$489$			8.89132e7i			0.760396i
$490$		0			0
$491$	1.59056e8	−	1.59056e8i	1.34371	−	1.34371i	0.451379	−	0.892332i	$-0.350932\pi$
$491$	1.59056e8	−	1.59056e8i	1.34371	−	1.34371i	0.892332	−	0.451379i	$-0.149068\pi$
$492$		0			0
$493$	2.90880e6	−	2.90880e6i	0.0242758	−	0.0242758i
$494$		0			0
$495$		−	1.97666e6i		−	0.0162973i
$496$		0			0
$497$	1.68309e8			1.37101
$498$		0			0
$499$	1.52626e8	+	1.52626e8i	1.22836	+	1.22836i	0.964583	+	0.263778i	$0.0849686\pi$
$499$	1.52626e8	+	1.52626e8i	1.22836	+	1.22836i	0.263778	+	0.964583i	$0.415031\pi$
$500$		0			0
$501$	1.31311e7	+	1.31311e7i	0.104421	+	0.104421i
$502$		0			0
$503$	−2.80504e7			−0.220412			−0.110206	−	0.993909i	$-0.535151\pi$
$503$	−2.80504e7			−0.220412			−0.110206	+	0.993909i	$0.535151\pi$
$504$		0			0
$505$			3.48086e7i			0.270279i
$506$		0			0
$507$	−1.26884e7	+	1.26884e7i	−0.0973605	+	0.0973605i
$508$		0			0
$509$	−1.33201e8	+	1.33201e8i	−1.01008	+	1.01008i	−0.0101280	+	0.999949i	$0.503224\pi$
$509$	−1.33201e8	+	1.33201e8i	−1.01008	+	1.01008i	−0.999949	+	0.0101280i	$0.996776\pi$
$510$		0			0
$511$			8.17841e7i			0.612924i
$512$		0			0
$513$	−1.76454e7			−0.130701
$514$		0			0
$515$	1.85801e7	+	1.85801e7i	0.136028	+	0.136028i
$516$		0			0
$517$	−5.57750e6	−	5.57750e6i	−0.0403615	−	0.0403615i
$518$		0			0
$519$	−9.45382e7			−0.676247
$520$		0			0
$521$			1.63500e8i			1.15612i	0.815993	+	0.578061i	$0.196191\pi$
$521$			1.63500e8i			1.15612i	−0.815993	+	0.578061i	$0.803809\pi$
$522$		0			0
$523$	−1.51209e8	+	1.51209e8i	−1.05700	+	1.05700i	−0.0587229	+	0.998274i	$0.518703\pi$
$523$	−1.51209e8	+	1.51209e8i	−1.05700	+	1.05700i	−0.998274	+	0.0587229i	$0.981297\pi$
$524$		0			0
$525$	6.32353e7	−	6.32353e7i	0.437000	−	0.437000i
$526$		0			0
$527$			1.71715e6i			0.0117321i
$528$		0			0
$529$	−1.30876e8			−0.884081
$530$		0			0
$531$	−1.72668e7	−	1.72668e7i	−0.115326	−	0.115326i
$532$		0			0
$533$	2.33963e8	+	2.33963e8i	1.54513	+	1.54513i
$534$		0			0
$535$	−5.77898e7			−0.377389
$536$		0			0
$537$			1.41195e8i			0.911793i
$538$		0			0
$539$	−6.93723e6	+	6.93723e6i	−0.0443017	+	0.0443017i
$540$		0			0
$541$	−3.15433e7	+	3.15433e7i	−0.199212	+	0.199212i	−0.799662	−	0.600450i	$-0.794988\pi$
$541$	−3.15433e7	+	3.15433e7i	−0.199212	+	0.199212i	0.600450	+	0.799662i	$0.294988\pi$
$542$		0			0
$543$		−	1.34307e8i		−	0.838880i
$544$		0			0
$545$	−5.90921e7			−0.365040
$546$		0			0
$547$	6.10938e7	+	6.10938e7i	0.373280	+	0.373280i	0.868671	−	0.495390i	$-0.164975\pi$
$547$	6.10938e7	+	6.10938e7i	0.373280	+	0.373280i	−0.495390	+	0.868671i	$0.664975\pi$
$548$		0			0
$549$	2.34202e7	+	2.34202e7i	0.141538	+	0.141538i
$550$		0			0
$551$	−1.72971e8			−1.03400
$552$		0			0
$553$			3.36287e8i			1.98854i
$554$		0			0
$555$	−2.45703e7	+	2.45703e7i	−0.143725	+	0.143725i
$556$		0			0
$557$	3.82316e7	−	3.82316e7i	0.221236	−	0.221236i	−0.587783	−	0.809019i	$-0.699999\pi$
$557$	3.82316e7	−	3.82316e7i	0.221236	−	0.221236i	0.809019	+	0.587783i	$0.199999\pi$
$558$		0			0
$559$			8.84443e7i			0.506331i
$560$		0			0
$561$	372874.			0.00211190
$562$		0			0
$563$	−1.98038e7	−	1.98038e7i	−0.110974	−	0.110974i	0.649439	−	0.760414i	$-0.275004\pi$
$563$	−1.98038e7	−	1.98038e7i	−0.110974	−	0.110974i	−0.760414	+	0.649439i	$0.775004\pi$
$564$		0			0
$565$	−1.02194e7	−	1.02194e7i	−0.0566603	−	0.0566603i
$566$		0			0
$567$	2.38464e7			0.130820
$568$		0			0
$569$		−	3.17667e8i		−	1.72439i	−0.506578	−	0.862194i	$-0.669090\pi$
$569$		−	3.17667e8i		−	1.72439i	0.506578	−	0.862194i	$-0.330910\pi$
$570$		0			0
$571$	1.14822e7	−	1.14822e7i	0.0616759	−	0.0616759i	−0.675596	−	0.737272i	$-0.736114\pi$
$571$	1.14822e7	−	1.14822e7i	0.0616759	−	0.0616759i	0.737272	+	0.675596i	$0.236114\pi$
$572$		0			0
$573$	3.02009e7	−	3.02009e7i	0.160530	−	0.160530i
$574$		0			0
$575$			5.88467e7i			0.309541i
$576$		0			0
$577$	2.85865e8			1.48810			0.744052	−	0.668122i	$-0.232902\pi$
$577$	2.85865e8			1.48810			0.744052	+	0.668122i	$0.232902\pi$
$578$		0			0
$579$	2.58824e6	+	2.58824e6i	0.0133343	+	0.0133343i
$580$		0			0
$581$	−6.34490e7	−	6.34490e7i	−0.323516	−	0.323516i
$582$		0			0
$583$	3.52140e7			0.177709
$584$		0			0
$585$			2.23832e7i			0.111803i
$586$		0			0
$587$	−1.94525e8	+	1.94525e8i	−0.961749	+	0.961749i	−0.999295	−	0.0375461i	$-0.988046\pi$
$587$	−1.94525e8	+	1.94525e8i	−0.961749	+	0.961749i	0.0375461	+	0.999295i	$0.488046\pi$
$588$		0			0
$589$	5.10551e7	−	5.10551e7i	0.249858	−	0.249858i
$590$		0			0
$591$		−	2.74528e7i		−	0.132991i
$592$		0			0
$593$	3.72075e8			1.78429			0.892147	−	0.451745i	$-0.149198\pi$
$593$	3.72075e8			1.78429			0.892147	+	0.451745i	$0.149198\pi$
$594$		0			0
$595$	−1.19182e6	−	1.19182e6i	−0.00565796	−	0.00565796i
$596$		0			0
$597$	−4.12188e7	−	4.12188e7i	−0.193719	−	0.193719i
$598$		0			0
$599$	−2.67399e8			−1.24417			−0.622084	−	0.782951i	$-0.713714\pi$
$599$	−2.67399e8			−1.24417			−0.622084	+	0.782951i	$0.713714\pi$
$600$		0			0
$601$			1.80794e8i			0.832836i	0.909173	+	0.416418i	$0.136715\pi$
$601$			1.80794e8i			0.832836i	−0.909173	+	0.416418i	$0.863285\pi$
$602$		0			0
$603$	−6.47309e7	+	6.47309e7i	−0.295229	+	0.295229i
$604$		0			0
$605$	−4.59516e7	+	4.59516e7i	−0.207508	+	0.207508i
$606$		0			0
$607$			5.44539e7i			0.243480i	0.992562	+	0.121740i	$0.0388473\pi$
$607$			5.44539e7i			0.243480i	−0.992562	+	0.121740i	$0.961153\pi$
$608$		0			0
$609$	2.33758e8			1.03494
$610$		0			0
$611$	6.31583e7	+	6.31583e7i	0.276890	+	0.276890i
$612$		0			0
$613$	2.02723e7	+	2.02723e7i	0.0880079	+	0.0880079i	0.749740	−	0.661732i	$-0.230178\pi$
$613$	2.02723e7	+	2.02723e7i	0.0880079	+	0.0880079i	−0.661732	+	0.749740i	$0.730178\pi$
$614$		0			0
$615$	7.94752e7			0.341669
$616$		0			0
$617$			1.68371e8i			0.716821i	0.933564	+	0.358410i	$0.116681\pi$
$617$			1.68371e8i			0.716821i	−0.933564	+	0.358410i	$0.883319\pi$
$618$		0			0
$619$	−2.13535e8	+	2.13535e8i	−0.900319	+	0.900319i	−0.995463	−	0.0951444i	$-0.969669\pi$
$619$	−2.13535e8	+	2.13535e8i	−0.900319	+	0.900319i	0.0951444	+	0.995463i	$0.469669\pi$
$620$		0			0
$621$	−1.10957e7	+	1.10957e7i	−0.0463319	+	0.0463319i
$622$		0			0
$623$		−	3.97793e8i		−	1.64510i
$624$		0			0
$625$	−1.79624e8			−0.735741
$626$		0			0
$627$	−1.10865e7	−	1.10865e7i	−0.0449770	−	0.0449770i
$628$		0			0
$629$	−4.63491e6	−	4.63491e6i	−0.0186247	−	0.0186247i
$630$		0			0
$631$	−3.27286e8			−1.30269			−0.651343	−	0.758783i	$-0.725794\pi$
$631$	−3.27286e8			−1.30269			−0.651343	+	0.758783i	$0.725794\pi$
$632$		0			0
$633$		−	7.48489e7i		−	0.295104i
$634$		0			0
$635$	−9.07337e7	+	9.07337e7i	−0.354362	+	0.354362i
$636$		0			0
$637$	7.85557e7	−	7.85557e7i	0.303920	−	0.303920i
$638$		0			0
$639$		−	1.01276e8i		−	0.388153i
$640$		0			0
$641$	3.54495e8			1.34597			0.672986	−	0.739655i	$-0.265011\pi$
$641$	3.54495e8			1.34597			0.672986	+	0.739655i	$0.265011\pi$
$642$		0			0
$643$	2.20361e8	+	2.20361e8i	0.828898	+	0.828898i	0.987364	−	0.158466i	$-0.0506548\pi$
$643$	2.20361e8	+	2.20361e8i	0.828898	+	0.828898i	−0.158466	+	0.987364i	$0.550655\pi$
$644$		0			0
$645$	1.50219e7	+	1.50219e7i	0.0559815	+	0.0559815i
$646$		0			0
$647$	2.98046e8			1.10045			0.550225	−	0.835017i	$-0.314542\pi$
$647$	2.98046e8			1.10045			0.550225	+	0.835017i	$0.314542\pi$
$648$		0			0
$649$		−	2.16972e7i		−	0.0793725i
$650$		0			0
$651$	−6.89970e7	+	6.89970e7i	−0.250085	+	0.250085i
$652$		0			0
$653$	4.46026e7	−	4.46026e7i	0.160185	−	0.160185i	−0.622464	−	0.782648i	$-0.713868\pi$
$653$	4.46026e7	−	4.46026e7i	0.160185	−	0.160185i	0.782648	+	0.622464i	$0.213868\pi$
$654$		0			0
$655$			1.04514e8i			0.371920i
$656$		0			0
$657$	4.92114e7			0.173528
$658$		0			0
$659$	1.68168e8	+	1.68168e8i	0.587607	+	0.587607i	0.936983	−	0.349375i	$-0.113606\pi$
$659$	1.68168e8	+	1.68168e8i	0.587607	+	0.587607i	−0.349375	+	0.936983i	$0.613606\pi$
$660$		0			0
$661$	−9.57897e7	−	9.57897e7i	−0.331676	−	0.331676i	0.521547	−	0.853223i	$-0.325355\pi$
$661$	−9.57897e7	−	9.57897e7i	−0.331676	−	0.331676i	−0.853223	+	0.521547i	$0.825355\pi$
$662$		0			0
$663$	−4.22234e6			−0.0144882
$664$		0			0
$665$			7.08715e7i			0.240994i
$666$		0			0
$667$	−1.08767e8	+	1.08767e8i	−0.366540	+	0.366540i
$668$		0			0
$669$	1.10783e8	−	1.10783e8i	0.369993	−	0.369993i
$670$		0			0
$671$			2.94296e7i			0.0974129i
$672$		0			0
$673$	−3.40113e8			−1.11578			−0.557889	−	0.829916i	$-0.688389\pi$
$673$	−3.40113e8			−1.11578			−0.557889	+	0.829916i	$0.688389\pi$
$674$		0			0
$675$	−3.80501e7	−	3.80501e7i	−0.123721	−	0.123721i
$676$		0			0
$677$	3.07721e8	+	3.07721e8i	0.991724	+	0.991724i	0.999966	−	0.00824207i	$-0.00262356\pi$
$677$	3.07721e8	+	3.07721e8i	0.991724	+	0.991724i	−0.00824207	+	0.999966i	$0.502624\pi$
$678$		0			0
$679$	−5.92843e8			−1.89379
$680$		0			0
$681$		−	6.68375e7i		−	0.211631i
$682$		0			0
$683$	3.12833e7	−	3.12833e7i	0.0981862	−	0.0981862i	−0.656307	−	0.754494i	$-0.727883\pi$
$683$	3.12833e7	−	3.12833e7i	0.0981862	−	0.0981862i	0.754494	+	0.656307i	$0.227883\pi$
$684$		0			0
$685$	−8.59099e7	+	8.59099e7i	−0.267283	+	0.267283i
$686$		0			0
$687$			9.89905e6i			0.0305297i
$688$		0			0
$689$	−3.98755e8			−1.21913
$690$		0			0
$691$	−3.09028e8	−	3.09028e8i	−0.936620	−	0.936620i	0.0614883	−	0.998108i	$-0.480415\pi$
$691$	−3.09028e8	−	3.09028e8i	−0.936620	−	0.936620i	−0.998108	+	0.0614883i	$0.980415\pi$
$692$		0			0
$693$	1.49825e7	+	1.49825e7i	0.0450179	+	0.0450179i
$694$		0			0
$695$	−1.35185e8			−0.402693
$696$		0			0
$697$			1.49921e7i			0.0442756i
$698$		0			0
$699$	1.78213e8	−	1.78213e8i	0.521805	−	0.521805i
$700$		0			0
$701$	−2.16593e8	+	2.16593e8i	−0.628767	+	0.628767i	−0.947758	−	0.318991i	$-0.896656\pi$
$701$	−2.16593e8	+	2.16593e8i	−0.628767	+	0.628767i	0.318991	+	0.947758i	$0.396656\pi$
$702$		0			0
$703$			2.75614e8i			0.793297i
$704$		0			0
$705$	2.14543e7			0.0612276
$706$		0			0
$707$	−2.63839e8	−	2.63839e8i	−0.746589	−	0.746589i
$708$		0			0
$709$	3.07048e8	+	3.07048e8i	0.861524	+	0.861524i	0.991515	−	0.129991i	$-0.0414948\pi$
$709$	3.07048e8	+	3.07048e8i	0.861524	+	0.861524i	−0.129991	+	0.991515i	$0.541495\pi$
$710$		0			0
$711$	2.02352e8			0.562986
$712$		0			0
$713$		−	6.42085e7i		−	0.177143i
$714$		0			0
$715$	−1.40632e7	+	1.40632e7i	−0.0384740	+	0.0384740i
$716$		0			0
$717$	−1.86641e8	+	1.86641e8i	−0.506347	+	0.506347i
$718$		0			0
$719$			3.88723e8i			1.04581i	0.852390	+	0.522906i	$0.175152\pi$
$719$			3.88723e8i			1.04581i	−0.852390	+	0.522906i	$0.824848\pi$
$720$		0			0
$721$	−2.81665e8			−0.751496
$722$		0			0
$723$	6.86865e7	+	6.86865e7i	0.181743	+	0.181743i
$724$		0			0
$725$	−3.72993e8	−	3.72993e8i	−0.978783	−	0.978783i
$726$		0			0
$727$	2.19025e8			0.570019			0.285010	−	0.958525i	$-0.408003\pi$
$727$	2.19025e8			0.570019			0.285010	+	0.958525i	$0.408003\pi$
$728$		0			0
$729$		−	1.43489e7i		−	0.0370370i
$730$		0			0
$731$	−2.83371e6	+	2.83371e6i	−0.00725442	+	0.00725442i
$732$		0			0
$733$	3.39039e7	−	3.39039e7i	0.0860870	−	0.0860870i	−0.662752	−	0.748839i	$-0.730612\pi$
$733$	3.39039e7	−	3.39039e7i	0.0860870	−	0.0860870i	0.748839	+	0.662752i	$0.230612\pi$
$734$		0			0
$735$		−	2.66847e7i		−	0.0672047i
$736$		0			0
$737$	−8.13400e7			−0.203190
$738$		0			0
$739$	1.32965e8	+	1.32965e8i	0.329461	+	0.329461i	0.852382	−	0.522920i	$-0.175157\pi$
$739$	1.32965e8	+	1.32965e8i	0.329461	+	0.329461i	−0.522920	+	0.852382i	$0.675157\pi$
$740$		0			0
$741$	1.25541e8	+	1.25541e8i	0.308553	+	0.308553i
$742$		0			0
$743$	4.53728e8			1.10619			0.553094	−	0.833119i	$-0.313447\pi$
$743$	4.53728e8			1.10619			0.553094	+	0.833119i	$0.313447\pi$
$744$		0			0
$745$			1.32959e8i			0.321549i
$746$		0			0
$747$	−3.81787e7	+	3.81787e7i	−0.0915924	+	0.0915924i
$748$		0			0
$749$	4.38030e8	−	4.38030e8i	1.04246	−	1.04246i
$750$		0			0
$751$		−	5.32097e7i		−	0.125623i	−0.998025	−	0.0628117i	$-0.979993\pi$
$751$		−	5.32097e7i		−	0.125623i	0.998025	−	0.0628117i	$-0.0200068\pi$
$752$		0			0
$753$	6.37477e7			0.149307
$754$		0			0
$755$	−1.67009e8	−	1.67009e8i	−0.388059	−	0.388059i
$756$		0			0
$757$	−2.48819e8	−	2.48819e8i	−0.573583	−	0.573583i	0.359545	−	0.933128i	$-0.382932\pi$
$757$	−2.48819e8	−	2.48819e8i	−0.573583	−	0.573583i	−0.933128	+	0.359545i	$0.882932\pi$
$758$		0			0
$759$	−1.39427e7			−0.0318876
$760$		0			0
$761$		−	1.77622e8i		−	0.403035i	−0.979485	−	0.201517i	$-0.935413\pi$
$761$		−	1.77622e8i		−	0.403035i	0.979485	−	0.201517i	$-0.0645872\pi$
$762$		0			0
$763$	4.47902e8	−	4.47902e8i	1.00835	−	1.00835i
$764$		0			0
$765$	−717146.	+	717146.i	−0.00160186	+	0.00160186i
$766$		0			0
$767$			2.45695e8i			0.544515i
$768$		0			0
$769$	5.49859e8			1.20913			0.604564	−	0.796556i	$-0.293347\pi$
$769$	5.49859e8			1.20913			0.604564	+	0.796556i	$0.293347\pi$
$770$		0			0
$771$	−3.34082e7	−	3.34082e7i	−0.0728937	−	0.0728937i
$772$		0			0
$773$	−1.63126e8	−	1.63126e8i	−0.353170	−	0.353170i	0.508118	−	0.861288i	$-0.330342\pi$
$773$	−1.63126e8	−	1.63126e8i	−0.353170	−	0.353170i	−0.861288	+	0.508118i	$0.830342\pi$
$774$		0			0
$775$	2.20188e8			0.473031
$776$		0			0
$777$		−	3.72472e8i		−	0.794018i
$778$		0			0
$779$	4.45752e8	−	4.45752e8i	0.942933	−	0.942933i
$780$		0			0
$781$	6.36309e7	−	6.36309e7i	0.133572	−	0.133572i
$782$		0			0
$783$		−	1.40657e8i		−	0.293007i
$784$		0			0
$785$	−1.49044e8			−0.308111
$786$		0			0
$787$	−3.65012e8	−	3.65012e8i	−0.748829	−	0.748829i	0.225431	−	0.974259i	$-0.427621\pi$
$787$	−3.65012e8	−	3.65012e8i	−0.748829	−	0.748829i	−0.974259	+	0.225431i	$0.927621\pi$
$788$		0			0
$789$	−1.42160e8	−	1.42160e8i	−0.289431	−	0.289431i
$790$		0			0
$791$	1.54920e8			0.313024
$792$		0			0
$793$		−	3.33254e8i		−	0.668276i
$794$		0			0
$795$	−6.77268e7	+	6.77268e7i	−0.134790	+	0.134790i
$796$		0			0
$797$	−1.74396e8	+	1.74396e8i	−0.344479	+	0.344479i	−0.858048	−	0.513569i	$-0.828323\pi$
$797$	−1.74396e8	+	1.74396e8i	−0.344479	+	0.344479i	0.513569	+	0.858048i	$0.328323\pi$
$798$		0			0
$799$			4.04712e6i			0.00793424i
$800$		0			0
$801$	−2.39361e8			−0.465754
$802$		0			0
$803$	3.09192e7	+	3.09192e7i	0.0597148	+	0.0597148i
$804$		0			0
$805$	4.45652e7	+	4.45652e7i	0.0854295	+	0.0854295i
$806$		0			0
$807$	−4.40788e8			−0.838705
$808$		0			0
$809$			5.26702e8i			0.994762i	0.867532	+	0.497381i	$0.165705\pi$
$809$			5.26702e8i			0.994762i	−0.867532	+	0.497381i	$0.834295\pi$
$810$		0			0
$811$	2.56605e8	−	2.56605e8i	0.481063	−	0.481063i	−0.424408	−	0.905471i	$-0.639518\pi$
$811$	2.56605e8	−	2.56605e8i	0.481063	−	0.481063i	0.905471	+	0.424408i	$0.139518\pi$
$812$		0			0
$813$	1.78122e8	−	1.78122e8i	0.331471	−	0.331471i
$814$		0			0
$815$		−	2.14884e8i		−	0.396946i
$816$		0			0
$817$	1.68506e8			0.308994
$818$		0			0
$819$	−1.69659e8	−	1.69659e8i	−0.308833	−	0.308833i
$820$		0			0
$821$	4.69870e7	+	4.69870e7i	0.0849080	+	0.0849080i	0.748285	−	0.663377i	$-0.230877\pi$
$821$	4.69870e7	+	4.69870e7i	0.0849080	+	0.0849080i	−0.663377	+	0.748285i	$0.730877\pi$
$822$		0			0
$823$	6.05096e8			1.08549			0.542744	−	0.839898i	$-0.317385\pi$
$823$	6.05096e8			1.08549			0.542744	+	0.839898i	$0.317385\pi$
$824$		0			0
$825$		−	4.78133e7i		−	0.0851504i
$826$		0			0
$827$	−5.66395e7	+	5.66395e7i	−0.100139	+	0.100139i	−0.755401	−	0.655262i	$-0.772558\pi$
$827$	−5.66395e7	+	5.66395e7i	−0.100139	+	0.100139i	0.655262	+	0.755401i	$0.272558\pi$
$828$		0			0
$829$	−2.70924e8	+	2.70924e8i	−0.475537	+	0.475537i	−0.903701	−	0.428164i	$-0.859161\pi$
$829$	−2.70924e8	+	2.70924e8i	−0.475537	+	0.475537i	0.428164	+	0.903701i	$0.359161\pi$
$830$		0			0
$831$			5.97507e8i			1.04121i
$832$		0			0
$833$	5.03376e6			0.00870879
$834$		0			0
$835$	−3.17350e7	−	3.17350e7i	−0.0545103	−	0.0545103i
$836$		0			0
$837$	4.15171e7	+	4.15171e7i	0.0708028	+	0.0708028i
$838$		0			0
$839$	−3.64457e8			−0.617107			−0.308554	−	0.951207i	$-0.599845\pi$
$839$	−3.64457e8			−0.617107			−0.308554	+	0.951207i	$0.599845\pi$
$840$		0			0
$841$		−	7.83994e8i		−	1.31803i
$842$		0			0
$843$	2.75784e8	−	2.75784e8i	0.460349	−	0.460349i
$844$		0			0
$845$	3.06651e7	−	3.06651e7i	0.0508247	−	0.0508247i
$846$		0			0
$847$		−	6.96601e8i		−	1.14639i
$848$		0			0
$849$	−4.38892e8			−0.717191
$850$		0			0
$851$	1.73311e8	+	1.73311e8i	0.281214	+	0.281214i
$852$		0			0
$853$	2.02133e8	+	2.02133e8i	0.325679	+	0.325679i	0.850941	−	0.525262i	$-0.176033\pi$
$853$	2.02133e8	+	2.02133e8i	0.325679	+	0.325679i	−0.525262	+	0.850941i	$0.676033\pi$
$854$		0			0
$855$	4.26450e7			0.0682292
$856$		0			0
$857$		−	3.51121e8i		−	0.557846i	−0.960314	−	0.278923i	$-0.910023\pi$
$857$		−	3.51121e8i		−	0.557846i	0.960314	−	0.278923i	$-0.0899774\pi$
$858$		0			0
$859$	3.33973e8	−	3.33973e8i	0.526904	−	0.526904i	−0.392744	−	0.919648i	$-0.628474\pi$
$859$	3.33973e8	−	3.33973e8i	0.526904	−	0.526904i	0.919648	+	0.392744i	$0.128474\pi$
$860$		0			0
$861$	−6.02400e8	+	6.02400e8i	−0.943790	+	0.943790i
$862$		0			0
$863$		−	3.35360e8i		−	0.521769i	−0.965370	−	0.260885i	$-0.915986\pi$
$863$		−	3.35360e8i		−	0.521769i	0.965370	−	0.260885i	$-0.0840142\pi$
$864$		0			0
$865$	2.28479e8			0.353018
$866$		0			0
$867$	2.65926e8	+	2.65926e8i	0.408041	+	0.408041i
$868$		0			0
$869$	1.27136e8	+	1.27136e8i	0.193736	+	0.193736i
$870$		0			0
$871$	9.21076e8			1.39393
$872$		0			0
$873$			3.56728e8i			0.536160i
$874$		0			0
$875$	−3.20921e8	+	3.20921e8i	−0.479043	+	0.479043i
$876$		0			0
$877$	−48710.2	+	48710.2i	−7.22139e−5	+	7.22139e-5i	−0.707143	−	0.707071i	$-0.750016\pi$
$877$	−48710.2	+	48710.2i	−7.22139e−5	+	7.22139e-5i	0.707071	+	0.707143i	$0.250016\pi$
$878$		0			0
$879$			4.05774e8i			0.597471i
$880$		0			0
$881$	−1.26485e9			−1.84974			−0.924868	−	0.380288i	$-0.875825\pi$
$881$	−1.26485e9			−1.84974			−0.924868	+	0.380288i	$0.875825\pi$
$882$		0			0
$883$	2.69441e8	+	2.69441e8i	0.391364	+	0.391364i	0.875173	−	0.483809i	$-0.160747\pi$
$883$	2.69441e8	+	2.69441e8i	0.391364	+	0.391364i	−0.483809	+	0.875173i	$0.660747\pi$
$884$		0			0
$885$	4.17301e7	+	4.17301e7i	0.0602033	+	0.0602033i
$886$		0			0
$887$	9.42264e8			1.35021			0.675106	−	0.737721i	$-0.264098\pi$
$887$	9.42264e8			1.35021			0.675106	+	0.737721i	$0.264098\pi$
$888$		0			0
$889$		−	1.37547e9i		−	1.95770i
$890$		0			0
$891$	9.01532e6	−	9.01532e6i	0.0127452	−	0.0127452i
$892$		0			0
$893$	1.20331e8	−	1.20331e8i	0.168975	−	0.168975i
$894$		0			0
$895$		−	3.41238e8i		−	0.475979i
$896$		0			0
$897$	1.57884e8			0.218757
$898$		0			0
$899$	4.06978e8	+	4.06978e8i	0.560134	+	0.560134i
$900$		0			0
$901$	−1.27759e7	−	1.27759e7i	−0.0174669	−	0.0174669i
$902$		0			0
$903$	−2.27723e8			−0.309274
$904$		0			0
$905$			3.24592e8i			0.437917i
$906$		0			0
$907$	6.98350e8	−	6.98350e8i	0.935946	−	0.935946i	−0.0621221	−	0.998069i	$-0.519787\pi$
$907$	6.98350e8	−	6.98350e8i	0.935946	−	0.935946i	0.998069	+	0.0621221i	$0.0197868\pi$
$908$		0			0
$909$	−1.58758e8	+	1.58758e8i	−0.211371	+	0.211371i
$910$		0			0
$911$		−	8.33932e8i		−	1.10300i	−0.834175	−	0.551500i	$-0.814056\pi$
$911$		−	8.33932e8i		−	1.10300i	0.834175	−	0.551500i	$-0.185944\pi$
$912$		0			0
$913$	−4.79749e7			−0.0630379
$914$		0			0
$915$	−5.66017e7	−	5.66017e7i	−0.0738867	−	0.0738867i
$916$		0			0
$917$	−7.92186e8	−	7.92186e8i	−1.02735	−	1.02735i
$918$		0			0
$919$	9.76779e7			0.125849			0.0629245	−	0.998018i	$-0.479957\pi$
$919$	9.76779e7			0.125849			0.0629245	+	0.998018i	$0.479957\pi$
$920$		0			0
$921$		−	1.89470e8i		−	0.242528i
$922$		0			0
$923$	−7.20542e8	+	7.20542e8i	−0.916335	+	0.916335i
$924$		0			0
$925$	−5.94330e8	+	5.94330e8i	−0.750935	+	0.750935i
$926$		0			0
$927$			1.69484e8i			0.212760i
$928$		0			0
$929$	−9.74514e8			−1.21546			−0.607731	−	0.794143i	$-0.707920\pi$
$929$	−9.74514e8			−1.21546			−0.607731	+	0.794143i	$0.707920\pi$
$930$		0			0
$931$	−1.49666e8	−	1.49666e8i	−0.185470	−	0.185470i
$932$		0			0
$933$	−2.51803e8	−	2.51803e8i	−0.310038	−	0.310038i
$934$		0			0
$935$	−901156.			−0.00110247
$936$		0			0
$937$			2.77324e8i			0.337107i	0.985692	+	0.168554i	$0.0539097\pi$
$937$			2.77324e8i			0.337107i	−0.985692	+	0.168554i	$0.946090\pi$
$938$		0			0
$939$	3.31499e8	−	3.31499e8i	0.400391	−	0.400391i
$940$		0			0
$941$	5.23882e8	−	5.23882e8i	0.628730	−	0.628730i	−0.319018	−	0.947749i	$-0.603353\pi$
$941$	5.23882e8	−	5.23882e8i	0.628730	−	0.628730i	0.947749	+	0.319018i	$0.103353\pi$
$942$		0			0
$943$		−	5.60592e8i		−	0.668517i
$944$		0			0
$945$	−5.76315e7			−0.0682912
$946$		0			0
$947$	4.98354e8	+	4.98354e8i	0.586798	+	0.586798i	0.936763	−	0.349965i	$-0.113807\pi$
$947$	4.98354e8	+	4.98354e8i	0.586798	+	0.586798i	−0.349965	+	0.936763i	$0.613807\pi$
$948$		0			0
$949$	−3.50122e8	−	3.50122e8i	−0.409658	−	0.409658i
$950$		0			0
$951$	1.33862e8			0.155638
$952$		0			0
$953$			1.60833e8i			0.185821i	0.995674	+	0.0929107i	$0.0296171\pi$
$953$			1.60833e8i			0.185821i	−0.995674	+	0.0929107i	$0.970383\pi$
$954$		0			0
$955$	−7.29890e7	+	7.29890e7i	−0.0838007	+	0.0838007i
$956$		0			0
$957$	8.83742e7	−	8.83742e7i	0.100830	−	0.100830i
$958$		0			0
$959$		−	1.30235e9i		−	1.47663i
$960$		0			0
$961$	6.47253e8			0.729296
$962$		0			0
$963$	−2.63573e8	−	2.63573e8i	−0.295136	−	0.295136i
$964$		0			0
$965$	−6.25522e6	−	6.25522e6i	−0.00696083	−	0.00696083i
$966$		0			0
$967$	−3.65197e8			−0.403875			−0.201938	−	0.979398i	$-0.564724\pi$
$967$	−3.65197e8			−0.403875			−0.201938	+	0.979398i	$0.564724\pi$
$968$		0			0
$969$			8.04451e6i			0.00884155i
$970$		0			0
$971$	2.95923e7	−	2.95923e7i	0.0323237	−	0.0323237i	−0.690760	−	0.723084i	$-0.742724\pi$
$971$	2.95923e7	−	2.95923e7i	0.0323237	−	0.0323237i	0.723084	+	0.690760i	$0.242724\pi$
$972$		0			0
$973$	1.02467e9	−	1.02467e9i	1.11235	−	1.11235i
$974$		0			0
$975$			5.41427e8i			0.584153i
$976$		0			0
$977$	−2.96856e7			−0.0318319			−0.0159159	−	0.999873i	$-0.505066\pi$
$977$	−2.96856e7			−0.0318319			−0.0159159	+	0.999873i	$0.505066\pi$
$978$		0			0
$979$	−1.50389e8	−	1.50389e8i	−0.160276	−	0.160276i
$980$		0			0
$981$	−2.69513e8	−	2.69513e8i	−0.285478	−	0.285478i
$982$		0			0
$983$	5.48457e7			0.0577407			0.0288704	−	0.999583i	$-0.490809\pi$
$983$	5.48457e7			0.0577407			0.0288704	+	0.999583i	$0.490809\pi$
$984$		0			0
$985$			6.63474e7i			0.0694249i
$986$		0			0
$987$	−1.62618e8	+	1.62618e8i	−0.169128	+	0.169128i
$988$		0			0
$989$	1.05959e8	−	1.05959e8i	0.109534	−	0.109534i
$990$		0			0
$991$		−	2.73901e8i		−	0.281431i	−0.990050	−	0.140716i	$-0.955060\pi$
$991$		−	2.73901e8i		−	0.281431i	0.990050	−	0.140716i	$-0.0449404\pi$
$992$		0			0
$993$	−2.03777e8			−0.208117
$994$		0			0
$995$	9.96170e7	+	9.96170e7i	0.101126	+	0.101126i
$996$		0			0
$997$	−1.69342e8	−	1.69342e8i	−0.170875	−	0.170875i	0.616489	−	0.787364i	$-0.288555\pi$
$997$	−1.69342e8	−	1.69342e8i	−0.170875	−	0.170875i	−0.787364	+	0.616489i	$0.788555\pi$
$998$		0			0
$999$	−2.24125e8			−0.224799

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.7.l.b.31.5		48
4.3	odd	2		384.7.l.a.31.20		48
8.3	odd	2		192.7.l.a.79.5		48
8.5	even	2		48.7.l.a.43.16	yes	48
16.3	odd	4	inner	384.7.l.b.223.5		48
16.5	even	4		192.7.l.a.175.5		48
16.11	odd	4		48.7.l.a.19.16	✓	48
16.13	even	4		384.7.l.a.223.20		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.l.a.19.16	✓	48	16.11	odd	4
48.7.l.a.43.16	yes	48	8.5	even	2
192.7.l.a.79.5		48	8.3	odd	2
192.7.l.a.175.5		48	16.5	even	4
384.7.l.a.31.20		48	4.3	odd	2
384.7.l.a.223.20		48	16.13	even	4
384.7.l.b.31.5		48	1.1	even	1	trivial
384.7.l.b.223.5		48	16.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	384.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-11.0227 - 11.0227i) q^{3} +(26.6395 + 26.6395i) q^{5} -403.840 q^{7} +243.000i q^{9} +O(q^{10})\)	\(q+(-11.0227 - 11.0227i) q^{3} +(26.6395 + 26.6395i) q^{5} -403.840 q^{7} +243.000i q^{9} +(-152.675 + 152.675i) q^{11} +(1728.86 - 1728.86i) q^{13} -587.279i q^{15} +110.784 q^{17} +(-3293.87 - 3293.87i) q^{19} +(4451.41 + 4451.41i) q^{21} -4142.48 q^{23} -14205.7i q^{25} +(2678.52 - 2678.52i) q^{27} +(26256.6 - 26256.6i) q^{29} +15500.0i q^{31} +3365.79 q^{33} +(-10758.1 - 10758.1i) q^{35} +(-41837.5 - 41837.5i) q^{37} -38113.5 q^{39} +135328. i q^{41} +(-25578.8 + 25578.8i) q^{43} +(-6473.40 + 6473.40i) q^{45} +36531.8i q^{47} +45437.8 q^{49} +(-1221.13 - 1221.13i) q^{51} +(-115323. - 115323. i) q^{53} -8134.39 q^{55} +72614.7i q^{57} +(-71056.8 + 71056.8i) q^{59} +(96379.6 - 96379.6i) q^{61} -98133.1i q^{63} +92112.0 q^{65} +(266382. + 266382. i) q^{67} +(45661.3 + 45661.3i) q^{69} -416772. q^{71} -202516. i q^{73} +(-156585. + 156585. i) q^{75} +(61656.4 - 61656.4i) q^{77} -832723. i q^{79} -59049.0 q^{81} +(157114. + 157114. i) q^{83} +(2951.22 + 2951.22i) q^{85} -578837. q^{87} +985026. i q^{89} +(-698184. + 698184. i) q^{91} +(170852. - 170852. i) q^{93} -175494. i q^{95} +1.46802e6 q^{97} +(-37100.1 - 37100.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 2720 q^{11} + 3936 q^{19} + 26240 q^{23} - 66400 q^{29} - 162336 q^{35} + 7200 q^{37} - 340704 q^{43} + 806736 q^{49} - 80352 q^{51} - 443680 q^{53} + 232704 q^{55} + 886144 q^{59} + 326496 q^{61} - 372832 q^{65} + 962112 q^{67} - 541728 q^{69} + 534016 q^{71} + 1073088 q^{75} + 932960 q^{77} - 2834352 q^{81} + 2497760 q^{83} + 372000 q^{85} - 775008 q^{91} + 660960 q^{99}+O(q^{100}) \) 48 * q + 2720 * q^11 + 3936 * q^19 + 26240 * q^23 - 66400 * q^29 - 162336 * q^35 + 7200 * q^37 - 340704 * q^43 + 806736 * q^49 - 80352 * q^51 - 443680 * q^53 + 232704 * q^55 + 886144 * q^59 + 326496 * q^61 - 372832 * q^65 + 962112 * q^67 - 541728 * q^69 + 534016 * q^71 + 1073088 * q^75 + 932960 * q^77 - 2834352 * q^81 + 2497760 * q^83 + 372000 * q^85 - 775008 * q^91 + 660960 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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