LMFDB - Embedded newform 320.6.l.a.241.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,6,Mod(81,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("320.81");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	320.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:	$51.3228223402$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			241.19
Character	$\chi$	$=$	320.241
Dual form			320.6.l.a.81.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.82595 + 2.82595i) q^{3} +(17.6777 + 17.6777i) q^{5} +197.416i q^{7} +227.028i q^{9} +O(q^{10})$	\(q+(-2.82595 + 2.82595i) q^{3} +(17.6777 + 17.6777i) q^{5} +197.416i q^{7} +227.028i q^{9} +(541.655 + 541.655i) q^{11} +(-657.010 + 657.010i) q^{13} -99.9125 q^{15} +152.646 q^{17} +(428.008 - 428.008i) q^{19} +(-557.887 - 557.887i) q^{21} -2103.77i q^{23} +625.000i q^{25} +(-1328.28 - 1328.28i) q^{27} +(-1313.03 + 1313.03i) q^{29} +8014.55 q^{31} -3061.38 q^{33} +(-3489.85 + 3489.85i) q^{35} +(-4174.18 - 4174.18i) q^{37} -3713.36i q^{39} +6836.92i q^{41} +(-367.257 - 367.257i) q^{43} +(-4013.33 + 4013.33i) q^{45} +6123.69 q^{47} -22165.9 q^{49} +(-431.370 + 431.370i) q^{51} +(-8837.44 - 8837.44i) q^{53} +19150.4i q^{55} +2419.06i q^{57} +(23628.5 + 23628.5i) q^{59} +(34685.8 - 34685.8i) q^{61} -44818.9 q^{63} -23228.8 q^{65} +(12889.4 - 12889.4i) q^{67} +(5945.16 + 5945.16i) q^{69} +56725.7i q^{71} -41485.9i q^{73} +(-1766.22 - 1766.22i) q^{75} +(-106931. + 106931. i) q^{77} -106416. q^{79} -47660.5 q^{81} +(49167.0 - 49167.0i) q^{83} +(2698.42 + 2698.42i) q^{85} -7421.13i q^{87} +62632.3i q^{89} +(-129704. - 129704. i) q^{91} +(-22648.8 + 22648.8i) q^{93} +15132.4 q^{95} +27802.9 q^{97} +(-122971. + 122971. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q+O(q^{10}) $ 80 * q	$ 80 q - 1208 q^{11} + 1800 q^{15} - 2360 q^{19} + 7464 q^{27} - 8144 q^{29} + 21296 q^{37} - 32072 q^{43} + 88360 q^{47} - 192080 q^{49} + 5920 q^{51} - 49456 q^{53} - 44984 q^{59} + 48080 q^{61} - 158760 q^{63} - 61160 q^{67} - 22320 q^{69} - 14896 q^{77} - 177680 q^{79} - 524880 q^{81} + 329240 q^{83} + 132400 q^{85} - 364832 q^{91} - 362352 q^{93} - 288800 q^{95} - 659000 q^{99}+O(q^{100}) $ 80 * q - 1208 * q^11 + 1800 * q^15 - 2360 * q^19 + 7464 * q^27 - 8144 * q^29 + 21296 * q^37 - 32072 * q^43 + 88360 * q^47 - 192080 * q^49 + 5920 * q^51 - 49456 * q^53 - 44984 * q^59 + 48080 * q^61 - 158760 * q^63 - 61160 * q^67 - 22320 * q^69 - 14896 * q^77 - 177680 * q^79 - 524880 * q^81 + 329240 * q^83 + 132400 * q^85 - 364832 * q^91 - 362352 * q^93 - 288800 * q^95 - 659000 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−2.82595	+	2.82595i	−0.181285	+	0.181285i	−0.791916	−	0.610631i	$-0.790916\pi$
$3$	−2.82595	+	2.82595i	−0.181285	+	0.181285i	0.610631	+	0.791916i	$0.290916\pi$
$4$		0			0
$5$	17.6777	+	17.6777i	0.316228	+	0.316228i
$5$	17.6777	+	17.6777i	0.316228	+	0.316228i
$6$		0			0
$7$			197.416i			1.52278i	0.648296	+	0.761389i	$0.275482\pi$
$7$			197.416i			1.52278i	−0.648296	+	0.761389i	$0.724518\pi$
$8$		0			0
$9$			227.028i			0.934272i
$10$		0			0
$11$	541.655	+	541.655i	1.34971	+	1.34971i	0.885972	+	0.463739i	$0.153493\pi$
$11$	541.655	+	541.655i	1.34971	+	1.34971i	0.463739	+	0.885972i	$0.346507\pi$
$12$		0			0
$13$	−657.010	+	657.010i	−1.07824	+	1.07824i	−0.0815680	+	0.996668i	$0.525993\pi$
$13$	−657.010	+	657.010i	−1.07824	+	1.07824i	−0.996668	+	0.0815680i	$0.974007\pi$
$14$		0			0
$15$	−99.9125			−0.114655
$16$		0			0
$17$	152.646			0.128104			0.0640520	−	0.997947i	$-0.479598\pi$
$17$	152.646			0.128104			0.0640520	+	0.997947i	$0.479598\pi$
$18$		0			0
$19$	428.008	−	428.008i	0.272000	−	0.272000i	−0.557905	−	0.829905i	$-0.688395\pi$
$19$	428.008	−	428.008i	0.272000	−	0.272000i	0.829905	+	0.557905i	$0.188395\pi$
$20$		0			0
$21$	−557.887	−	557.887i	−0.276057	−	0.276057i
$22$		0			0
$23$		−	2103.77i		−	0.829237i	−0.909995	−	0.414619i	$-0.863915\pi$
$23$		−	2103.77i		−	0.829237i	0.909995	−	0.414619i	$-0.136085\pi$
$24$		0			0
$25$			625.000i			0.200000i
$26$		0			0
$27$	−1328.28	−	1328.28i	−0.350654	−	0.350654i
$28$		0			0
$29$	−1313.03	+	1313.03i	−0.289921	+	0.289921i	−0.837049	−	0.547128i	$-0.815721\pi$
$29$	−1313.03	+	1313.03i	−0.289921	+	0.289921i	0.547128	+	0.837049i	$0.315721\pi$
$30$		0			0
$31$	8014.55			1.49787			0.748937	−	0.662642i	$-0.230565\pi$
$31$	8014.55			1.49787			0.748937	+	0.662642i	$0.230565\pi$
$32$		0			0
$33$	−3061.38			−0.489365
$34$		0			0
$35$	−3489.85	+	3489.85i	−0.481544	+	0.481544i
$36$		0			0
$37$	−4174.18	−	4174.18i	−0.501265	−	0.501265i	0.410566	−	0.911831i	$-0.365331\pi$
$37$	−4174.18	−	4174.18i	−0.501265	−	0.501265i	−0.911831	+	0.410566i	$0.865331\pi$
$38$		0			0
$39$		−	3713.36i		−	0.390936i
$40$		0			0
$41$			6836.92i			0.635186i	0.948227	+	0.317593i	$0.102874\pi$
$41$			6836.92i			0.635186i	−0.948227	+	0.317593i	$0.897126\pi$
$42$		0			0
$43$	−367.257	−	367.257i	−0.0302900	−	0.0302900i	0.691800	−	0.722090i	$-0.256818\pi$
$43$	−367.257	−	367.257i	−0.0302900	−	0.0302900i	−0.722090	+	0.691800i	$0.756818\pi$
$44$		0			0
$45$	−4013.33	+	4013.33i	−0.295443	+	0.295443i
$46$		0			0
$47$	6123.69			0.404360			0.202180	−	0.979348i	$-0.435197\pi$
$47$	6123.69			0.404360			0.202180	+	0.979348i	$0.435197\pi$
$48$		0			0
$49$	−22165.9			−1.31885
$50$		0			0
$51$	−431.370	+	431.370i	−0.0232233	+	0.0232233i
$52$		0			0
$53$	−8837.44	−	8837.44i	−0.432152	−	0.432152i	0.457208	−	0.889360i	$-0.348850\pi$
$53$	−8837.44	−	8837.44i	−0.432152	−	0.432152i	−0.889360	+	0.457208i	$0.848850\pi$
$54$		0			0
$55$			19150.4i			0.853632i
$56$		0			0
$57$			2419.06i			0.0986189i
$58$		0			0
$59$	23628.5	+	23628.5i	0.883704	+	0.883704i	0.993909	−	0.110205i	$-0.0351508\pi$
$59$	23628.5	+	23628.5i	0.883704	+	0.883704i	−0.110205	+	0.993909i	$0.535151\pi$
$60$		0			0
$61$	34685.8	−	34685.8i	1.19351	−	1.19351i	0.217437	−	0.976074i	$-0.430230\pi$
$61$	34685.8	−	34685.8i	1.19351	−	1.19351i	0.976074	−	0.217437i	$-0.0697698\pi$
$62$		0			0
$63$	−44818.9			−1.42269
$64$		0			0
$65$	−23228.8			−0.681936
$66$		0			0
$67$	12889.4	−	12889.4i	0.350790	−	0.350790i	−0.509613	−	0.860403i	$-0.670212\pi$
$67$	12889.4	−	12889.4i	0.350790	−	0.350790i	0.860403	+	0.509613i	$0.170212\pi$
$68$		0			0
$69$	5945.16	+	5945.16i	0.150328	+	0.150328i
$70$		0			0
$71$			56725.7i			1.33547i	0.744399	+	0.667735i	$0.232736\pi$
$71$			56725.7i			1.33547i	−0.744399	+	0.667735i	$0.767264\pi$
$72$		0			0
$73$		−	41485.9i		−	0.911158i	−0.890195	−	0.455579i	$-0.849432\pi$
$73$		−	41485.9i		−	0.911158i	0.890195	−	0.455579i	$-0.150568\pi$
$74$		0			0
$75$	−1766.22	−	1766.22i	−0.0362570	−	0.0362570i
$76$		0			0
$77$	−106931.	+	106931.i	−2.05531	+	2.05531i
$78$		0			0
$79$	−106416.			−1.91839			−0.959196	−	0.282743i	$-0.908756\pi$
$79$	−106416.			−1.91839			−0.959196	+	0.282743i	$0.908756\pi$
$80$		0			0
$81$	−47660.5			−0.807135
$82$		0			0
$83$	49167.0	−	49167.0i	0.783390	−	0.783390i	−0.197011	−	0.980401i	$-0.563124\pi$
$83$	49167.0	−	49167.0i	0.783390	−	0.783390i	0.980401	+	0.197011i	$0.0631235\pi$
$84$		0			0
$85$	2698.42	+	2698.42i	0.0405100	+	0.0405100i
$86$		0			0
$87$		−	7421.13i		−	0.105117i
$88$		0			0
$89$			62632.3i			0.838154i	0.907951	+	0.419077i	$0.137646\pi$
$89$			62632.3i			0.838154i	−0.907951	+	0.419077i	$0.862354\pi$
$90$		0			0
$91$	−129704.	−	129704.i	−1.64191	−	1.64191i
$92$		0			0
$93$	−22648.8	+	22648.8i	−0.271542	+	0.271542i
$94$		0			0
$95$	15132.4			0.172028
$96$		0			0
$97$	27802.9			0.300027			0.150014	−	0.988684i	$-0.452068\pi$
$97$	27802.9			0.300027			0.150014	+	0.988684i	$0.452068\pi$
$98$		0			0
$99$	−122971.	+	122971.i	−1.26100	+	1.26100i
$100$		0			0
$101$	−86867.1	−	86867.1i	−0.847328	−	0.847328i	0.142471	−	0.989799i	$-0.454495\pi$
$101$	−86867.1	−	86867.1i	−0.847328	−	0.847328i	−0.989799	+	0.142471i	$0.954495\pi$
$102$		0			0
$103$			37838.9i			0.351436i	0.984441	+	0.175718i	$0.0562246\pi$
$103$			37838.9i			0.351436i	−0.984441	+	0.175718i	$0.943775\pi$
$104$		0			0
$105$		−	19724.3i		−	0.174594i
$106$		0			0
$107$	−1871.29	−	1871.29i	−0.0158009	−	0.0158009i	0.699162	−	0.714963i	$-0.253557\pi$
$107$	−1871.29	−	1871.29i	−0.0158009	−	0.0158009i	−0.714963	+	0.699162i	$0.753557\pi$
$108$		0			0
$109$	39905.8	−	39905.8i	0.321714	−	0.321714i	−0.527710	−	0.849424i	$-0.676949\pi$
$109$	39905.8	−	39905.8i	0.321714	−	0.321714i	0.849424	+	0.527710i	$0.176949\pi$
$110$		0			0
$111$	23592.1			0.181743
$112$		0			0
$113$	179127.			1.31967			0.659834	−	0.751412i	$-0.270627\pi$
$113$	179127.			1.31967			0.659834	+	0.751412i	$0.270627\pi$
$114$		0			0
$115$	37189.8	−	37189.8i	0.262228	−	0.262228i
$116$		0			0
$117$	−149160.	−	149160.i	−1.00736	−	1.00736i
$118$		0			0
$119$			30134.7i			0.195074i
$120$		0			0
$121$			425729.i			2.64344i
$122$		0			0
$123$	−19320.8	−	19320.8i	−0.115150	−	0.115150i
$124$		0			0
$125$	−11048.5	+	11048.5i	−0.0632456	+	0.0632456i
$126$		0			0
$127$	−54658.8			−0.300712			−0.150356	−	0.988632i	$-0.548042\pi$
$127$	−54658.8			−0.300712			−0.150356	+	0.988632i	$0.548042\pi$
$128$		0			0
$129$	2075.70			0.0109822
$130$		0			0
$131$	−75263.3	+	75263.3i	−0.383182	+	0.383182i	−0.872247	−	0.489065i	$-0.837338\pi$
$131$	−75263.3	+	75263.3i	−0.383182	+	0.383182i	0.489065	+	0.872247i	$0.337338\pi$
$132$		0			0
$133$	84495.5	+	84495.5i	0.414195	+	0.414195i
$134$		0			0
$135$		−	46961.7i		−	0.221773i
$136$		0			0
$137$			82268.7i			0.374484i	0.982314	+	0.187242i	$0.0599549\pi$
$137$			82268.7i			0.374484i	−0.982314	+	0.187242i	$0.940045\pi$
$138$		0			0
$139$	30619.7	+	30619.7i	0.134420	+	0.134420i	0.771115	−	0.636696i	$-0.219699\pi$
$139$	30619.7	+	30619.7i	0.134420	+	0.134420i	−0.636696	+	0.771115i	$0.719699\pi$
$140$		0			0
$141$	−17305.2	+	17305.2i	−0.0733044	+	0.0733044i
$142$		0			0
$143$	−711745.			−2.91061
$144$		0			0
$145$	−46422.6			−0.183362
$146$		0			0
$147$	62639.8	−	62639.8i	0.239088	−	0.239088i
$148$		0			0
$149$	−209646.	−	209646.i	−0.773607	−	0.773607i	0.205128	−	0.978735i	$-0.434239\pi$
$149$	−209646.	−	209646.i	−0.773607	−	0.773607i	−0.978735	+	0.205128i	$0.934239\pi$
$150$		0			0
$151$			202737.i			0.723586i	0.932258	+	0.361793i	$0.117835\pi$
$151$			202737.i			0.723586i	−0.932258	+	0.361793i	$0.882165\pi$
$152$		0			0
$153$			34654.9i			0.119684i
$154$		0			0
$155$	141679.	+	141679.i	0.473669	+	0.473669i
$156$		0			0
$157$	343510.	−	343510.i	1.11222	−	1.11222i	0.119369	−	0.992850i	$-0.461913\pi$
$157$	343510.	−	343510.i	1.11222	−	1.11222i	0.992850	−	0.119369i	$-0.0380872\pi$
$158$		0			0
$159$	49948.4			0.156685
$160$		0			0
$161$	415317.			1.26274
$162$		0			0
$163$	163012.	−	163012.i	0.480564	−	0.480564i	−0.424748	−	0.905312i	$-0.639637\pi$
$163$	163012.	−	163012.i	0.480564	−	0.480564i	0.905312	+	0.424748i	$0.139637\pi$
$164$		0			0
$165$	−54118.1	−	54118.1i	−0.154751	−	0.154751i
$166$		0			0
$167$		−	12174.1i		−	0.0337790i	−0.999857	−	0.0168895i	$-0.994624\pi$
$167$		−	12174.1i		−	0.0337790i	0.999857	−	0.0168895i	$-0.00537634\pi$
$168$		0			0
$169$		−	492032.i		−	1.32518i
$170$		0			0
$171$	97169.9	+	97169.9i	0.254121	+	0.254121i
$172$		0			0
$173$	−536526.	+	536526.i	−1.36294	+	1.36294i	−0.492783	+	0.870152i	$0.664020\pi$
$173$	−536526.	+	536526.i	−1.36294	+	1.36294i	−0.870152	+	0.492783i	$0.835980\pi$
$174$		0			0
$175$	−123385.			−0.304555
$176$		0			0
$177$	−133546.			−0.320404
$178$		0			0
$179$	496149.	−	496149.i	1.15739	−	1.15739i	0.172356	−	0.985035i	$-0.444862\pi$
$179$	496149.	−	496149.i	1.15739	−	1.15739i	0.985035	−	0.172356i	$-0.0551378\pi$
$180$		0			0
$181$	189857.	+	189857.i	0.430754	+	0.430754i	0.888885	−	0.458131i	$-0.151481\pi$
$181$	189857.	+	189857.i	0.430754	+	0.430754i	−0.458131	+	0.888885i	$0.651481\pi$
$182$		0			0
$183$			196041.i			0.432731i
$184$		0			0
$185$		−	147580.i		−	0.317028i
$186$		0			0
$187$	82681.3	+	82681.3i	0.172903	+	0.172903i
$188$		0			0
$189$	262223.	−	262223.i	0.533968	−	0.533968i
$190$		0			0
$191$	216777.			0.429962			0.214981	−	0.976618i	$-0.431031\pi$
$191$	216777.			0.429962			0.214981	+	0.976618i	$0.431031\pi$
$192$		0			0
$193$	−129059.			−0.249399			−0.124700	−	0.992195i	$-0.539797\pi$
$193$	−129059.			−0.249399			−0.124700	+	0.992195i	$0.539797\pi$
$194$		0			0
$195$	65643.6	−	65643.6i	0.123625	−	0.123625i
$196$		0			0
$197$	−384351.	−	384351.i	−0.705607	−	0.705607i	0.260001	−	0.965608i	$-0.416277\pi$
$197$	−384351.	−	384351.i	−0.705607	−	0.705607i	−0.965608	+	0.260001i	$0.916277\pi$
$198$		0			0
$199$			754358.i			1.35035i	0.737660	+	0.675173i	$0.235931\pi$
$199$			754358.i			1.35035i	−0.737660	+	0.675173i	$0.764069\pi$
$200$		0			0
$201$			72849.9i			0.127186i
$202$		0			0
$203$	−259213.	−	259213.i	−0.441485	−	0.441485i
$204$		0			0
$205$	−120861.	+	120861.i	−0.200863	+	0.200863i
$206$		0			0
$207$	477615.			0.774733
$208$		0			0
$209$	463665.			0.734242
$210$		0			0
$211$	508214.	−	508214.i	0.785851	−	0.785851i	−0.194960	−	0.980811i	$-0.562458\pi$
$211$	508214.	−	508214.i	0.785851	−	0.785851i	0.980811	+	0.194960i	$0.0624577\pi$
$212$		0			0
$213$	−160304.	−	160304.i	−0.242101	−	0.242101i
$214$		0			0
$215$		−	12984.5i		−	0.0191571i
$216$		0			0
$217$			1.58220e6i			2.28093i
$218$		0			0
$219$	117237.	+	117237.i	0.165179	+	0.165179i
$220$		0			0
$221$	−100290.	+	100290.i	−0.138126	+	0.138126i
$222$		0			0
$223$	−162588.			−0.218940			−0.109470	−	0.993990i	$-0.534915\pi$
$223$	−162588.			−0.218940			−0.109470	+	0.993990i	$0.534915\pi$
$224$		0			0
$225$	−141892.			−0.186854
$226$		0			0
$227$	517939.	−	517939.i	0.667135	−	0.667135i	−0.289917	−	0.957052i	$-0.593628\pi$
$227$	517939.	−	517939.i	0.667135	−	0.667135i	0.957052	+	0.289917i	$0.0936275\pi$
$228$		0			0
$229$	−814473.	−	814473.i	−1.02633	−	1.02633i	−0.999644	−	0.0266888i	$-0.991504\pi$
$229$	−814473.	−	814473.i	−1.02633	−	1.02633i	−0.0266888	−	0.999644i	$-0.508496\pi$
$230$		0			0
$231$		−	604364.i		−	0.745193i
$232$		0			0
$233$			453287.i			0.546995i	0.961873	+	0.273498i	$0.0881805\pi$
$233$			453287.i			0.546995i	−0.961873	+	0.273498i	$0.911819\pi$
$234$		0			0
$235$	108252.	+	108252.i	0.127870	+	0.127870i
$236$		0			0
$237$	300725.	−	300725.i	0.347776	−	0.347776i
$238$		0			0
$239$	1.02509e6			1.16083			0.580413	−	0.814322i	$-0.302891\pi$
$239$	1.02509e6			1.16083			0.580413	+	0.814322i	$0.302891\pi$
$240$		0			0
$241$	1.33741e6			1.48328			0.741638	−	0.670800i	$-0.234049\pi$
$241$	1.33741e6			1.48328			0.741638	+	0.670800i	$0.234049\pi$
$242$		0			0
$243$	457458.	−	457458.i	0.496976	−	0.496976i
$244$		0			0
$245$	−391842.	−	391842.i	−0.417057	−	0.417057i
$246$		0			0
$247$			562412.i			0.586559i
$248$		0			0
$249$			277887.i			0.284034i
$250$		0			0
$251$	949915.	+	949915.i	0.951701	+	0.951701i	0.998886	−	0.0471855i	$-0.0150252\pi$
$251$	949915.	+	949915.i	0.951701	+	0.951701i	−0.0471855	+	0.998886i	$0.515025\pi$
$252$		0			0
$253$	1.13952e6	−	1.13952e6i	1.11923	−	1.11923i
$254$		0			0
$255$	−15251.2			−0.0146877
$256$		0			0
$257$	1.04686e6			0.988681			0.494341	−	0.869268i	$-0.335410\pi$
$257$	1.04686e6			0.988681			0.494341	+	0.869268i	$0.335410\pi$
$258$		0			0
$259$	824048.	−	824048.i	0.763314	−	0.763314i
$260$		0			0
$261$	−298095.	−	298095.i	−0.270865	−	0.270865i
$262$		0			0
$263$		−	1.88612e6i		−	1.68144i	−0.541472	−	0.840719i	$-0.682133\pi$
$263$		−	1.88612e6i		−	1.68144i	0.541472	−	0.840719i	$-0.317867\pi$
$264$		0			0
$265$		−	312451.i		−	0.273317i
$266$		0			0
$267$	−176996.	−	176996.i	−0.151945	−	0.151945i
$268$		0			0
$269$	−225955.	+	225955.i	−0.190388	+	0.190388i	−0.795864	−	0.605476i	$-0.792983\pi$
$269$	−225955.	+	225955.i	−0.190388	+	0.190388i	0.605476	+	0.795864i	$0.292983\pi$
$270$		0			0
$271$	−751159.			−0.621310			−0.310655	−	0.950523i	$-0.600548\pi$
$271$	−751159.			−0.621310			−0.310655	+	0.950523i	$0.600548\pi$
$272$		0			0
$273$	733075.			0.595308
$274$		0			0
$275$	−338534.	+	338534.i	−0.269942	+	0.269942i
$276$		0			0
$277$	991598.	+	991598.i	0.776491	+	0.776491i	0.979232	−	0.202742i	$-0.0649852\pi$
$277$	991598.	+	991598.i	0.776491	+	0.776491i	−0.202742	+	0.979232i	$0.564985\pi$
$278$		0			0
$279$			1.81953e6i			1.39942i
$280$		0			0
$281$		−	1.15437e6i		−	0.872126i	−0.899916	−	0.436063i	$-0.856373\pi$
$281$		−	1.15437e6i		−	0.872126i	0.899916	−	0.436063i	$-0.143627\pi$
$282$		0			0
$283$	−1.22003e6	−	1.22003e6i	−0.905530	−	0.905530i	0.0903777	−	0.995908i	$-0.471193\pi$
$283$	−1.22003e6	−	1.22003e6i	−0.905530	−	0.905530i	−0.995908	+	0.0903777i	$0.971193\pi$
$284$		0			0
$285$	−42763.4	+	42763.4i	−0.0311860	+	0.0311860i
$286$		0			0
$287$	−1.34971e6			−0.967246
$288$		0			0
$289$	−1.39656e6			−0.983589
$290$		0			0
$291$	−78569.6	+	78569.6i	−0.0543904	+	0.0543904i
$292$		0			0
$293$	203103.	+	203103.i	0.138213	+	0.138213i	0.772828	−	0.634615i	$-0.218841\pi$
$293$	203103.	+	203103.i	0.138213	+	0.138213i	−0.634615	+	0.772828i	$0.718841\pi$
$294$		0			0
$295$			835395.i			0.558903i
$296$		0			0
$297$		−	1.43893e6i		−	0.946564i
$298$		0			0
$299$	1.38220e6	+	1.38220e6i	0.894114	+	0.894114i
$300$		0			0
$301$	72502.2	−	72502.2i	0.0461249	−	0.0461249i
$302$		0			0
$303$	490965.			0.307216
$304$		0			0
$305$	1.22633e6			0.754843
$306$		0			0
$307$	−559308.	+	559308.i	−0.338692	+	0.338692i	−0.855875	−	0.517183i	$-0.826981\pi$
$307$	−559308.	+	559308.i	−0.338692	+	0.338692i	0.517183	+	0.855875i	$0.326981\pi$
$308$		0			0
$309$	−106931.	−	106931.i	−0.0637100	−	0.0637100i
$310$		0			0
$311$			1.23935e6i			0.726598i	0.931673	+	0.363299i	$0.118350\pi$
$311$			1.23935e6i			0.726598i	−0.931673	+	0.363299i	$0.881650\pi$
$312$		0			0
$313$			859630.i			0.495965i	0.968765	+	0.247982i	$0.0797675\pi$
$313$			859630.i			0.495965i	−0.968765	+	0.247982i	$0.920233\pi$
$314$		0			0
$315$	−792293.	−	792293.i	−0.449893	−	0.449893i
$316$		0			0
$317$	227313.	−	227313.i	0.127051	−	0.127051i	−0.640722	−	0.767773i	$-0.721365\pi$
$317$	227313.	−	227313.i	0.127051	−	0.127051i	0.767773	+	0.640722i	$0.221365\pi$
$318$		0			0
$319$	−1.42242e6			−0.782619
$320$		0			0
$321$	10576.4			0.00572894
$322$		0			0
$323$	65333.7	−	65333.7i	0.0348442	−	0.0348442i
$324$		0			0
$325$	−410631.	−	410631.i	−0.215647	−	0.215647i
$326$		0			0
$327$			225544.i			0.116644i
$328$		0			0
$329$			1.20891e6i			0.615750i
$330$		0			0
$331$	−781848.	−	781848.i	−0.392240	−	0.392240i	0.483245	−	0.875485i	$-0.339458\pi$
$331$	−781848.	−	781848.i	−0.392240	−	0.392240i	−0.875485	+	0.483245i	$0.839458\pi$
$332$		0			0
$333$	947656.	−	947656.i	0.468317	−	0.468317i
$334$		0			0
$335$	455711.			0.221859
$336$		0			0
$337$	3.22360e6			1.54620			0.773102	−	0.634282i	$-0.218704\pi$
$337$	3.22360e6			1.54620			0.773102	+	0.634282i	$0.218704\pi$
$338$		0			0
$339$	−506204.	+	506204.i	−0.239236	+	0.239236i
$340$		0			0
$341$	4.34112e6	+	4.34112e6i	2.02170	+	2.02170i
$342$		0			0
$343$		−	1.05793e6i		−	0.485537i
$344$		0			0
$345$			210193.i			0.0950760i
$346$		0			0
$347$	−336317.	−	336317.i	−0.149942	−	0.149942i	0.628150	−	0.778092i	$-0.283812\pi$
$347$	−336317.	−	336317.i	−0.149942	−	0.149942i	−0.778092	+	0.628150i	$0.783812\pi$
$348$		0			0
$349$	−1.30701e6	+	1.30701e6i	−0.574400	+	0.574400i	−0.933355	−	0.358955i	$-0.883133\pi$
$349$	−1.30701e6	+	1.30701e6i	−0.574400	+	0.574400i	0.358955	+	0.933355i	$0.383133\pi$
$350$		0			0
$351$	1.74538e6			0.756176
$352$		0			0
$353$	−4.18476e6			−1.78745			−0.893725	−	0.448615i	$-0.851917\pi$
$353$	−4.18476e6			−1.78745			−0.893725	+	0.448615i	$0.851917\pi$
$354$		0			0
$355$	−1.00278e6	+	1.00278e6i	−0.422313	+	0.422313i
$356$		0			0
$357$	−85159.1	−	85159.1i	−0.0353639	−	0.0353639i
$358$		0			0
$359$		−	1.30242e6i		−	0.533354i	−0.963786	−	0.266677i	$-0.914074\pi$
$359$		−	1.30242e6i		−	0.533354i	0.963786	−	0.266677i	$-0.0859257\pi$
$360$		0			0
$361$			2.10972e6i			0.852032i
$362$		0			0
$363$	−1.20309e6	−	1.20309e6i	−0.479216	−	0.479216i
$364$		0			0
$365$	733374.	−	733374.i	0.288133	−	0.288133i
$366$		0			0
$367$	−442787.			−0.171605			−0.0858025	−	0.996312i	$-0.527345\pi$
$367$	−442787.			−0.171605			−0.0858025	+	0.996312i	$0.527345\pi$
$368$		0			0
$369$	−1.55217e6			−0.593436
$370$		0			0
$371$	1.74465e6	−	1.74465e6i	0.658071	−	0.658071i
$372$		0			0
$373$	−3.38472e6	−	3.38472e6i	−1.25965	−	1.25965i	−0.951259	−	0.308392i	$-0.900209\pi$
$373$	−3.38472e6	−	3.38472e6i	−1.25965	−	1.25965i	−0.308392	−	0.951259i	$-0.599791\pi$
$374$		0			0
$375$		−	62445.3i		−	0.0229309i
$376$		0			0
$377$		−	1.72535e6i		−	0.625207i
$378$		0			0
$379$	1.74454e6	+	1.74454e6i	0.623852	+	0.623852i	0.946514	−	0.322662i	$-0.104578\pi$
$379$	1.74454e6	+	1.74454e6i	0.623852	+	0.623852i	−0.322662	+	0.946514i	$0.604578\pi$
$380$		0			0
$381$	154463.	−	154463.i	0.0545146	−	0.0545146i
$382$		0			0
$383$	−3.91329e6			−1.36315			−0.681577	−	0.731746i	$-0.738706\pi$
$383$	−3.91329e6			−1.36315			−0.681577	+	0.731746i	$0.738706\pi$
$384$		0			0
$385$	−3.78058e6			−1.29989
$386$		0			0
$387$	83377.6	−	83377.6i	0.0282991	−	0.0282991i
$388$		0			0
$389$	521316.	+	521316.i	0.174674	+	0.174674i	0.789029	−	0.614356i	$-0.210584\pi$
$389$	521316.	+	521316.i	0.174674	+	0.174674i	−0.614356	+	0.789029i	$0.710584\pi$
$390$		0			0
$391$		−	321132.i		−	0.106229i
$392$		0			0
$393$		−	425381.i		−	0.138930i
$394$		0			0
$395$	−1.88118e6	−	1.88118e6i	−0.606649	−	0.606649i
$396$		0			0
$397$	−2.14350e6	+	2.14350e6i	−0.682569	+	0.682569i	−0.960578	−	0.278009i	$-0.910325\pi$
$397$	−2.14350e6	+	2.14350e6i	−0.682569	+	0.682569i	0.278009	+	0.960578i	$0.410325\pi$
$398$		0			0
$399$	−477561.			−0.150175
$400$		0			0
$401$	−2.38412e6			−0.740403			−0.370201	−	0.928952i	$-0.620711\pi$
$401$	−2.38412e6			−0.740403			−0.370201	+	0.928952i	$0.620711\pi$
$402$		0			0
$403$	−5.26564e6	+	5.26564e6i	−1.61506	+	1.61506i
$404$		0			0
$405$	−842527.	−	842527.i	−0.255238	−	0.255238i
$406$		0			0
$407$		−	4.52193e6i		−	1.35312i
$408$		0			0
$409$		−	4.74247e6i		−	1.40183i	−0.713244	−	0.700916i	$-0.752775\pi$
$409$		−	4.74247e6i		−	1.40183i	0.713244	−	0.700916i	$-0.247225\pi$
$410$		0			0
$411$	−232488.	−	232488.i	−0.0678883	−	0.0678883i
$412$		0			0
$413$	−4.66464e6	+	4.66464e6i	−1.34568	+	1.34568i
$414$		0			0
$415$	1.73831e6			0.495459
$416$		0			0
$417$	−173059.			−0.0487366
$418$		0			0
$419$	−1.30162e6	+	1.30162e6i	−0.362199	+	0.362199i	−0.864622	−	0.502423i	$-0.832442\pi$
$419$	−1.30162e6	+	1.30162e6i	−0.362199	+	0.362199i	0.502423	+	0.864622i	$0.332442\pi$
$420$		0			0
$421$	945631.	+	945631.i	0.260026	+	0.260026i	0.825064	−	0.565039i	$-0.191139\pi$
$421$	945631.	+	945631.i	0.260026	+	0.260026i	−0.565039	+	0.825064i	$0.691139\pi$
$422$		0			0
$423$			1.39025e6i			0.377782i
$424$		0			0
$425$			95403.6i			0.0256208i
$426$		0			0
$427$	6.84751e6	+	6.84751e6i	1.81745	+	1.81745i
$428$		0			0
$429$	2.01136e6	−	2.01136e6i	0.527650	−	0.527650i
$430$		0			0
$431$	5.90106e6			1.53016			0.765080	−	0.643935i	$-0.222699\pi$
$431$	5.90106e6			1.53016			0.765080	+	0.643935i	$0.222699\pi$
$432$		0			0
$433$	−3.70654e6			−0.950055			−0.475027	−	0.879971i	$-0.657562\pi$
$433$	−3.70654e6			−0.950055			−0.475027	+	0.879971i	$0.657562\pi$
$434$		0			0
$435$	131188.	−	131188.i	0.0332408	−	0.0332408i
$436$		0			0
$437$	−900432.	−	900432.i	−0.225552	−	0.225552i
$438$		0			0
$439$		−	2.43564e6i		−	0.603186i	−0.953437	−	0.301593i	$-0.902482\pi$
$439$		−	2.43564e6i		−	0.603186i	0.953437	−	0.301593i	$-0.0975184\pi$
$440$		0			0
$441$		−	5.03228e6i		−	1.23216i
$442$		0			0
$443$	−4.75839e6	−	4.75839e6i	−1.15200	−	1.15200i	−0.986152	−	0.165843i	$-0.946966\pi$
$443$	−4.75839e6	−	4.75839e6i	−1.15200	−	1.15200i	−0.165843	−	0.986152i	$-0.553034\pi$
$444$		0			0
$445$	−1.10719e6	+	1.10719e6i	−0.265047	+	0.265047i
$446$		0			0
$447$	1.18490e6			0.280487
$448$		0			0
$449$	1.20625e6			0.282372			0.141186	−	0.989983i	$-0.454908\pi$
$449$	1.20625e6			0.282372			0.141186	+	0.989983i	$0.454908\pi$
$450$		0			0
$451$	−3.70325e6	+	3.70325e6i	−0.857317	+	0.857317i
$452$		0			0
$453$	−572925.	−	572925.i	−0.131175	−	0.131175i
$454$		0			0
$455$		−	4.58573e6i		−	1.03844i
$456$		0			0
$457$			8.30542e6i			1.86025i	0.367245	+	0.930124i	$0.380301\pi$
$457$			8.30542e6i			1.86025i	−0.367245	+	0.930124i	$0.619699\pi$
$458$		0			0
$459$	−202756.	−	202756.i	−0.0449202	−	0.0449202i
$460$		0			0
$461$	−3.51089e6	+	3.51089e6i	−0.769422	+	0.769422i	−0.978005	−	0.208583i	$-0.933115\pi$
$461$	−3.51089e6	+	3.51089e6i	−0.769422	+	0.769422i	0.208583	+	0.978005i	$0.433115\pi$
$462$		0			0
$463$	−558945.			−0.121176			−0.0605880	−	0.998163i	$-0.519298\pi$
$463$	−558945.			−0.121176			−0.0605880	+	0.998163i	$0.519298\pi$
$464$		0			0
$465$	−800754.			−0.171738
$466$		0			0
$467$	−2.74891e6	+	2.74891e6i	−0.583268	+	0.583268i	−0.935800	−	0.352532i	$-0.885321\pi$
$467$	−2.74891e6	+	2.74891e6i	−0.583268	+	0.583268i	0.352532	+	0.935800i	$0.385321\pi$
$468$		0			0
$469$	2.54458e6	+	2.54458e6i	0.534175	+	0.534175i
$470$		0			0
$471$			1.94149e6i			0.403257i
$472$		0			0
$473$		−	397853.i		−	0.0817654i
$474$		0			0
$475$	267505.	+	267505.i	0.0543999	+	0.0543999i
$476$		0			0
$477$	2.00634e6	−	2.00634e6i	0.403747	−	0.403747i
$478$		0			0
$479$	1.32442e6			0.263746			0.131873	−	0.991267i	$-0.457901\pi$
$479$	1.32442e6			0.263746			0.131873	+	0.991267i	$0.457901\pi$
$480$		0			0
$481$	5.48496e6			1.08096
$482$		0			0
$483$	−1.17367e6	+	1.17367e6i	−0.228916	+	0.228916i
$484$		0			0
$485$	491490.	+	491490.i	0.0948769	+	0.0948769i
$486$		0			0
$487$			8.10722e6i			1.54899i	0.632578	+	0.774496i	$0.281997\pi$
$487$			8.10722e6i			1.54899i	−0.632578	+	0.774496i	$0.718003\pi$
$488$		0			0
$489$			921329.i			0.174238i
$490$		0			0
$491$	406525.	+	406525.i	0.0760998	+	0.0760998i	0.744132	−	0.668032i	$-0.232863\pi$
$491$	406525.	+	406525.i	0.0760998	+	0.0760998i	−0.668032	+	0.744132i	$0.732863\pi$
$492$		0			0
$493$	−200429.	+	200429.i	−0.0371400	+	0.0371400i
$494$		0			0
$495$	−4.34767e6			−0.797524
$496$		0			0
$497$	−1.11985e7			−2.03362
$498$		0			0
$499$	−193908.	+	193908.i	−0.0348614	+	0.0348614i	−0.724323	−	0.689461i	$-0.757847\pi$
$499$	−193908.	+	193908.i	−0.0348614	+	0.0348614i	0.689461	+	0.724323i	$0.257847\pi$
$500$		0			0
$501$	34403.5	+	34403.5i	0.00612362	+	0.00612362i
$502$		0			0
$503$			1.67379e6i			0.294973i	0.989064	+	0.147486i	$0.0471183\pi$
$503$			1.67379e6i			0.294973i	−0.989064	+	0.147486i	$0.952882\pi$
$504$		0			0
$505$		−	3.07121e6i		−	0.535897i
$506$		0			0
$507$	1.39046e6	+	1.39046e6i	0.240236	+	0.240236i
$508$		0			0
$509$	1.50765e6	−	1.50765e6i	0.257932	−	0.257932i	−0.566280	−	0.824213i	$-0.691618\pi$
$509$	1.50765e6	−	1.50765e6i	0.257932	−	0.257932i	0.824213	+	0.566280i	$0.191618\pi$
$510$		0			0
$511$	8.18996e6			1.38749
$512$		0			0
$513$	−1.13703e6			−0.190756
$514$		0			0
$515$	−668904.	+	668904.i	−0.111134	+	0.111134i
$516$		0			0
$517$	3.31692e6	+	3.31692e6i	0.545769	+	0.545769i
$518$		0			0
$519$		−	3.03239e6i		−	0.494159i
$520$		0			0
$521$		−	2.57563e6i		−	0.415708i	−0.978160	−	0.207854i	$-0.933352\pi$
$521$		−	2.57563e6i		−	0.415708i	0.978160	−	0.207854i	$-0.0666479\pi$
$522$		0			0
$523$	2.13633e6	+	2.13633e6i	0.341518	+	0.341518i	0.856938	−	0.515420i	$-0.172364\pi$
$523$	2.13633e6	+	2.13633e6i	0.341518	+	0.341518i	−0.515420	+	0.856938i	$0.672364\pi$
$524$		0			0
$525$	348679.	−	348679.i	0.0552113	−	0.0552113i
$526$		0			0
$527$	1.22339e6			0.191883
$528$		0			0
$529$	2.01049e6			0.312365
$530$		0			0
$531$	−5.36434e6	+	5.36434e6i	−0.825619	+	0.825619i
$532$		0			0
$533$	−4.49192e6	−	4.49192e6i	−0.684880	−	0.684880i
$534$		0			0
$535$		−	66160.2i		−	0.00999338i
$536$		0			0
$537$			2.80419e6i			0.419635i
$538$		0			0
$539$	−1.20063e7	−	1.20063e7i	−1.78007	−	1.78007i
$540$		0			0
$541$	1.65184e6	−	1.65184e6i	0.242647	−	0.242647i	−0.575297	−	0.817944i	$-0.695114\pi$
$541$	1.65184e6	−	1.65184e6i	0.242647	−	0.242647i	0.817944	+	0.575297i	$0.195114\pi$
$542$		0			0
$543$	−1.07305e6			−0.156178
$544$		0			0
$545$	1.41088e6			0.203470
$546$		0			0
$547$	6.74481e6	−	6.74481e6i	0.963833	−	0.963833i	−0.0355356	−	0.999368i	$-0.511314\pi$
$547$	6.74481e6	−	6.74481e6i	0.963833	−	0.963833i	0.999368	+	0.0355356i	$0.0113137\pi$
$548$		0			0
$549$	7.87464e6	+	7.87464e6i	1.11506	+	1.11506i
$550$		0			0
$551$			1.12398e6i			0.157717i
$552$		0			0
$553$		−	2.10081e7i		−	2.92128i
$554$		0			0
$555$	417053.	+	417053.i	0.0574723	+	0.0574723i
$556$		0			0
$557$	3.42824e6	−	3.42824e6i	0.468202	−	0.468202i	−0.433130	−	0.901332i	$-0.642591\pi$
$557$	3.42824e6	−	3.42824e6i	0.468202	−	0.468202i	0.901332	+	0.433130i	$0.142591\pi$
$558$		0			0
$559$	482583.			0.0653194
$560$		0			0
$561$	−467307.			−0.0626895
$562$		0			0
$563$	9.10019e6	−	9.10019e6i	1.20998	−	1.20998i	0.238952	−	0.971031i	$-0.423196\pi$
$563$	9.10019e6	−	9.10019e6i	1.20998	−	1.20998i	0.971031	−	0.238952i	$-0.0768040\pi$
$564$		0			0
$565$	3.16654e6	+	3.16654e6i	0.417316	+	0.417316i
$566$		0			0
$567$		−	9.40893e6i		−	1.22909i
$568$		0			0
$569$			5.49614e6i			0.711668i	0.934549	+	0.355834i	$0.115803\pi$
$569$			5.49614e6i			0.711668i	−0.934549	+	0.355834i	$0.884197\pi$
$570$		0			0
$571$	6.26904e6	+	6.26904e6i	0.804657	+	0.804657i	0.983820	−	0.179162i	$-0.0573387\pi$
$571$	6.26904e6	+	6.26904e6i	0.804657	+	0.804657i	−0.179162	+	0.983820i	$0.557339\pi$
$572$		0			0
$573$	−612602.	+	612602.i	−0.0779457	+	0.0779457i
$574$		0			0
$575$	1.31486e6			0.165847
$576$		0			0
$577$	2.00756e6			0.251031			0.125516	−	0.992092i	$-0.459941\pi$
$577$	2.00756e6			0.251031			0.125516	+	0.992092i	$0.459941\pi$
$578$		0			0
$579$	364714.	−	364714.i	0.0452123	−	0.0452123i
$580$		0			0
$581$	9.70632e6	+	9.70632e6i	1.19293	+	1.19293i
$582$		0			0
$583$		−	9.57368e6i		−	1.16656i
$584$		0			0
$585$		−	5.27359e6i		−	0.637114i
$586$		0			0
$587$	−5.11196e6	−	5.11196e6i	−0.612339	−	0.612339i	0.331216	−	0.943555i	$-0.392541\pi$
$587$	−5.11196e6	−	5.11196e6i	−0.612339	−	0.612339i	−0.943555	+	0.331216i	$0.892541\pi$
$588$		0			0
$589$	3.43030e6	−	3.43030e6i	0.407421	−	0.407421i
$590$		0			0
$591$	2.17232e6			0.255832
$592$		0			0
$593$	−5.60846e6			−0.654948			−0.327474	−	0.944860i	$-0.606197\pi$
$593$	−5.60846e6			−0.654948			−0.327474	+	0.944860i	$0.606197\pi$
$594$		0			0
$595$	−532710.	+	532710.i	−0.0616877	+	0.0616877i
$596$		0			0
$597$	−2.13178e6	−	2.13178e6i	−0.244797	−	0.244797i
$598$		0			0
$599$		−	3.57303e6i		−	0.406883i	−0.979087	−	0.203441i	$-0.934787\pi$
$599$		−	3.57303e6i		−	0.406883i	0.979087	−	0.203441i	$-0.0652126\pi$
$600$		0			0
$601$		−	7.00344e6i		−	0.790907i	−0.918486	−	0.395453i	$-0.870587\pi$
$601$		−	7.00344e6i		−	0.790907i	0.918486	−	0.395453i	$-0.129413\pi$
$602$		0			0
$603$	2.92626e6	+	2.92626e6i	0.327733	+	0.327733i
$604$		0			0
$605$	−7.52589e6	+	7.52589e6i	−0.835929	+	0.835929i
$606$		0			0
$607$	7.15190e6			0.787861			0.393930	−	0.919140i	$-0.371115\pi$
$607$	7.15190e6			0.787861			0.393930	+	0.919140i	$0.371115\pi$
$608$		0			0
$609$	1.46505e6			0.160069
$610$		0			0
$611$	−4.02332e6	+	4.02332e6i	−0.435995	+	0.435995i
$612$		0			0
$613$	1.00171e7	+	1.00171e7i	1.07669	+	1.07669i	0.996804	+	0.0798818i	$0.0254543\pi$
$613$	1.00171e7	+	1.00171e7i	1.07669	+	1.07669i	0.0798818	+	0.996804i	$0.474546\pi$
$614$		0			0
$615$		−	683094.i		−	0.0728270i
$616$		0			0
$617$			6.37727e6i			0.674407i	0.941432	+	0.337203i	$0.109481\pi$
$617$			6.37727e6i			0.674407i	−0.941432	+	0.337203i	$0.890519\pi$
$618$		0			0
$619$	1.04107e7	+	1.04107e7i	1.09208	+	1.09208i	0.995307	+	0.0967688i	$0.0308508\pi$
$619$	1.04107e7	+	1.04107e7i	1.09208	+	1.09208i	0.0967688	+	0.995307i	$0.469149\pi$
$620$		0			0
$621$	−2.79439e6	+	2.79439e6i	−0.290776	+	0.290776i
$622$		0			0
$623$	−1.23646e7			−1.27632
$624$		0			0
$625$	−390625.			−0.0400000
$626$		0			0
$627$	−1.31030e6	+	1.31030e6i	−0.133107	+	0.133107i
$628$		0			0
$629$	−637171.	−	637171.i	−0.0642140	−	0.0642140i
$630$		0			0
$631$			7.50163e6i			0.750036i	0.927018	+	0.375018i	$0.122363\pi$
$631$			7.50163e6i			0.750036i	−0.927018	+	0.375018i	$0.877637\pi$
$632$		0			0
$633$			2.87238e6i			0.284926i
$634$		0			0
$635$	−966241.	−	966241.i	−0.0950935	−	0.0950935i
$636$		0			0
$637$	1.45632e7	−	1.45632e7i	1.42203	−	1.42203i
$638$		0			0
$639$	−1.28783e7			−1.24769
$640$		0			0
$641$	1.89084e7			1.81765			0.908825	−	0.417177i	$-0.136980\pi$
$641$	1.89084e7			1.81765			0.908825	+	0.417177i	$0.136980\pi$
$642$		0			0
$643$	−5.88611e6	+	5.88611e6i	−0.561437	+	0.561437i	−0.929716	−	0.368278i	$-0.879947\pi$
$643$	−5.88611e6	+	5.88611e6i	−0.561437	+	0.561437i	0.368278	+	0.929716i	$0.379947\pi$
$644$		0			0
$645$	36693.6	+	36693.6i	0.00347289	+	0.00347289i
$646$		0			0
$647$			1.84161e6i			0.172956i	0.996254	+	0.0864782i	$0.0275613\pi$
$647$			1.84161e6i			0.172956i	−0.996254	+	0.0864782i	$0.972439\pi$
$648$		0			0
$649$			2.55970e7i			2.38549i
$650$		0			0
$651$	−4.47122e6	−	4.47122e6i	−0.413498	−	0.413498i
$652$		0			0
$653$	7.63776e6	−	7.63776e6i	0.700944	−	0.700944i	−0.263670	−	0.964613i	$-0.584933\pi$
$653$	7.63776e6	−	7.63776e6i	0.700944	−	0.700944i	0.964613	+	0.263670i	$0.0849328\pi$
$654$		0			0
$655$	−2.66096e6			−0.242345
$656$		0			0
$657$	9.41846e6			0.851269
$658$		0			0
$659$	−4.80399e6	+	4.80399e6i	−0.430912	+	0.430912i	−0.888939	−	0.458027i	$-0.848556\pi$
$659$	−4.80399e6	+	4.80399e6i	−0.430912	+	0.430912i	0.458027	+	0.888939i	$0.348556\pi$
$660$		0			0
$661$	2.67220e6	+	2.67220e6i	0.237884	+	0.237884i	0.815974	−	0.578089i	$-0.196201\pi$
$661$	2.67220e6	+	2.67220e6i	0.237884	+	0.237884i	−0.578089	+	0.815974i	$0.696201\pi$
$662$		0			0
$663$		−	566829.i		−	0.0500804i
$664$		0			0
$665$			2.98737e6i			0.261960i
$666$		0			0
$667$	2.76232e6	+	2.76232e6i	0.240413	+	0.240413i
$668$		0			0
$669$	459465.	−	459465.i	0.0396906	−	0.0396906i
$670$		0			0
$671$	3.75754e7			3.22179
$672$		0			0
$673$	−7.91971e6			−0.674019			−0.337009	−	0.941501i	$-0.609415\pi$
$673$	−7.91971e6			−0.674019			−0.337009	+	0.941501i	$0.609415\pi$
$674$		0			0
$675$	830173.	−	830173.i	0.0701309	−	0.0701309i
$676$		0			0
$677$	−8.95269e6	−	8.95269e6i	−0.750727	−	0.750727i	0.223888	−	0.974615i	$-0.428125\pi$
$677$	−8.95269e6	−	8.95269e6i	−0.750727	−	0.750727i	−0.974615	+	0.223888i	$0.928125\pi$
$678$		0			0
$679$			5.48872e6i			0.456874i
$680$		0			0
$681$			2.92734e6i			0.241883i
$682$		0			0
$683$	843476.	+	843476.i	0.0691865	+	0.0691865i	0.740853	−	0.671667i	$-0.234421\pi$
$683$	843476.	+	843476.i	0.0691865	+	0.0691865i	−0.671667	+	0.740853i	$0.734421\pi$
$684$		0			0
$685$	−1.45432e6	+	1.45432e6i	−0.118422	+	0.118422i
$686$		0			0
$687$	4.60333e6			0.372117
$688$		0			0
$689$	1.16126e7			0.931924
$690$		0			0
$691$	5.68228e6	−	5.68228e6i	0.452717	−	0.452717i	−0.443538	−	0.896256i	$-0.646277\pi$
$691$	5.68228e6	−	5.68228e6i	0.452717	−	0.452717i	0.896256	+	0.443538i	$0.146277\pi$
$692$		0			0
$693$	−2.42763e7	−	2.42763e7i	−1.92022	−	1.92022i
$694$		0			0
$695$			1.08257e6i			0.0850146i
$696$		0			0
$697$			1.04363e6i			0.0813698i
$698$		0			0
$699$	−1.28097e6	−	1.28097e6i	−0.0991620	−	0.0991620i
$700$		0			0
$701$	1.14378e7	−	1.14378e7i	0.879118	−	0.879118i	−0.114325	−	0.993443i	$-0.536471\pi$
$701$	1.14378e7	−	1.14378e7i	0.879118	−	0.879118i	0.993443	+	0.114325i	$0.0364705\pi$
$702$		0			0
$703$	−3.57317e6			−0.272688
$704$		0			0
$705$	−611833.			−0.0463618
$706$		0			0
$707$	1.71489e7	−	1.71489e7i	1.29029	−	1.29029i
$708$		0			0
$709$	−1.13313e7	−	1.13313e7i	−0.846576	−	0.846576i	0.143128	−	0.989704i	$-0.454284\pi$
$709$	−1.13313e7	−	1.13313e7i	−0.846576	−	0.846576i	−0.989704	+	0.143128i	$0.954284\pi$
$710$		0			0
$711$		−	2.41593e7i		−	1.79230i
$712$		0			0
$713$		−	1.68608e7i		−	1.24209i
$714$		0			0
$715$	−1.25820e7	−	1.25820e7i	−0.920417	−	0.920417i
$716$		0			0
$717$	−2.89685e6	+	2.89685e6i	−0.210440	+	0.210440i
$718$		0			0
$719$	−3.31295e6			−0.238997			−0.119499	−	0.992834i	$-0.538129\pi$
$719$	−3.31295e6			−0.238997			−0.119499	+	0.992834i	$0.538129\pi$
$720$		0			0
$721$	−7.46999e6			−0.535158
$722$		0			0
$723$	−3.77946e6	+	3.77946e6i	−0.268896	+	0.268896i
$724$		0			0
$725$	−820644.	−	820644.i	−0.0579842	−	0.0579842i
$726$		0			0
$727$			1.99116e7i			1.39723i	0.715496	+	0.698617i	$0.246201\pi$
$727$			1.99116e7i			1.39723i	−0.715496	+	0.698617i	$0.753799\pi$
$728$		0			0
$729$		−	8.99599e6i		−	0.626946i
$730$		0			0
$731$	−56060.2	−	56060.2i	−0.00388026	−	0.00388026i
$732$		0			0
$733$	−7.01608e6	+	7.01608e6i	−0.482319	+	0.482319i	−0.905872	−	0.423553i	$-0.860783\pi$
$733$	−7.01608e6	+	7.01608e6i	−0.482319	+	0.482319i	0.423553	+	0.905872i	$0.360783\pi$
$734$		0			0
$735$	2.21465e6			0.151212
$736$		0			0
$737$	1.39633e7			0.946930
$738$		0			0
$739$	1.40622e7	−	1.40622e7i	0.947199	−	0.947199i	−0.0514751	−	0.998674i	$-0.516392\pi$
$739$	1.40622e7	−	1.40622e7i	0.947199	−	0.947199i	0.998674	+	0.0514751i	$0.0163923\pi$
$740$		0			0
$741$	−1.58935e6	−	1.58935e6i	−0.106334	−	0.106334i
$742$		0			0
$743$			6.27904e6i			0.417274i	0.977993	+	0.208637i	$0.0669027\pi$
$743$			6.27904e6i			0.417274i	−0.977993	+	0.208637i	$0.933097\pi$
$744$		0			0
$745$		−	7.41210e6i		−	0.489272i
$746$		0			0
$747$	1.11623e7	+	1.11623e7i	0.731899	+	0.731899i
$748$		0			0
$749$	369422.	−	369422.i	0.0240613	−	0.0240613i
$750$		0			0
$751$	6.01668e6			0.389275			0.194638	−	0.980875i	$-0.437647\pi$
$751$	6.01668e6			0.389275			0.194638	+	0.980875i	$0.437647\pi$
$752$		0			0
$753$	−5.36883e6			−0.345058
$754$		0			0
$755$	−3.58392e6	+	3.58392e6i	−0.228818	+	0.228818i
$756$		0			0
$757$	3.36457e6	+	3.36457e6i	0.213398	+	0.213398i	0.805709	−	0.592311i	$-0.201784\pi$
$757$	3.36457e6	+	3.36457e6i	0.213398	+	0.213398i	−0.592311	+	0.805709i	$0.701784\pi$
$758$		0			0
$759$			6.44045e6i			0.405799i
$760$		0			0
$761$		−	1.95367e7i		−	1.22290i	−0.791284	−	0.611448i	$-0.790587\pi$
$761$		−	1.95367e7i		−	1.22290i	0.791284	−	0.611448i	$-0.209413\pi$
$762$		0			0
$763$	7.87803e6	+	7.87803e6i	0.489899	+	0.489899i
$764$		0			0
$765$	−612617.	+	612617.i	−0.0378474	+	0.0378474i
$766$		0			0
$767$	−3.10484e7			−1.90568
$768$		0			0
$769$	−2.30217e6			−0.140386			−0.0701928	−	0.997533i	$-0.522361\pi$
$769$	−2.30217e6			−0.140386			−0.0701928	+	0.997533i	$0.522361\pi$
$770$		0			0
$771$	−2.95838e6	+	2.95838e6i	−0.179233	+	0.179233i
$772$		0			0
$773$	3.83662e6	+	3.83662e6i	0.230941	+	0.230941i	0.813085	−	0.582145i	$-0.197786\pi$
$773$	3.83662e6	+	3.83662e6i	0.230941	+	0.230941i	−0.582145	+	0.813085i	$0.697786\pi$
$774$		0			0
$775$			5.00910e6i			0.299575i
$776$		0			0
$777$			4.65744e6i			0.276755i
$778$		0			0
$779$	2.92626e6	+	2.92626e6i	0.172770	+	0.172770i
$780$		0			0
$781$	−3.07257e7	+	3.07257e7i	−1.80250	+	1.80250i
$782$		0			0
$783$	3.48814e6			0.203324
$784$		0			0
$785$	1.21449e7			0.703429
$786$		0			0
$787$	−1.11181e6	+	1.11181e6i	−0.0639874	+	0.0639874i	−0.738376	−	0.674389i	$-0.764407\pi$
$787$	−1.11181e6	+	1.11181e6i	−0.0639874	+	0.0639874i	0.674389	+	0.738376i	$0.264407\pi$
$788$		0			0
$789$	5.33010e6	+	5.33010e6i	0.304819	+	0.304819i
$790$		0			0
$791$			3.53624e7i			2.00956i
$792$		0			0
$793$			4.55778e7i			2.57377i
$794$		0			0
$795$	882971.	+	882971.i	0.0495483	+	0.0495483i
$796$		0			0
$797$	−8.17500e6	+	8.17500e6i	−0.455871	+	0.455871i	−0.897297	−	0.441426i	$-0.854473\pi$
$797$	−8.17500e6	+	8.17500e6i	−0.455871	+	0.455871i	0.441426	+	0.897297i	$0.354473\pi$
$798$		0			0
$799$	934755.			0.0518001
$800$		0			0
$801$	−1.42193e7			−0.783063
$802$		0			0
$803$	2.24710e7	−	2.24710e7i	1.22980	−	1.22980i
$804$		0			0
$805$	7.34184e6	+	7.34184e6i	0.399315	+	0.399315i
$806$		0			0
$807$		−	1.27707e6i		−	0.0690291i
$808$		0			0
$809$			1.30916e7i			0.703266i	0.936138	+	0.351633i	$0.114374\pi$
$809$			1.30916e7i			0.703266i	−0.936138	+	0.351633i	$0.885626\pi$
$810$		0			0
$811$	−1.54235e7	−	1.54235e7i	−0.823438	−	0.823438i	0.163162	−	0.986599i	$-0.447831\pi$
$811$	−1.54235e7	−	1.54235e7i	−0.823438	−	0.823438i	−0.986599	+	0.163162i	$0.947831\pi$
$812$		0			0
$813$	2.12274e6	−	2.12274e6i	0.112634	−	0.112634i
$814$		0			0
$815$	5.76335e6			0.303935
$816$		0			0
$817$	−314378.			−0.0164777
$818$		0			0
$819$	2.94464e7	−	2.94464e7i	1.53399	−	1.53399i
$820$		0			0
$821$	1.29282e7	+	1.29282e7i	0.669393	+	0.669393i	0.957576	−	0.288182i	$-0.0930509\pi$
$821$	1.29282e7	+	1.29282e7i	0.669393	+	0.669393i	−0.288182	+	0.957576i	$0.593051\pi$
$822$		0			0
$823$			2.14212e6i			0.110241i	0.998480	+	0.0551207i	$0.0175544\pi$
$823$			2.14212e6i			0.110241i	−0.998480	+	0.0551207i	$0.982446\pi$
$824$		0			0
$825$		−	1.91336e6i		−	0.0978729i
$826$		0			0
$827$	1.68100e7	+	1.68100e7i	0.854681	+	0.854681i	0.990705	−	0.136024i	$-0.0434326\pi$
$827$	1.68100e7	+	1.68100e7i	0.854681	+	0.854681i	−0.136024	+	0.990705i	$0.543433\pi$
$828$		0			0
$829$	−1.41517e7	+	1.41517e7i	−0.715192	+	0.715192i	−0.967617	−	0.252424i	$-0.918772\pi$
$829$	−1.41517e7	+	1.41517e7i	−0.715192	+	0.715192i	0.252424	+	0.967617i	$0.418772\pi$
$830$		0			0
$831$	−5.60442e6			−0.281532
$832$		0			0
$833$	−3.38353e6			−0.168950
$834$		0			0
$835$	215210.	−	215210.i	0.0106818	−	0.0106818i
$836$		0			0
$837$	−1.06455e7	−	1.06455e7i	−0.525236	−	0.525236i
$838$		0			0
$839$		−	2.57808e7i		−	1.26442i	−0.774797	−	0.632210i	$-0.782148\pi$
$839$		−	2.57808e7i		−	1.26442i	0.774797	−	0.632210i	$-0.217852\pi$
$840$		0			0
$841$			1.70630e7i			0.831891i
$842$		0			0
$843$	3.26219e6	+	3.26219e6i	0.158103	+	0.158103i
$844$		0			0
$845$	8.69798e6	−	8.69798e6i	0.419060	−	0.419060i
$846$		0			0
$847$	−8.40454e7			−4.02537
$848$		0			0
$849$	6.89547e6			0.328318
$850$		0			0
$851$	−8.78152e6	+	8.78152e6i	−0.415667	+	0.415667i
$852$		0			0
$853$	−1.33299e7	−	1.33299e7i	−0.627270	−	0.627270i	0.320110	−	0.947380i	$-0.396280\pi$
$853$	−1.33299e7	−	1.33299e7i	−0.627270	−	0.627270i	−0.947380	+	0.320110i	$0.896280\pi$
$854$		0			0
$855$			3.43547e6i			0.160721i
$856$		0			0
$857$			1.84183e6i			0.0856637i	0.999082	+	0.0428318i	$0.0136380\pi$
$857$			1.84183e6i			0.0856637i	−0.999082	+	0.0428318i	$0.986362\pi$
$858$		0			0
$859$	1.06784e7	+	1.06784e7i	0.493768	+	0.493768i	0.909491	−	0.415723i	$-0.136471\pi$
$859$	1.06784e7	+	1.06784e7i	0.493768	+	0.493768i	−0.415723	+	0.909491i	$0.636471\pi$
$860$		0			0
$861$	3.81423e6	−	3.81423e6i	0.175347	−	0.175347i
$862$		0			0
$863$	1.02613e7			0.469004			0.234502	−	0.972116i	$-0.424654\pi$
$863$	1.02613e7			0.469004			0.234502	+	0.972116i	$0.424654\pi$
$864$		0			0
$865$	−1.89690e7			−0.861996
$866$		0			0
$867$	3.94660e6	−	3.94660e6i	0.178310	−	0.178310i
$868$		0			0
$869$	−5.76405e7	−	5.76405e7i	−2.58927	−	2.58927i
$870$		0			0
$871$			1.69370e7i			0.756469i
$872$		0			0
$873$			6.31203e6i			0.280307i
$874$		0			0
$875$	−2.18115e6	−	2.18115e6i	−0.0963089	−	0.0963089i
$876$		0			0
$877$	1.60206e7	−	1.60206e7i	0.703364	−	0.703364i	−0.261767	−	0.965131i	$-0.584305\pi$
$877$	1.60206e7	−	1.60206e7i	0.703364	−	0.703364i	0.965131	+	0.261767i	$0.0843053\pi$
$878$		0			0
$879$	−1.14792e6			−0.0501118
$880$		0			0
$881$	−1.47936e7			−0.642146			−0.321073	−	0.947054i	$-0.604043\pi$
$881$	−1.47936e7			−0.642146			−0.321073	+	0.947054i	$0.604043\pi$
$882$		0			0
$883$	−2.96145e7	+	2.96145e7i	−1.27821	+	1.27821i	−0.336546	+	0.941667i	$0.609259\pi$
$883$	−2.96145e7	+	2.96145e7i	−1.27821	+	1.27821i	−0.941667	+	0.336546i	$0.890741\pi$
$884$		0			0
$885$	−2.36079e6	−	2.36079e6i	−0.101321	−	0.101321i
$886$		0			0
$887$		−	2.34254e7i		−	0.999720i	−0.866106	−	0.499860i	$-0.833385\pi$
$887$		−	2.34254e7i		−	0.999720i	0.866106	−	0.499860i	$-0.166615\pi$
$888$		0			0
$889$		−	1.07905e7i		−	0.457918i
$890$		0			0
$891$	−2.58155e7	−	2.58155e7i	−1.08940	−	1.08940i
$892$		0			0
$893$	2.62099e6	−	2.62099e6i	0.109986	−	0.109986i
$894$		0			0
$895$	1.75415e7			0.731998
$896$		0			0
$897$	−7.81206e6			−0.324179
$898$		0			0
$899$	−1.05234e7	+	1.05234e7i	−0.434265	+	0.434265i
$900$		0			0
$901$	−1.34900e6	−	1.34900e6i	−0.0553604	−	0.0553604i
$902$		0			0
$903$			409776.i			0.0167235i
$904$		0			0
$905$			6.71245e6i			0.272433i
$906$		0			0
$907$	4.48366e6	+	4.48366e6i	0.180973	+	0.180973i	0.791780	−	0.610806i	$-0.209155\pi$
$907$	4.48366e6	+	4.48366e6i	0.180973	+	0.180973i	−0.610806	+	0.791780i	$0.709155\pi$
$908$		0			0
$909$	1.97213e7	−	1.97213e7i	0.791635	−	0.791635i
$910$		0			0
$911$	−2.32020e7			−0.926251			−0.463126	−	0.886293i	$-0.653272\pi$
$911$	−2.32020e7			−0.926251			−0.463126	+	0.886293i	$0.653272\pi$
$912$		0			0
$913$	5.32630e7			2.11470
$914$		0			0
$915$	−3.46554e6	+	3.46554e6i	−0.136842	+	0.136842i
$916$		0			0
$917$	−1.48581e7	−	1.48581e7i	−0.583500	−	0.583500i
$918$		0			0
$919$			1.53427e7i			0.599258i	0.954056	+	0.299629i	$0.0968629\pi$
$919$			1.53427e7i			0.599258i	−0.954056	+	0.299629i	$0.903137\pi$
$920$		0			0
$921$		−	3.16116e6i		−	0.122800i
$922$		0			0
$923$	−3.72694e7	−	3.72694e7i	−1.43995	−	1.43995i
$924$		0			0
$925$	2.60886e6	−	2.60886e6i	0.100253	−	0.100253i
$926$		0			0
$927$	−8.59049e6			−0.328336
$928$		0			0
$929$	−2.42104e7			−0.920369			−0.460184	−	0.887823i	$-0.652217\pi$
$929$	−2.42104e7			−0.920369			−0.460184	+	0.887823i	$0.652217\pi$
$930$		0			0
$931$	−9.48720e6	+	9.48720e6i	−0.358727	+	0.358727i
$932$		0			0
$933$	−3.50235e6	−	3.50235e6i	−0.131721	−	0.131721i
$934$		0			0
$935$			2.92322e6i			0.109354i
$936$		0			0
$937$			4.92615e7i			1.83298i	0.400054	+	0.916492i	$0.368991\pi$
$937$			4.92615e7i			1.83298i	−0.400054	+	0.916492i	$0.631009\pi$
$938$		0			0
$939$	−2.42927e6	−	2.42927e6i	−0.0899109	−	0.0899109i
$940$		0			0
$941$	−2.82940e7	+	2.82940e7i	−1.04165	+	1.04165i	−0.0425521	+	0.999094i	$0.513549\pi$
$941$	−2.82940e7	+	2.82940e7i	−1.04165	+	1.04165i	−0.999094	+	0.0425521i	$0.986451\pi$
$942$		0			0
$943$	1.43833e7			0.526720
$944$		0			0
$945$	9.27097e6			0.337711
$946$		0			0
$947$	−8.26404e6	+	8.26404e6i	−0.299445	+	0.299445i	−0.840797	−	0.541351i	$-0.817913\pi$
$947$	−8.26404e6	+	8.26404e6i	−0.299445	+	0.299445i	0.541351	+	0.840797i	$0.317913\pi$
$948$		0			0
$949$	2.72567e7	+	2.72567e7i	0.982443	+	0.982443i
$950$		0			0
$951$			1.28475e6i			0.0460647i
$952$		0			0
$953$			3.54568e7i			1.26464i	0.774707	+	0.632321i	$0.217897\pi$
$953$			3.54568e7i			1.26464i	−0.774707	+	0.632321i	$0.782103\pi$
$954$		0			0
$955$	3.83212e6	+	3.83212e6i	0.135966	+	0.135966i
$956$		0			0
$957$	4.01969e6	−	4.01969e6i	0.141877	−	0.141877i
$958$		0			0
$959$	−1.62411e7			−0.570256
$960$		0			0
$961$	3.56039e7			1.24362
$962$		0			0
$963$	424836.	−	424836.i	0.0147623	−	0.0147623i
$964$		0			0
$965$	−2.28146e6	−	2.28146e6i	−0.0788669	−	0.0788669i
$966$		0			0
$967$			8.52361e6i			0.293128i	0.989201	+	0.146564i	$0.0468214\pi$
$967$			8.52361e6i			0.293128i	−0.989201	+	0.146564i	$0.953179\pi$
$968$		0			0
$969$			369260.i			0.0126335i
$970$		0			0
$971$	2.55609e6	+	2.55609e6i	0.0870019	+	0.0870019i	0.749268	−	0.662266i	$-0.230405\pi$
$971$	2.55609e6	+	2.55609e6i	0.0870019	+	0.0870019i	−0.662266	+	0.749268i	$0.730405\pi$
$972$		0			0
$973$	−6.04480e6	+	6.04480e6i	−0.204691	+	0.204691i
$974$		0			0
$975$	2.32085e6			0.0781872
$976$		0			0
$977$	−1.27814e7			−0.428392			−0.214196	−	0.976791i	$-0.568713\pi$
$977$	−1.27814e7			−0.428392			−0.214196	+	0.976791i	$0.568713\pi$
$978$		0			0
$979$	−3.39251e7	+	3.39251e7i	−1.13127	+	1.13127i
$980$		0			0
$981$	9.05974e6	+	9.05974e6i	0.300568	+	0.300568i
$982$		0			0
$983$			3.00862e7i			0.993079i	0.868014	+	0.496539i	$0.165396\pi$
$983$			3.00862e7i			0.993079i	−0.868014	+	0.496539i	$0.834604\pi$
$984$		0			0
$985$		−	1.35889e7i		−	0.446265i
$986$		0			0
$987$	−3.41633e6	−	3.41633e6i	−0.111626	−	0.111626i
$988$		0			0
$989$	−772624.	+	772624.i	−0.0251176	+	0.0251176i
$990$		0			0
$991$	8.58399e6			0.277655			0.138827	−	0.990317i	$-0.455667\pi$
$991$	8.58399e6			0.277655			0.138827	+	0.990317i	$0.455667\pi$
$992$		0			0
$993$	4.41893e6			0.142215
$994$		0			0
$995$	−1.33353e7	+	1.33353e7i	−0.427017	+	0.427017i
$996$		0			0
$997$	−3.57413e6	−	3.57413e6i	−0.113876	−	0.113876i	0.647873	−	0.761749i	$-0.275659\pi$
$997$	−3.57413e6	−	3.57413e6i	−0.113876	−	0.113876i	−0.761749	+	0.647873i	$0.775659\pi$
$998$		0			0
$999$			1.10889e7i			0.351541i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.6.l.a.241.19		80
4.3	odd	2		80.6.l.a.21.15	✓	80
16.3	odd	4		80.6.l.a.61.15	yes	80
16.13	even	4	inner	320.6.l.a.81.19		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.15	✓	80	4.3	odd	2
80.6.l.a.61.15	yes	80	16.3	odd	4
320.6.l.a.81.19		80	16.13	even	4	inner
320.6.l.a.241.19		80	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	320.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.82595 + 2.82595i) q^{3} +(17.6777 + 17.6777i) q^{5} +197.416i q^{7} +227.028i q^{9} +O(q^{10})\)	\(q+(-2.82595 + 2.82595i) q^{3} +(17.6777 + 17.6777i) q^{5} +197.416i q^{7} +227.028i q^{9} +(541.655 + 541.655i) q^{11} +(-657.010 + 657.010i) q^{13} -99.9125 q^{15} +152.646 q^{17} +(428.008 - 428.008i) q^{19} +(-557.887 - 557.887i) q^{21} -2103.77i q^{23} +625.000i q^{25} +(-1328.28 - 1328.28i) q^{27} +(-1313.03 + 1313.03i) q^{29} +8014.55 q^{31} -3061.38 q^{33} +(-3489.85 + 3489.85i) q^{35} +(-4174.18 - 4174.18i) q^{37} -3713.36i q^{39} +6836.92i q^{41} +(-367.257 - 367.257i) q^{43} +(-4013.33 + 4013.33i) q^{45} +6123.69 q^{47} -22165.9 q^{49} +(-431.370 + 431.370i) q^{51} +(-8837.44 - 8837.44i) q^{53} +19150.4i q^{55} +2419.06i q^{57} +(23628.5 + 23628.5i) q^{59} +(34685.8 - 34685.8i) q^{61} -44818.9 q^{63} -23228.8 q^{65} +(12889.4 - 12889.4i) q^{67} +(5945.16 + 5945.16i) q^{69} +56725.7i q^{71} -41485.9i q^{73} +(-1766.22 - 1766.22i) q^{75} +(-106931. + 106931. i) q^{77} -106416. q^{79} -47660.5 q^{81} +(49167.0 - 49167.0i) q^{83} +(2698.42 + 2698.42i) q^{85} -7421.13i q^{87} +62632.3i q^{89} +(-129704. - 129704. i) q^{91} +(-22648.8 + 22648.8i) q^{93} +15132.4 q^{95} +27802.9 q^{97} +(-122971. + 122971. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q+O(q^{10}) \) 80 * q	\( 80 q - 1208 q^{11} + 1800 q^{15} - 2360 q^{19} + 7464 q^{27} - 8144 q^{29} + 21296 q^{37} - 32072 q^{43} + 88360 q^{47} - 192080 q^{49} + 5920 q^{51} - 49456 q^{53} - 44984 q^{59} + 48080 q^{61} - 158760 q^{63} - 61160 q^{67} - 22320 q^{69} - 14896 q^{77} - 177680 q^{79} - 524880 q^{81} + 329240 q^{83} + 132400 q^{85} - 364832 q^{91} - 362352 q^{93} - 288800 q^{95} - 659000 q^{99}+O(q^{100}) \) 80 * q - 1208 * q^11 + 1800 * q^15 - 2360 * q^19 + 7464 * q^27 - 8144 * q^29 + 21296 * q^37 - 32072 * q^43 + 88360 * q^47 - 192080 * q^49 + 5920 * q^51 - 49456 * q^53 - 44984 * q^59 + 48080 * q^61 - 158760 * q^63 - 61160 * q^67 - 22320 * q^69 - 14896 * q^77 - 177680 * q^79 - 524880 * q^81 + 329240 * q^83 + 132400 * q^85 - 364832 * q^91 - 362352 * q^93 - 288800 * q^95 - 659000 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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