LMFDB - Embedded newform 320.6.l.a.81.17

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			81.17
Character	$\chi$	$=$	320.81
Dual form			320.6.l.a.241.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.86003 - 3.86003i) q^{3} +(-17.6777 + 17.6777i) q^{5} +20.3706i q^{7} -213.200i q^{9} +O(q^{10})$	\(q+(-3.86003 - 3.86003i) q^{3} +(-17.6777 + 17.6777i) q^{5} +20.3706i q^{7} -213.200i q^{9} +(268.702 - 268.702i) q^{11} +(621.797 + 621.797i) q^{13} +136.473 q^{15} -2094.53 q^{17} +(370.318 + 370.318i) q^{19} +(78.6312 - 78.6312i) q^{21} +3608.29i q^{23} -625.000i q^{25} +(-1760.95 + 1760.95i) q^{27} +(-5957.69 - 5957.69i) q^{29} +10314.0 q^{31} -2074.39 q^{33} +(-360.105 - 360.105i) q^{35} +(2830.29 - 2830.29i) q^{37} -4800.32i q^{39} -2923.54i q^{41} +(7107.96 - 7107.96i) q^{43} +(3768.88 + 3768.88i) q^{45} +470.452 q^{47} +16392.0 q^{49} +(8084.96 + 8084.96i) q^{51} +(-5934.20 + 5934.20i) q^{53} +9500.04i q^{55} -2858.88i q^{57} +(8405.61 - 8405.61i) q^{59} +(-27548.1 - 27548.1i) q^{61} +4343.02 q^{63} -21983.9 q^{65} +(-49797.3 - 49797.3i) q^{67} +(13928.1 - 13928.1i) q^{69} -70220.5i q^{71} -54478.8i q^{73} +(-2412.52 + 2412.52i) q^{75} +(5473.61 + 5473.61i) q^{77} +69249.4 q^{79} -38213.0 q^{81} +(21656.9 + 21656.9i) q^{83} +(37026.4 - 37026.4i) q^{85} +45993.8i q^{87} +3328.58i q^{89} +(-12666.4 + 12666.4i) q^{91} +(-39812.5 - 39812.5i) q^{93} -13092.7 q^{95} +128648. q^{97} +(-57287.2 - 57287.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−3.86003	−	3.86003i	−0.247621	−	0.247621i	0.572372	−	0.819994i	$-0.306023\pi$
$3$	−3.86003	−	3.86003i	−0.247621	−	0.247621i	−0.819994	+	0.572372i	$0.806023\pi$
$4$		0			0
$5$	−17.6777	+	17.6777i	−0.316228	+	0.316228i
$5$	−17.6777	+	17.6777i	−0.316228	+	0.316228i
$6$		0			0
$7$			20.3706i			0.157130i	0.996909	+	0.0785649i	$0.0250338\pi$
$7$			20.3706i			0.157130i	−0.996909	+	0.0785649i	$0.974966\pi$
$8$		0			0
$9$		−	213.200i		−	0.877367i
$10$		0			0
$11$	268.702	−	268.702i	0.669558	−	0.669558i	−0.288055	−	0.957614i	$-0.593009\pi$
$11$	268.702	−	268.702i	0.669558	−	0.669558i	0.957614	+	0.288055i	$0.0930087\pi$
$12$		0			0
$13$	621.797	+	621.797i	1.02045	+	1.02045i	0.999787	+	0.0206604i	$0.00657687\pi$
$13$	621.797	+	621.797i	1.02045	+	1.02045i	0.0206604	+	0.999787i	$0.493423\pi$
$14$		0			0
$15$	136.473			0.156609
$16$		0			0
$17$	−2094.53			−1.75778			−0.878890	−	0.477025i	$-0.841715\pi$
$17$	−2094.53			−1.75778			−0.878890	+	0.477025i	$0.841715\pi$
$18$		0			0
$19$	370.318	+	370.318i	0.235337	+	0.235337i	0.814916	−	0.579579i	$-0.196783\pi$
$19$	370.318	+	370.318i	0.235337	+	0.235337i	−0.579579	+	0.814916i	$0.696783\pi$
$20$		0			0
$21$	78.6312	−	78.6312i	0.0389087	−	0.0389087i
$22$		0			0
$23$			3608.29i			1.42227i	0.703055	+	0.711135i	$0.251819\pi$
$23$			3608.29i			1.42227i	−0.703055	+	0.711135i	$0.748181\pi$
$24$		0			0
$25$		−	625.000i		−	0.200000i
$26$		0			0
$27$	−1760.95	+	1760.95i	−0.464876	+	0.464876i
$28$		0			0
$29$	−5957.69	−	5957.69i	−1.31548	−	1.31548i	−0.917316	−	0.398160i	$-0.869649\pi$
$29$	−5957.69	−	5957.69i	−1.31548	−	1.31548i	−0.398160	−	0.917316i	$-0.630351\pi$
$30$		0			0
$31$	10314.0			1.92763			0.963816	−	0.266569i	$-0.0858902\pi$
$31$	10314.0			1.92763			0.963816	+	0.266569i	$0.0858902\pi$
$32$		0			0
$33$	−2074.39			−0.331594
$34$		0			0
$35$	−360.105	−	360.105i	−0.0496888	−	0.0496888i
$36$		0			0
$37$	2830.29	−	2830.29i	0.339881	−	0.339881i	−0.516441	−	0.856322i	$-0.672744\pi$
$37$	2830.29	−	2830.29i	0.339881	−	0.339881i	0.856322	+	0.516441i	$0.172744\pi$
$38$		0			0
$39$		−	4800.32i		−	0.505369i
$40$		0			0
$41$		−	2923.54i		−	0.271612i	−0.990735	−	0.135806i	$-0.956638\pi$
$41$		−	2923.54i		−	0.271612i	0.990735	−	0.135806i	$-0.0433624\pi$
$42$		0			0
$43$	7107.96	−	7107.96i	0.586238	−	0.586238i	−0.350372	−	0.936610i	$-0.613945\pi$
$43$	7107.96	−	7107.96i	0.586238	−	0.586238i	0.936610	+	0.350372i	$0.113945\pi$
$44$		0			0
$45$	3768.88	+	3768.88i	0.277448	+	0.277448i
$46$		0			0
$47$	470.452			0.0310650			0.0155325	−	0.999879i	$-0.495056\pi$
$47$	470.452			0.0310650			0.0155325	+	0.999879i	$0.495056\pi$
$48$		0			0
$49$	16392.0			0.975310
$50$		0			0
$51$	8084.96	+	8084.96i	0.435264	+	0.435264i
$52$		0			0
$53$	−5934.20	+	5934.20i	−0.290183	+	0.290183i	−0.837153	−	0.546969i	$-0.815781\pi$
$53$	−5934.20	+	5934.20i	−0.290183	+	0.290183i	0.546969	+	0.837153i	$0.315781\pi$
$54$		0			0
$55$			9500.04i			0.423466i
$56$		0			0
$57$		−	2858.88i		−	0.116549i
$58$		0			0
$59$	8405.61	−	8405.61i	0.314369	−	0.314369i	−0.532231	−	0.846599i	$-0.678646\pi$
$59$	8405.61	−	8405.61i	0.314369	−	0.314369i	0.846599	+	0.532231i	$0.178646\pi$
$60$		0			0
$61$	−27548.1	−	27548.1i	−0.947911	−	0.947911i	0.0507975	−	0.998709i	$-0.483824\pi$
$61$	−27548.1	−	27548.1i	−0.947911	−	0.947911i	−0.998709	+	0.0507975i	$0.983824\pi$
$62$		0			0
$63$	4343.02			0.137861
$64$		0			0
$65$	−21983.9			−0.645387
$66$		0			0
$67$	−49797.3	−	49797.3i	−1.35525	−	1.35525i	−0.879678	−	0.475570i	$-0.842242\pi$
$67$	−49797.3	−	49797.3i	−1.35525	−	1.35525i	−0.475570	−	0.879678i	$-0.657758\pi$
$68$		0			0
$69$	13928.1	−	13928.1i	0.352185	−	0.352185i
$70$		0			0
$71$		−	70220.5i		−	1.65317i	−0.562811	−	0.826586i	$-0.690280\pi$
$71$		−	70220.5i		−	1.65317i	0.562811	−	0.826586i	$-0.309720\pi$
$72$		0			0
$73$		−	54478.8i		−	1.19652i	−0.801302	−	0.598260i	$-0.795859\pi$
$73$		−	54478.8i		−	1.19652i	0.801302	−	0.598260i	$-0.204141\pi$
$74$		0			0
$75$	−2412.52	+	2412.52i	−0.0495243	+	0.0495243i
$76$		0			0
$77$	5473.61	+	5473.61i	0.105208	+	0.105208i
$78$		0			0
$79$	69249.4			1.24838			0.624192	−	0.781271i	$-0.285428\pi$
$79$	69249.4			1.24838			0.624192	+	0.781271i	$0.285428\pi$
$80$		0			0
$81$	−38213.0			−0.647141
$82$		0			0
$83$	21656.9	+	21656.9i	0.345066	+	0.345066i	0.858268	−	0.513202i	$-0.171541\pi$
$83$	21656.9	+	21656.9i	0.345066	+	0.345066i	−0.513202	+	0.858268i	$0.671541\pi$
$84$		0			0
$85$	37026.4	−	37026.4i	0.555859	−	0.555859i
$86$		0			0
$87$			45993.8i			0.651480i
$88$		0			0
$89$			3328.58i			0.0445435i	0.999752	+	0.0222718i	$0.00708990\pi$
$89$			3328.58i			0.0445435i	−0.999752	+	0.0222718i	$0.992910\pi$
$90$		0			0
$91$	−12666.4	+	12666.4i	−0.160343	+	0.160343i
$92$		0			0
$93$	−39812.5	−	39812.5i	−0.477323	−	0.477323i
$94$		0			0
$95$	−13092.7			−0.148840
$96$		0			0
$97$	128648.			1.38826			0.694132	−	0.719848i	$-0.255788\pi$
$97$	128648.			1.38826			0.694132	+	0.719848i	$0.255788\pi$
$98$		0			0
$99$	−57287.2	−	57287.2i	−0.587449	−	0.587449i
$100$		0			0
$101$	6522.13	−	6522.13i	0.0636189	−	0.0636189i	−0.674582	−	0.738200i	$-0.735676\pi$
$101$	6522.13	−	6522.13i	0.0636189	−	0.0636189i	0.738200	+	0.674582i	$0.235676\pi$
$102$		0			0
$103$		−	138377.i		−	1.28520i	−0.766202	−	0.642600i	$-0.777856\pi$
$103$		−	138377.i		−	1.28520i	0.766202	−	0.642600i	$-0.222144\pi$
$104$		0			0
$105$			2780.03i			0.0246080i
$106$		0			0
$107$	55482.2	−	55482.2i	0.468483	−	0.468483i	−0.432940	−	0.901423i	$-0.642524\pi$
$107$	55482.2	−	55482.2i	0.468483	−	0.468483i	0.901423	+	0.432940i	$0.142524\pi$
$108$		0			0
$109$	−71569.6	−	71569.6i	−0.576982	−	0.576982i	0.357089	−	0.934071i	$-0.383769\pi$
$109$	−71569.6	−	71569.6i	−0.576982	−	0.576982i	−0.934071	+	0.357089i	$0.883769\pi$
$110$		0			0
$111$	−21850.0			−0.168324
$112$		0			0
$113$	56679.7			0.417572			0.208786	−	0.977961i	$-0.433049\pi$
$113$	56679.7			0.417572			0.208786	+	0.977961i	$0.433049\pi$
$114$		0			0
$115$	−63786.2	−	63786.2i	−0.449762	−	0.449762i
$116$		0			0
$117$	132567.	−	132567.i	0.895307	−	0.895307i
$118$		0			0
$119$		−	42666.8i		−	0.276200i
$120$		0			0
$121$			16649.9i			0.103383i
$122$		0			0
$123$	−11284.9	+	11284.9i	−0.0672569	+	0.0672569i
$124$		0			0
$125$	11048.5	+	11048.5i	0.0632456	+	0.0632456i
$126$		0			0
$127$	12378.2			0.0681002			0.0340501	−	0.999420i	$-0.489159\pi$
$127$	12378.2			0.0681002			0.0340501	+	0.999420i	$0.489159\pi$
$128$		0			0
$129$	−54874.0			−0.290330
$130$		0			0
$131$	−106355.	−	106355.i	−0.541476	−	0.541476i	0.382485	−	0.923962i	$-0.375068\pi$
$131$	−106355.	−	106355.i	−0.541476	−	0.541476i	−0.923962	+	0.382485i	$0.875068\pi$
$132$		0			0
$133$	−7543.59	+	7543.59i	−0.0369785	+	0.0369785i
$134$		0			0
$135$		−	62258.9i		−	0.294014i
$136$		0			0
$137$			12703.6i			0.0578264i	0.999582	+	0.0289132i	$0.00920465\pi$
$137$			12703.6i			0.0578264i	−0.999582	+	0.0289132i	$0.990795\pi$
$138$		0			0
$139$	−94848.3	+	94848.3i	−0.416383	+	0.416383i	−0.883955	−	0.467572i	$-0.845129\pi$
$139$	−94848.3	+	94848.3i	−0.416383	+	0.416383i	0.467572	+	0.883955i	$0.345129\pi$
$140$		0			0
$141$	−1815.96	−	1815.96i	−0.00769235	−	0.00769235i
$142$		0			0
$143$	334156.			1.36650
$144$		0			0
$145$	210636.			0.831980
$146$		0			0
$147$	−63273.8	−	63273.8i	−0.241508	−	0.241508i
$148$		0			0
$149$	227916.	−	227916.i	0.841026	−	0.841026i	−0.147966	−	0.988992i	$-0.547273\pi$
$149$	227916.	−	227916.i	0.841026	−	0.841026i	0.988992	+	0.147966i	$0.0472727\pi$
$150$		0			0
$151$		−	17188.0i		−	0.0613454i	−0.999529	−	0.0306727i	$-0.990235\pi$
$151$		−	17188.0i		−	0.0613454i	0.999529	−	0.0306727i	$-0.00976496\pi$
$152$		0			0
$153$			446554.i			1.54222i
$154$		0			0
$155$	−182328.	+	182328.i	−0.609571	+	0.609571i
$156$		0			0
$157$	−36276.9	−	36276.9i	−0.117458	−	0.117458i	0.645935	−	0.763393i	$-0.276468\pi$
$157$	−36276.9	−	36276.9i	−0.117458	−	0.117458i	−0.763393	+	0.645935i	$0.776468\pi$
$158$		0			0
$159$	45812.4			0.143711
$160$		0			0
$161$	−73503.1			−0.223481
$162$		0			0
$163$	41418.5	+	41418.5i	0.122103	+	0.122103i	0.765518	−	0.643415i	$-0.222483\pi$
$163$	41418.5	+	41418.5i	0.122103	+	0.122103i	−0.643415	+	0.765518i	$0.722483\pi$
$164$		0			0
$165$	36670.5	−	36670.5i	0.104859	−	0.104859i
$166$		0			0
$167$		−	400566.i		−	1.11143i	−0.831372	−	0.555717i	$-0.812444\pi$
$167$		−	400566.i		−	1.11143i	0.831372	−	0.555717i	$-0.187556\pi$
$168$		0			0
$169$			401971.i			1.08262i
$170$		0			0
$171$	78951.8	−	78951.8i	0.206477	−	0.206477i
$172$		0			0
$173$	−241650.	−	241650.i	−0.613862	−	0.613862i	0.330088	−	0.943950i	$-0.392922\pi$
$173$	−241650.	−	241650.i	−0.613862	−	0.613862i	−0.943950	+	0.330088i	$0.892922\pi$
$174$		0			0
$175$	12731.6			0.0314260
$176$		0			0
$177$	−64891.9			−0.155689
$178$		0			0
$179$	−143567.	−	143567.i	−0.334905	−	0.334905i	0.519541	−	0.854446i	$-0.326103\pi$
$179$	−143567.	−	143567.i	−0.334905	−	0.334905i	−0.854446	+	0.519541i	$0.826103\pi$
$180$		0			0
$181$	189284.	−	189284.i	0.429454	−	0.429454i	−0.458988	−	0.888442i	$-0.651788\pi$
$181$	189284.	−	189284.i	0.429454	−	0.429454i	0.888442	+	0.458988i	$0.151788\pi$
$182$		0			0
$183$			212674.i			0.469446i
$184$		0			0
$185$			100066.i			0.214960i
$186$		0			0
$187$	−562804.	+	562804.i	−1.17694	+	1.17694i
$188$		0			0
$189$	−35871.6	−	35871.6i	−0.0730459	−	0.0730459i
$190$		0			0
$191$	218440.			0.433259			0.216630	−	0.976254i	$-0.430494\pi$
$191$	218440.			0.433259			0.216630	+	0.976254i	$0.430494\pi$
$192$		0			0
$193$	−627669.			−1.21293			−0.606467	−	0.795109i	$-0.707414\pi$
$193$	−627669.			−1.21293			−0.606467	+	0.795109i	$0.707414\pi$
$194$		0			0
$195$	84858.4	+	84858.4i	0.159812	+	0.159812i
$196$		0			0
$197$	−145767.	+	145767.i	−0.267605	+	0.267605i	−0.828134	−	0.560530i	$-0.810598\pi$
$197$	−145767.	+	145767.i	−0.267605	+	0.267605i	0.560530	+	0.828134i	$0.310598\pi$
$198$		0			0
$199$			874377.i			1.56519i	0.622534	+	0.782593i	$0.286103\pi$
$199$			874377.i			1.56519i	−0.622534	+	0.782593i	$0.713897\pi$
$200$		0			0
$201$			384439.i			0.671177i
$202$		0			0
$203$	121362.	−	121362.i	0.206701	−	0.206701i
$204$		0			0
$205$	51681.3	+	51681.3i	0.0858912	+	0.0858912i
$206$		0			0
$207$	769289.			1.24785
$208$		0			0
$209$	199010.			0.315144
$210$		0			0
$211$	−278056.	−	278056.i	−0.429958	−	0.429958i	0.458656	−	0.888614i	$-0.348331\pi$
$211$	−278056.	−	278056.i	−0.429958	−	0.429958i	−0.888614	+	0.458656i	$0.848331\pi$
$212$		0			0
$213$	−271053.	+	271053.i	−0.409361	+	0.409361i
$214$		0			0
$215$			251304.i			0.370770i
$216$		0			0
$217$			210103.i			0.302888i
$218$		0			0
$219$	−210290.	+	210290.i	−0.296284	+	0.296284i
$220$		0			0
$221$	−1.30237e6	−	1.30237e6i	−1.79372	−	1.79372i
$222$		0			0
$223$	1.12642e6			1.51684			0.758420	−	0.651767i	$-0.225972\pi$
$223$	1.12642e6			1.51684			0.758420	+	0.651767i	$0.225972\pi$
$224$		0			0
$225$	−133250.			−0.175473
$226$		0			0
$227$	290194.	+	290194.i	0.373787	+	0.373787i	0.868854	−	0.495068i	$-0.164857\pi$
$227$	290194.	+	290194.i	0.373787	+	0.373787i	−0.495068	+	0.868854i	$0.664857\pi$
$228$		0			0
$229$	726941.	−	726941.i	0.916031	−	0.916031i	−0.0807066	−	0.996738i	$-0.525718\pi$
$229$	726941.	−	726941.i	0.916031	−	0.916031i	0.996738	+	0.0807066i	$0.0257177\pi$
$230$		0			0
$231$		−	42256.7i		−	0.0521033i
$232$		0			0
$233$			929560.i			1.12173i	0.827908	+	0.560864i	$0.189531\pi$
$233$			929560.i			1.12173i	−0.827908	+	0.560864i	$0.810469\pi$
$234$		0			0
$235$	−8316.50	+	8316.50i	−0.00982360	+	0.00982360i
$236$		0			0
$237$	−267305.	−	267305.i	−0.309127	−	0.309127i
$238$		0			0
$239$	−743046.			−0.841436			−0.420718	−	0.907192i	$-0.638222\pi$
$239$	−743046.			−0.841436			−0.420718	+	0.907192i	$0.638222\pi$
$240$		0			0
$241$	−226030.			−0.250682			−0.125341	−	0.992114i	$-0.540003\pi$
$241$	−226030.			−0.250682			−0.125341	+	0.992114i	$0.540003\pi$
$242$		0			0
$243$	575414.	+	575414.i	0.625122	+	0.625122i
$244$		0			0
$245$	−289773.	+	289773.i	−0.308420	+	0.308420i
$246$		0			0
$247$			460525.i			0.480298i
$248$		0			0
$249$		−	167193.i		−	0.170891i
$250$		0			0
$251$	−904818.	+	904818.i	−0.906519	+	0.906519i	−0.995989	−	0.0894704i	$-0.971483\pi$
$251$	−904818.	+	904818.i	−0.906519	+	0.906519i	0.0894704	+	0.995989i	$0.471483\pi$
$252$		0			0
$253$	969554.	+	969554.i	0.952294	+	0.952294i
$254$		0			0
$255$	−285847.			−0.275285
$256$		0			0
$257$	−296966.			−0.280462			−0.140231	−	0.990119i	$-0.544785\pi$
$257$	−296966.			−0.280462			−0.140231	+	0.990119i	$0.544785\pi$
$258$		0			0
$259$	57654.7	+	57654.7i	0.0534054	+	0.0534054i
$260$		0			0
$261$	−1.27018e6	+	1.27018e6i	−1.15416	+	1.15416i
$262$		0			0
$263$			1.00748e6i			0.898144i	0.893495	+	0.449072i	$0.148245\pi$
$263$			1.00748e6i			0.898144i	−0.893495	+	0.449072i	$0.851755\pi$
$264$		0			0
$265$		−	209806.i		−	0.183528i
$266$		0			0
$267$	12848.4	−	12848.4i	0.0110299	−	0.0110299i
$268$		0			0
$269$	612624.	+	612624.i	0.516195	+	0.516195i	0.916418	−	0.400223i	$-0.131067\pi$
$269$	612624.	+	612624.i	0.516195	+	0.516195i	−0.400223	+	0.916418i	$0.631067\pi$
$270$		0			0
$271$	1.44682e6			1.19672			0.598358	−	0.801229i	$-0.295820\pi$
$271$	1.44682e6			1.19672			0.598358	+	0.801229i	$0.295820\pi$
$272$		0			0
$273$	97785.3			0.0794085
$274$		0			0
$275$	−167938.	−	167938.i	−0.133912	−	0.133912i
$276$		0			0
$277$	−134739.	+	134739.i	−0.105510	+	0.105510i	−0.757891	−	0.652381i	$-0.773770\pi$
$277$	−134739.	+	134739.i	−0.105510	+	0.105510i	0.652381	+	0.757891i	$0.273770\pi$
$278$		0			0
$279$		−	2.19895e6i		−	1.69124i
$280$		0			0
$281$			718447.i			0.542786i	0.962469	+	0.271393i	$0.0874844\pi$
$281$			718447.i			0.542786i	−0.962469	+	0.271393i	$0.912516\pi$
$282$		0			0
$283$	−23252.5	+	23252.5i	−0.0172585	+	0.0172585i	−0.715683	−	0.698425i	$-0.753885\pi$
$283$	−23252.5	+	23252.5i	−0.0172585	+	0.0172585i	0.698425	+	0.715683i	$0.253885\pi$
$284$		0			0
$285$	50538.3	+	50538.3i	0.0368560	+	0.0368560i
$286$		0			0
$287$	59554.1			0.0426783
$288$		0			0
$289$	2.96720e6			2.08979
$290$		0			0
$291$	−496584.	−	496584.i	−0.343764	−	0.343764i
$292$		0			0
$293$	509773.	−	509773.i	0.346903	−	0.346903i	−0.512052	−	0.858954i	$-0.671114\pi$
$293$	509773.	−	509773.i	0.346903	−	0.346903i	0.858954	+	0.512052i	$0.171114\pi$
$294$		0			0
$295$			297183.i			0.198824i
$296$		0			0
$297$			946339.i			0.622524i
$298$		0			0
$299$	−2.24363e6	+	2.24363e6i	−1.45135	+	1.45135i
$300$		0			0
$301$	144793.	+	144793.i	0.0921155	+	0.0921155i
$302$		0			0
$303$	−50351.3			−0.0315068
$304$		0			0
$305$	973974.			0.599512
$306$		0			0
$307$	−1.48996e6	−	1.48996e6i	−0.902253	−	0.902253i	0.0933775	−	0.995631i	$-0.470234\pi$
$307$	−1.48996e6	−	1.48996e6i	−0.902253	−	0.902253i	−0.995631	+	0.0933775i	$0.970234\pi$
$308$		0			0
$309$	−534140.	+	534140.i	−0.318243	+	0.318243i
$310$		0			0
$311$		−	431469.i		−	0.252958i	−0.991969	−	0.126479i	$-0.959632\pi$
$311$		−	431469.i		−	0.252958i	0.991969	−	0.126479i	$-0.0403676\pi$
$312$		0			0
$313$			1.81612e6i			1.04781i	0.851776	+	0.523906i	$0.175526\pi$
$313$			1.81612e6i			1.04781i	−0.851776	+	0.523906i	$0.824474\pi$
$314$		0			0
$315$	−76774.4	+	76774.4i	−0.0435953	+	0.0435953i
$316$		0			0
$317$	735496.	+	735496.i	0.411086	+	0.411086i	0.882117	−	0.471031i	$-0.156118\pi$
$317$	735496.	+	735496.i	0.411086	+	0.411086i	−0.471031	+	0.882117i	$0.656118\pi$
$318$		0			0
$319$	−3.20168e6			−1.76158
$320$		0			0
$321$	−428326.			−0.232013
$322$		0			0
$323$	−775642.	−	775642.i	−0.413671	−	0.413671i
$324$		0			0
$325$	388623.	−	388623.i	0.204089	−	0.204089i
$326$		0			0
$327$			552522.i			0.285746i
$328$		0			0
$329$			9583.39i			0.00488123i
$330$		0			0
$331$	1.14396e6	−	1.14396e6i	0.573907	−	0.573907i	−0.359311	−	0.933218i	$-0.616988\pi$
$331$	1.14396e6	−	1.14396e6i	0.573907	−	0.573907i	0.933218	+	0.359311i	$0.116988\pi$
$332$		0			0
$333$	−603419.	−	603419.i	−0.298200	−	0.298200i
$334$		0			0
$335$	1.76060e6			0.857134
$336$		0			0
$337$	−3.71312e6			−1.78100			−0.890500	−	0.454983i	$-0.849645\pi$
$337$	−3.71312e6			−1.78100			−0.890500	+	0.454983i	$0.849645\pi$
$338$		0			0
$339$	−218785.	−	218785.i	−0.103400	−	0.103400i
$340$		0			0
$341$	2.77140e6	−	2.77140e6i	1.29066	−	1.29066i
$342$		0			0
$343$			676284.i			0.310380i
$344$		0			0
$345$			492434.i			0.222741i
$346$		0			0
$347$	2.30050e6	−	2.30050e6i	1.02565	−	1.02565i	0.0259845	−	0.999662i	$-0.491728\pi$
$347$	2.30050e6	−	2.30050e6i	1.02565	−	1.02565i	0.999662	−	0.0259845i	$-0.00827206\pi$
$348$		0			0
$349$	−458011.	−	458011.i	−0.201286	−	0.201286i	0.599265	−	0.800551i	$-0.295460\pi$
$349$	−458011.	−	458011.i	−0.201286	−	0.201286i	−0.800551	+	0.599265i	$0.795460\pi$
$350$		0			0
$351$	−2.18991e6			−0.948763
$352$		0			0
$353$	1.98245e6			0.846768			0.423384	−	0.905950i	$-0.360842\pi$
$353$	1.98245e6			0.846768			0.423384	+	0.905950i	$0.360842\pi$
$354$		0			0
$355$	1.24133e6	+	1.24133e6i	0.522779	+	0.522779i
$356$		0			0
$357$	−164695.	+	164695.i	−0.0683929	+	0.0683929i
$358$		0			0
$359$			3.42438e6i			1.40232i	0.713006	+	0.701158i	$0.247333\pi$
$359$			3.42438e6i			1.40232i	−0.713006	+	0.701158i	$0.752667\pi$
$360$		0			0
$361$		−	2.20183e6i		−	0.889233i
$362$		0			0
$363$	64269.3	−	64269.3i	0.0255998	−	0.0255998i
$364$		0			0
$365$	963057.	+	963057.i	0.378373	+	0.378373i
$366$		0			0
$367$	553446.			0.214491			0.107246	−	0.994233i	$-0.465797\pi$
$367$	553446.			0.214491			0.107246	+	0.994233i	$0.465797\pi$
$368$		0			0
$369$	−623298.			−0.238303
$370$		0			0
$371$	−120883.	−	120883.i	−0.0455964	−	0.0455964i
$372$		0			0
$373$	−1.82003e6	+	1.82003e6i	−0.677341	+	0.677341i	−0.959398	−	0.282057i	$-0.908983\pi$
$373$	−1.82003e6	+	1.82003e6i	−0.677341	+	0.677341i	0.282057	+	0.959398i	$0.408983\pi$
$374$		0			0
$375$		−	85295.5i		−	0.0313219i
$376$		0			0
$377$		−	7.40895e6i		−	2.68475i
$378$		0			0
$379$	3.47422e6	−	3.47422e6i	1.24239	−	1.24239i	0.283388	−	0.959005i	$-0.408542\pi$
$379$	3.47422e6	−	3.47422e6i	1.24239	−	1.24239i	0.959005	−	0.283388i	$-0.0914584\pi$
$380$		0			0
$381$	−47780.3	−	47780.3i	−0.0168631	−	0.0168631i
$382$		0			0
$383$	1.64390e6			0.572634			0.286317	−	0.958135i	$-0.407569\pi$
$383$	1.64390e6			0.572634			0.286317	+	0.958135i	$0.407569\pi$
$384$		0			0
$385$	−193521.			−0.0665391
$386$		0			0
$387$	−1.51542e6	−	1.51542e6i	−0.514346	−	0.514346i
$388$		0			0
$389$	1.26514e6	−	1.26514e6i	0.423902	−	0.423902i	−0.462643	−	0.886545i	$-0.653099\pi$
$389$	1.26514e6	−	1.26514e6i	0.423902	−	0.423902i	0.886545	+	0.462643i	$0.153099\pi$
$390$		0			0
$391$		−	7.55768e6i		−	2.50004i
$392$		0			0
$393$			821068.i			0.268162i
$394$		0			0
$395$	−1.22417e6	+	1.22417e6i	−0.394774	+	0.394774i
$396$		0			0
$397$	−881275.	−	881275.i	−0.280631	−	0.280631i	0.552730	−	0.833361i	$-0.313586\pi$
$397$	−881275.	−	881275.i	−0.280631	−	0.280631i	−0.833361	+	0.552730i	$0.813586\pi$
$398$		0			0
$399$	58237.1			0.0183133
$400$		0			0
$401$	−1.43364e6			−0.445225			−0.222613	−	0.974907i	$-0.571459\pi$
$401$	−1.43364e6			−0.445225			−0.222613	+	0.974907i	$0.571459\pi$
$402$		0			0
$403$	6.41323e6	+	6.41323e6i	1.96705	+	1.96705i
$404$		0			0
$405$	675517.	−	675517.i	0.204644	−	0.204644i
$406$		0			0
$407$		−	1.52101e6i		−	0.455140i
$408$		0			0
$409$		−	2.61233e6i		−	0.772182i	−0.922461	−	0.386091i	$-0.873825\pi$
$409$		−	2.61233e6i		−	0.772182i	0.922461	−	0.386091i	$-0.126175\pi$
$410$		0			0
$411$	49036.5	−	49036.5i	0.0143191	−	0.0143191i
$412$		0			0
$413$	171227.	+	171227.i	0.0493967	+	0.0493967i
$414$		0			0
$415$	−765689.			−0.218239
$416$		0			0
$417$	732235.			0.206210
$418$		0			0
$419$	−1.79144e6	−	1.79144e6i	−0.498502	−	0.498502i	0.412470	−	0.910971i	$-0.364666\pi$
$419$	−1.79144e6	−	1.79144e6i	−0.498502	−	0.498502i	−0.910971	+	0.412470i	$0.864666\pi$
$420$		0			0
$421$	−1.02803e6	+	1.02803e6i	−0.282684	+	0.282684i	−0.834179	−	0.551494i	$-0.814058\pi$
$421$	−1.02803e6	+	1.02803e6i	−0.282684	+	0.282684i	0.551494	+	0.834179i	$0.314058\pi$
$422$		0			0
$423$		−	100301.i		−	0.0272554i
$424$		0			0
$425$			1.30908e6i			0.351556i
$426$		0			0
$427$	561172.	−	561172.i	0.148945	−	0.148945i
$428$		0			0
$429$	−1.28985e6	−	1.28985e6i	−0.338374	−	0.338374i
$430$		0			0
$431$	−2.46985e6			−0.640438			−0.320219	−	0.947343i	$-0.603757\pi$
$431$	−2.46985e6			−0.640438			−0.320219	+	0.947343i	$0.603757\pi$
$432$		0			0
$433$	2.37472e6			0.608685			0.304343	−	0.952563i	$-0.401563\pi$
$433$	2.37472e6			0.608685			0.304343	+	0.952563i	$0.401563\pi$
$434$		0			0
$435$	−813063.	−	813063.i	−0.206016	−	0.206016i
$436$		0			0
$437$	−1.33622e6	+	1.33622e6i	−0.334713	+	0.334713i
$438$		0			0
$439$		−	2.14558e6i		−	0.531352i	−0.964062	−	0.265676i	$-0.914405\pi$
$439$		−	2.14558e6i		−	0.531352i	0.964062	−	0.265676i	$-0.0855952\pi$
$440$		0			0
$441$		−	3.49479e6i		−	0.855705i
$442$		0			0
$443$	202439.	−	202439.i	0.0490100	−	0.0490100i	−0.682177	−	0.731187i	$-0.738967\pi$
$443$	202439.	−	202439.i	0.0490100	−	0.0490100i	0.731187	+	0.682177i	$0.238967\pi$
$444$		0			0
$445$	−58841.6	−	58841.6i	−0.0140859	−	0.0140859i
$446$		0			0
$447$	−1.75953e6			−0.416512
$448$		0			0
$449$	−7.11149e6			−1.66473			−0.832367	−	0.554225i	$-0.813015\pi$
$449$	−7.11149e6			−1.66473			−0.832367	+	0.554225i	$0.813015\pi$
$450$		0			0
$451$	−785559.	−	785559.i	−0.181860	−	0.181860i
$452$		0			0
$453$	−66346.2	+	66346.2i	−0.0151904	+	0.0151904i
$454$		0			0
$455$		−	447824.i		−	0.101410i
$456$		0			0
$457$		−	3.03083e6i		−	0.678846i	−0.940634	−	0.339423i	$-0.889768\pi$
$457$		−	3.03083e6i		−	0.678846i	0.940634	−	0.339423i	$-0.110232\pi$
$458$		0			0
$459$	3.68836e6	−	3.68836e6i	0.817150	−	0.817150i
$460$		0			0
$461$	−4.79592e6	−	4.79592e6i	−1.05104	−	1.05104i	−0.998625	−	0.0524147i	$-0.983308\pi$
$461$	−4.79592e6	−	4.79592e6i	−1.05104	−	1.05104i	−0.0524147	−	0.998625i	$-0.516692\pi$
$462$		0			0
$463$	−3.25096e6			−0.704789			−0.352395	−	0.935851i	$-0.614633\pi$
$463$	−3.25096e6			−0.704789			−0.352395	+	0.935851i	$0.614633\pi$
$464$		0			0
$465$	1.40758e6			0.301885
$466$		0			0
$467$	3.68299e6	+	3.68299e6i	0.781463	+	0.781463i	0.980078	−	0.198615i	$-0.0636443\pi$
$467$	3.68299e6	+	3.68299e6i	0.781463	+	0.781463i	−0.198615	+	0.980078i	$0.563644\pi$
$468$		0			0
$469$	1.01440e6	−	1.01440e6i	0.212950	−	0.212950i
$470$		0			0
$471$			280060.i			0.0581700i
$472$		0			0
$473$		−	3.81984e6i		−	0.785041i
$474$		0			0
$475$	231449.	−	231449.i	0.0470674	−	0.0470674i
$476$		0			0
$477$	1.26517e6	+	1.26517e6i	0.254597	+	0.254597i
$478$		0			0
$479$	629120.			0.125284			0.0626419	−	0.998036i	$-0.480047\pi$
$479$	629120.			0.125284			0.0626419	+	0.998036i	$0.480047\pi$
$480$		0			0
$481$	3.51974e6			0.693661
$482$		0			0
$483$	283724.	+	283724.i	0.0553387	+	0.0553387i
$484$		0			0
$485$	−2.27419e6	+	2.27419e6i	−0.439008	+	0.439008i
$486$		0			0
$487$		−	639056.i		−	0.122100i	−0.998135	−	0.0610501i	$-0.980555\pi$
$487$		−	639056.i		−	0.122100i	0.998135	−	0.0610501i	$-0.0194450\pi$
$488$		0			0
$489$		−	319754.i		−	0.0604704i
$490$		0			0
$491$	306275.	−	306275.i	0.0573334	−	0.0573334i	−0.677859	−	0.735192i	$-0.737092\pi$
$491$	306275.	−	306275.i	0.0573334	−	0.0573334i	0.735192	+	0.677859i	$0.237092\pi$
$492$		0			0
$493$	1.24786e7	+	1.24786e7i	2.31232	+	2.31232i
$494$		0			0
$495$	2.02541e6			0.371535
$496$		0			0
$497$	1.43043e6			0.259763
$498$		0			0
$499$	3.63733e6	+	3.63733e6i	0.653931	+	0.653931i	0.953937	−	0.300007i	$-0.0969889\pi$
$499$	3.63733e6	+	3.63733e6i	0.653931	+	0.653931i	−0.300007	+	0.953937i	$0.596989\pi$
$500$		0			0
$501$	−1.54620e6	+	1.54620e6i	−0.275215	+	0.275215i
$502$		0			0
$503$			8.04809e6i			1.41832i	0.705050	+	0.709158i	$0.250925\pi$
$503$			8.04809e6i			1.41832i	−0.705050	+	0.709158i	$0.749075\pi$
$504$		0			0
$505$			230592.i			0.0402361i
$506$		0			0
$507$	1.55162e6	−	1.55162e6i	0.268081	−	0.268081i
$508$		0			0
$509$	2.18413e6	+	2.18413e6i	0.373666	+	0.373666i	0.868811	−	0.495145i	$-0.164885\pi$
$509$	2.18413e6	+	2.18413e6i	0.373666	+	0.373666i	−0.495145	+	0.868811i	$0.664885\pi$
$510$		0			0
$511$	1.10976e6			0.188009
$512$		0			0
$513$	−1.30422e6			−0.218805
$514$		0			0
$515$	2.44618e6	+	2.44618e6i	0.406416	+	0.406416i
$516$		0			0
$517$	126411.	−	126411.i	0.0207998	−	0.0207998i
$518$		0			0
$519$			1.86555e6i			0.304011i
$520$		0			0
$521$		−	7.59494e6i		−	1.22583i	−0.790149	−	0.612914i	$-0.789997\pi$
$521$		−	7.59494e6i		−	1.22583i	0.790149	−	0.612914i	$-0.210003\pi$
$522$		0			0
$523$	7.40239e6	−	7.40239e6i	1.18336	−	1.18336i	0.204495	−	0.978868i	$-0.434445\pi$
$523$	7.40239e6	−	7.40239e6i	1.18336	−	1.18336i	0.978868	−	0.204495i	$-0.0655553\pi$
$524$		0			0
$525$	−49144.5	−	49144.5i	−0.00778174	−	0.00778174i
$526$		0			0
$527$	−2.16030e7			−3.38835
$528$		0			0
$529$	−6.58344e6			−1.02285
$530$		0			0
$531$	−1.79208e6	−	1.79208e6i	−0.275817	−	0.275817i
$532$		0			0
$533$	1.81785e6	−	1.81785e6i	0.277165	−	0.277165i
$534$		0			0
$535$			1.96159e6i			0.296295i
$536$		0			0
$537$			1.10835e6i			0.165859i
$538$		0			0
$539$	4.40457e6	−	4.40457e6i	0.653027	−	0.653027i
$540$		0			0
$541$	−4.81695e6	−	4.81695e6i	−0.707585	−	0.707585i	0.258442	−	0.966027i	$-0.416791\pi$
$541$	−4.81695e6	−	4.81695e6i	−0.707585	−	0.707585i	−0.966027	+	0.258442i	$0.916791\pi$
$542$		0			0
$543$	−1.46128e6			−0.212684
$544$		0			0
$545$	2.53037e6			0.364915
$546$		0			0
$547$	−6.11181e6	−	6.11181e6i	−0.873377	−	0.873377i	0.119462	−	0.992839i	$-0.461883\pi$
$547$	−6.11181e6	−	6.11181e6i	−0.873377	−	0.873377i	−0.992839	+	0.119462i	$0.961883\pi$
$548$		0			0
$549$	−5.87327e6	+	5.87327e6i	−0.831667	+	0.831667i
$550$		0			0
$551$		−	4.41248e6i		−	0.619161i
$552$		0			0
$553$			1.41065e6i			0.196158i
$554$		0			0
$555$	386258.	−	386258.i	0.0532286	−	0.0532286i
$556$		0			0
$557$	3.95240e6	+	3.95240e6i	0.539788	+	0.539788i	0.923467	−	0.383679i	$-0.125343\pi$
$557$	3.95240e6	+	3.95240e6i	0.539788	+	0.539788i	−0.383679	+	0.923467i	$0.625343\pi$
$558$		0			0
$559$	8.83943e6			1.19645
$560$		0			0
$561$	4.34488e6			0.582869
$562$		0			0
$563$	1.30447e6	+	1.30447e6i	0.173445	+	0.173445i	0.788491	−	0.615046i	$-0.210863\pi$
$563$	1.30447e6	+	1.30447e6i	0.173445	+	0.173445i	−0.615046	+	0.788491i	$0.710863\pi$
$564$		0			0
$565$	−1.00196e6	+	1.00196e6i	−0.132048	+	0.132048i
$566$		0			0
$567$		−	778422.i		−	0.101685i
$568$		0			0
$569$			259548.i			0.0336075i	0.999859	+	0.0168038i	$0.00534906\pi$
$569$			259548.i			0.0336075i	−0.999859	+	0.0168038i	$0.994651\pi$
$570$		0			0
$571$	−8.20992e6	+	8.20992e6i	−1.05378	+	1.05378i	−0.0553069	+	0.998469i	$0.517614\pi$
$571$	−8.20992e6	+	8.20992e6i	−1.05378	+	1.05378i	−0.998469	+	0.0553069i	$0.982386\pi$
$572$		0			0
$573$	−843184.	−	843184.i	−0.107284	−	0.107284i
$574$		0			0
$575$	2.25518e6			0.284454
$576$		0			0
$577$	−32512.1			−0.00406542			−0.00203271	−	0.999998i	$-0.500647\pi$
$577$	−32512.1			−0.00406542			−0.00203271	+	0.999998i	$0.500647\pi$
$578$		0			0
$579$	2.42282e6	+	2.42282e6i	0.300348	+	0.300348i
$580$		0			0
$581$	−441165.	+	441165.i	−0.0542201	+	0.0542201i
$582$		0			0
$583$			3.18906e6i			0.388589i
$584$		0			0
$585$			4.68696e6i			0.566242i
$586$		0			0
$587$	−7.33552e6	+	7.33552e6i	−0.878690	+	0.878690i	−0.993399	−	0.114709i	$-0.963406\pi$
$587$	−7.33552e6	+	7.33552e6i	−0.878690	+	0.878690i	0.114709	+	0.993399i	$0.463406\pi$
$588$		0			0
$589$	3.81947e6	+	3.81947e6i	0.453643	+	0.453643i
$590$		0			0
$591$	1.12533e6			0.132529
$592$		0			0
$593$	3.74815e6			0.437704			0.218852	−	0.975758i	$-0.429769\pi$
$593$	3.74815e6			0.437704			0.218852	+	0.975758i	$0.429769\pi$
$594$		0			0
$595$	754250.	+	754250.i	0.0873420	+	0.0873420i
$596$		0			0
$597$	3.37512e6	−	3.37512e6i	0.387573	−	0.387573i
$598$		0			0
$599$		−	32116.0i		−	0.00365725i	−0.999998	−	0.00182862i	$-0.999418\pi$
$599$		−	32116.0i		−	0.00365725i	0.999998	−	0.00182862i	$-0.000582069\pi$
$600$		0			0
$601$			1.53233e7i			1.73047i	0.501364	+	0.865236i	$0.332832\pi$
$601$			1.53233e7i			1.73047i	−0.501364	+	0.865236i	$0.667168\pi$
$602$		0			0
$603$	−1.06168e7	+	1.06168e7i	−1.18905	+	1.18905i
$604$		0			0
$605$	−294332.	−	294332.i	−0.0326925	−	0.0326925i
$606$		0			0
$607$	9.26259e6			1.02038			0.510189	−	0.860063i	$-0.329576\pi$
$607$	9.26259e6			1.02038			0.510189	+	0.860063i	$0.329576\pi$
$608$		0			0
$609$	−936921.			−0.102367
$610$		0			0
$611$	292526.	+	292526.i	0.0317001	+	0.0317001i
$612$		0			0
$613$	−4.22409e6	+	4.22409e6i	−0.454027	+	0.454027i	−0.896689	−	0.442662i	$-0.854034\pi$
$613$	−4.22409e6	+	4.22409e6i	−0.454027	+	0.454027i	0.442662	+	0.896689i	$0.354034\pi$
$614$		0			0
$615$		−	398983.i		−	0.0425370i
$616$		0			0
$617$		−	1.06955e7i		−	1.13107i	−0.824725	−	0.565534i	$-0.808670\pi$
$617$		−	1.06955e7i		−	1.13107i	0.824725	−	0.565534i	$-0.191330\pi$
$618$		0			0
$619$	−1.29776e6	+	1.29776e6i	−0.136135	+	0.136135i	−0.771890	−	0.635756i	$-0.780689\pi$
$619$	−1.29776e6	+	1.29776e6i	−0.136135	+	0.136135i	0.635756	+	0.771890i	$0.280689\pi$
$620$		0			0
$621$	−6.35402e6	−	6.35402e6i	−0.661180	−	0.661180i
$622$		0			0
$623$	−67805.2			−0.00699911
$624$		0			0
$625$	−390625.			−0.0400000
$626$		0			0
$627$	−768185.	−	768185.i	−0.0780364	−	0.0780364i
$628$		0			0
$629$	−5.92813e6	+	5.92813e6i	−0.597436	+	0.597436i
$630$		0			0
$631$		−	1.23969e6i		−	0.123948i	−0.998078	−	0.0619738i	$-0.980260\pi$
$631$		−	1.23969e6i		−	0.123948i	0.998078	−	0.0619738i	$-0.0197395\pi$
$632$		0			0
$633$			2.14661e6i			0.212934i
$634$		0			0
$635$	−218818.	+	218818.i	−0.0215352	+	0.0215352i
$636$		0			0
$637$	1.01925e7	+	1.01925e7i	0.995252	+	0.995252i
$638$		0			0
$639$	−1.49710e7			−1.45044
$640$		0			0
$641$	3.96999e6			0.381632			0.190816	−	0.981626i	$-0.438887\pi$
$641$	3.96999e6			0.381632			0.190816	+	0.981626i	$0.438887\pi$
$642$		0			0
$643$	5.11306e6	+	5.11306e6i	0.487701	+	0.487701i	0.907580	−	0.419879i	$-0.137928\pi$
$643$	5.11306e6	+	5.11306e6i	0.487701	+	0.487701i	−0.419879	+	0.907580i	$0.637928\pi$
$644$		0			0
$645$	970044.	−	970044.i	0.0918105	−	0.0918105i
$646$		0			0
$647$			1.08958e7i			1.02329i	0.859196	+	0.511646i	$0.170964\pi$
$647$			1.08958e7i			1.02329i	−0.859196	+	0.511646i	$0.829036\pi$
$648$		0			0
$649$		−	4.51720e6i		−	0.420976i
$650$		0			0
$651$	811004.	−	811004.i	0.0750016	−	0.0750016i
$652$		0			0
$653$	7.99690e6	+	7.99690e6i	0.733903	+	0.733903i	0.971391	−	0.237488i	$-0.0763240\pi$
$653$	7.99690e6	+	7.99690e6i	0.733903	+	0.733903i	−0.237488	+	0.971391i	$0.576324\pi$
$654$		0			0
$655$	3.76022e6			0.342460
$656$		0			0
$657$	−1.16149e7			−1.04979
$658$		0			0
$659$	−5.10943e6	−	5.10943e6i	−0.458310	−	0.458310i	0.439791	−	0.898100i	$-0.355053\pi$
$659$	−5.10943e6	−	5.10943e6i	−0.458310	−	0.458310i	−0.898100	+	0.439791i	$0.855053\pi$
$660$		0			0
$661$	−1.30768e6	+	1.30768e6i	−0.116412	+	0.116412i	−0.762913	−	0.646501i	$-0.776232\pi$
$661$	−1.30768e6	+	1.30768e6i	−0.116412	+	0.116412i	0.646501	+	0.762913i	$0.276232\pi$
$662$		0			0
$663$			1.00544e7i			0.888327i
$664$		0			0
$665$		−	266706.i		−	0.0233872i
$666$		0			0
$667$	2.14971e7	−	2.14971e7i	1.87096	−	1.87096i
$668$		0			0
$669$	−4.34803e6	−	4.34803e6i	−0.375602	−	0.375602i
$670$		0			0
$671$	−1.48045e7			−1.26936
$672$		0			0
$673$	1.39705e7			1.18898			0.594491	−	0.804102i	$-0.297353\pi$
$673$	1.39705e7			1.18898			0.594491	+	0.804102i	$0.297353\pi$
$674$		0			0
$675$	1.10059e6	+	1.10059e6i	0.0929752	+	0.0929752i
$676$		0			0
$677$	3.27475e6	−	3.27475e6i	0.274603	−	0.274603i	−0.556347	−	0.830950i	$-0.687797\pi$
$677$	3.27475e6	−	3.27475e6i	0.274603	−	0.274603i	0.830950	+	0.556347i	$0.187797\pi$
$678$		0			0
$679$			2.62063e6i			0.218138i
$680$		0			0
$681$		−	2.24032e6i		−	0.185115i
$682$		0			0
$683$	−1.37218e7	+	1.37218e7i	−1.12554	+	1.12554i	−0.134641	+	0.990894i	$0.542988\pi$
$683$	−1.37218e7	+	1.37218e7i	−1.12554	+	1.12554i	−0.990894	+	0.134641i	$0.957012\pi$
$684$		0			0
$685$	−224571.	−	224571.i	−0.0182863	−	0.0182863i
$686$		0			0
$687$	−5.61203e6			−0.453658
$688$		0			0
$689$	−7.37973e6			−0.592233
$690$		0			0
$691$	−1.41091e7	−	1.41091e7i	−1.12410	−	1.12410i	−0.991119	−	0.132978i	$-0.957546\pi$
$691$	−1.41091e7	−	1.41091e7i	−1.12410	−	1.12410i	−0.132978	−	0.991119i	$-0.542454\pi$
$692$		0			0
$693$	1.16698e6	−	1.16698e6i	0.0923057	−	0.0923057i
$694$		0			0
$695$		−	3.35339e6i		−	0.263343i
$696$		0			0
$697$			6.12343e6i			0.477434i
$698$		0			0
$699$	3.58813e6	−	3.58813e6i	0.277764	−	0.277764i
$700$		0			0
$701$	−4.66155e6	−	4.66155e6i	−0.358290	−	0.358290i	0.504892	−	0.863182i	$-0.331532\pi$
$701$	−4.66155e6	−	4.66155e6i	−0.358290	−	0.358290i	−0.863182	+	0.504892i	$0.831532\pi$
$702$		0			0
$703$	2.09621e6			0.159973
$704$		0			0
$705$	64203.9			0.00486507
$706$		0			0
$707$	132860.	+	132860.i	0.00999642	+	0.00999642i
$708$		0			0
$709$	−5.95157e6	+	5.95157e6i	−0.444648	+	0.444648i	−0.893570	−	0.448923i	$-0.851808\pi$
$709$	−5.95157e6	+	5.95157e6i	−0.444648	+	0.444648i	0.448923	+	0.893570i	$0.351808\pi$
$710$		0			0
$711$		−	1.47640e7i		−	1.09529i
$712$		0			0
$713$			3.72160e7i			2.74161i
$714$		0			0
$715$	−5.90710e6	+	5.90710e6i	−0.432125	+	0.432125i
$716$		0			0
$717$	2.86818e6	+	2.86818e6i	0.208357	+	0.208357i
$718$		0			0
$719$	1.53105e7			1.10450			0.552251	−	0.833678i	$-0.313769\pi$
$719$	1.53105e7			1.10450			0.552251	+	0.833678i	$0.313769\pi$
$720$		0			0
$721$	2.81882e6			0.201943
$722$		0			0
$723$	872484.	+	872484.i	0.0620743	+	0.0620743i
$724$		0			0
$725$	−3.72356e6	+	3.72356e6i	−0.263095	+	0.263095i
$726$		0			0
$727$			1.84545e7i			1.29499i	0.762070	+	0.647494i	$0.224183\pi$
$727$			1.84545e7i			1.29499i	−0.762070	+	0.647494i	$0.775817\pi$
$728$		0			0
$729$			4.84353e6i			0.337554i
$730$		0			0
$731$	−1.48878e7	+	1.48878e7i	−1.03048	+	1.03048i
$732$		0			0
$733$	−4.32766e6	−	4.32766e6i	−0.297504	−	0.297504i	0.542531	−	0.840036i	$-0.317466\pi$
$733$	−4.32766e6	−	4.32766e6i	−0.297504	−	0.297504i	−0.840036	+	0.542531i	$0.817466\pi$
$734$		0			0
$735$	2.23707e6			0.152743
$736$		0			0
$737$	−2.67612e7			−1.81484
$738$		0			0
$739$	1.35979e7	+	1.35979e7i	0.915924	+	0.915924i	0.996730	−	0.0808056i	$-0.0257493\pi$
$739$	1.35979e7	+	1.35979e7i	0.915924	+	0.915924i	−0.0808056	+	0.996730i	$0.525749\pi$
$740$		0			0
$741$	1.77764e6	−	1.77764e6i	0.118932	−	0.118932i
$742$		0			0
$743$		−	2.95819e6i		−	0.196586i	−0.995157	−	0.0982932i	$-0.968662\pi$
$743$		−	2.95819e6i		−	0.196586i	0.995157	−	0.0982932i	$-0.0313383\pi$
$744$		0			0
$745$			8.05806e6i			0.531912i
$746$		0			0
$747$	4.61727e6	−	4.61727e6i	0.302749	−	0.302749i
$748$		0			0
$749$	1.13020e6	+	1.13020e6i	0.0736127	+	0.0736127i
$750$		0			0
$751$	2.94196e7			1.90343			0.951715	−	0.306982i	$-0.0993191\pi$
$751$	2.94196e7			1.90343			0.951715	+	0.306982i	$0.0993191\pi$
$752$		0			0
$753$	6.98526e6			0.448947
$754$		0			0
$755$	303843.	+	303843.i	0.0193991	+	0.0193991i
$756$		0			0
$757$	9.32272e6	−	9.32272e6i	0.591293	−	0.591293i	−0.346688	−	0.937981i	$-0.612694\pi$
$757$	9.32272e6	−	9.32272e6i	0.591293	−	0.591293i	0.937981	+	0.346688i	$0.112694\pi$
$758$		0			0
$759$		−	7.48503e6i		−	0.471616i
$760$		0			0
$761$		−	5.78866e6i		−	0.362340i	−0.983452	−	0.181170i	$-0.942012\pi$
$761$		−	5.78866e6i		−	0.362340i	0.983452	−	0.181170i	$-0.0579884\pi$
$762$		0			0
$763$	1.45791e6	−	1.45791e6i	0.0906611	−	0.0906611i
$764$		0			0
$765$	−7.89404e6	−	7.89404e6i	−0.487692	−	0.487692i
$766$		0			0
$767$	1.04532e7			0.641593
$768$		0			0
$769$	1.52452e7			0.929647			0.464823	−	0.885403i	$-0.346118\pi$
$769$	1.52452e7			0.929647			0.464823	+	0.885403i	$0.346118\pi$
$770$		0			0
$771$	1.14630e6	+	1.14630e6i	0.0694485	+	0.0694485i
$772$		0			0
$773$	1.56687e7	−	1.56687e7i	0.943159	−	0.943159i	−0.0553104	−	0.998469i	$-0.517615\pi$
$773$	1.56687e7	−	1.56687e7i	0.943159	−	0.943159i	0.998469	+	0.0553104i	$0.0176148\pi$
$774$		0			0
$775$		−	6.44627e6i		−	0.385526i
$776$		0			0
$777$		−	445098.i		−	0.0264487i
$778$		0			0
$779$	1.08264e6	−	1.08264e6i	0.0639204	−	0.0639204i
$780$		0			0
$781$	−1.88684e7	−	1.88684e7i	−1.10689	−	1.10689i
$782$		0			0
$783$	2.09824e7			1.22307
$784$		0			0
$785$	1.28258e6			0.0742867
$786$		0			0
$787$	1.22035e7	+	1.22035e7i	0.702340	+	0.702340i	0.964912	−	0.262573i	$-0.0845709\pi$
$787$	1.22035e7	+	1.22035e7i	0.702340	+	0.702340i	−0.262573	+	0.964912i	$0.584571\pi$
$788$		0			0
$789$	3.88890e6	−	3.88890e6i	0.222400	−	0.222400i
$790$		0			0
$791$			1.15460e6i			0.0656130i
$792$		0			0
$793$		−	3.42587e7i		−	1.93459i
$794$		0			0
$795$	−809857.	+	809857.i	−0.0454454	+	0.0454454i
$796$		0			0
$797$	−1.69545e7	−	1.69545e7i	−0.945452	−	0.945452i	0.0531355	−	0.998587i	$-0.483078\pi$
$797$	−1.69545e7	−	1.69545e7i	−0.945452	−	0.945452i	−0.998587	+	0.0531355i	$0.983078\pi$
$798$		0			0
$799$	−985376.			−0.0546054
$800$		0			0
$801$	709655.			0.0390810
$802$		0			0
$803$	−1.46385e7	−	1.46385e7i	−0.801140	−	0.801140i
$804$		0			0
$805$	1.29936e6	−	1.29936e6i	0.0706709	−	0.0706709i
$806$		0			0
$807$		−	4.72950e6i		−	0.255642i
$808$		0			0
$809$		−	1.37569e7i		−	0.739006i	−0.929229	−	0.369503i	$-0.879528\pi$
$809$		−	1.37569e7i		−	0.739006i	0.929229	−	0.369503i	$-0.120472\pi$
$810$		0			0
$811$	−2.07314e7	+	2.07314e7i	−1.10682	+	1.10682i	−0.113255	+	0.993566i	$0.536128\pi$
$811$	−2.07314e7	+	2.07314e7i	−1.10682	+	1.10682i	−0.993566	+	0.113255i	$0.963872\pi$
$812$		0			0
$813$	−5.58478e6	−	5.58478e6i	−0.296333	−	0.296333i
$814$		0			0
$815$	−1.46436e6			−0.0772245
$816$		0			0
$817$	5.26441e6			0.275927
$818$		0			0
$819$	2.70048e6	+	2.70048e6i	0.140679	+	0.140679i
$820$		0			0
$821$	9.28682e6	−	9.28682e6i	0.480849	−	0.480849i	−0.424553	−	0.905403i	$-0.639569\pi$
$821$	9.28682e6	−	9.28682e6i	0.480849	−	0.480849i	0.905403	+	0.424553i	$0.139569\pi$
$822$		0			0
$823$			1.87853e6i			0.0966760i	0.998831	+	0.0483380i	$0.0153925\pi$
$823$			1.87853e6i			0.0966760i	−0.998831	+	0.0483380i	$0.984608\pi$
$824$		0			0
$825$			1.29650e6i			0.0663188i
$826$		0			0
$827$	2.33574e7	−	2.33574e7i	1.18757	−	1.18757i	0.209838	−	0.977736i	$-0.432706\pi$
$827$	2.33574e7	−	2.33574e7i	1.18757	−	1.18757i	0.977736	−	0.209838i	$-0.0672936\pi$
$828$		0			0
$829$	1.11096e7	+	1.11096e7i	0.561450	+	0.561450i	0.929719	−	0.368269i	$-0.120049\pi$
$829$	1.11096e7	+	1.11096e7i	0.561450	+	0.561450i	−0.368269	+	0.929719i	$0.620049\pi$
$830$		0			0
$831$	1.04020e6			0.0522532
$832$		0			0
$833$	−3.43336e7			−1.71438
$834$		0			0
$835$	7.08108e6	+	7.08108e6i	0.351466	+	0.351466i
$836$		0			0
$837$	−1.81625e7	+	1.81625e7i	−0.896110	+	0.896110i
$838$		0			0
$839$		−	1.47182e6i		−	0.0721853i	−0.999348	−	0.0360926i	$-0.988509\pi$
$839$		−	1.47182e6i		−	0.0721853i	0.999348	−	0.0360926i	$-0.0114911\pi$
$840$		0			0
$841$			5.04770e7i			2.46096i
$842$		0			0
$843$	2.77323e6	−	2.77323e6i	0.134405	−	0.134405i
$844$		0			0
$845$	−7.10590e6	−	7.10590e6i	−0.342356	−	0.342356i
$846$		0			0
$847$	−339169.			−0.0162445
$848$		0			0
$849$	179511.			0.00854716
$850$		0			0
$851$	1.02125e7	+	1.02125e7i	0.483403	+	0.483403i
$852$		0			0
$853$	3.67062e6	−	3.67062e6i	0.172730	−	0.172730i	−0.615448	−	0.788178i	$-0.711025\pi$
$853$	3.67062e6	−	3.67062e6i	0.172730	−	0.172730i	0.788178	+	0.615448i	$0.211025\pi$
$854$		0			0
$855$			2.79137e6i			0.130588i
$856$		0			0
$857$			1.14522e7i			0.532644i	0.963884	+	0.266322i	$0.0858084\pi$
$857$			1.14522e7i			0.532644i	−0.963884	+	0.266322i	$0.914192\pi$
$858$		0			0
$859$	−1.11225e7	+	1.11225e7i	−0.514303	+	0.514303i	−0.915842	−	0.401539i	$-0.868476\pi$
$859$	−1.11225e7	+	1.11225e7i	−0.514303	+	0.514303i	0.401539	+	0.915842i	$0.368476\pi$
$860$		0			0
$861$	−229881.	−	229881.i	−0.0105681	−	0.0105681i
$862$		0			0
$863$	−1.49268e7			−0.682243			−0.341122	−	0.940019i	$-0.610807\pi$
$863$	−1.49268e7			−0.682243			−0.341122	+	0.940019i	$0.610807\pi$
$864$		0			0
$865$	8.54360e6			0.388240
$866$		0			0
$867$	−1.14535e7	−	1.14535e7i	−0.517476	−	0.517476i
$868$		0			0
$869$	1.86074e7	−	1.86074e7i	0.835866	−	0.835866i
$870$		0			0
$871$		−	6.19276e7i		−	2.76592i
$872$		0			0
$873$		−	2.74277e7i		−	1.21802i
$874$		0			0
$875$	−225065.	+	225065.i	−0.00993776	+	0.00993776i
$876$		0			0
$877$	−3.03648e6	−	3.03648e6i	−0.133312	−	0.133312i	0.637302	−	0.770614i	$-0.280050\pi$
$877$	−3.03648e6	−	3.03648e6i	−0.133312	−	0.133312i	−0.770614	+	0.637302i	$0.780050\pi$
$878$		0			0
$879$	−3.93548e6			−0.171801
$880$		0			0
$881$	7.54197e6			0.327374			0.163687	−	0.986512i	$-0.447661\pi$
$881$	7.54197e6			0.327374			0.163687	+	0.986512i	$0.447661\pi$
$882$		0			0
$883$	−6.20139e6	−	6.20139e6i	−0.267662	−	0.267662i	0.560495	−	0.828158i	$-0.310611\pi$
$883$	−6.20139e6	−	6.20139e6i	−0.267662	−	0.267662i	−0.828158	+	0.560495i	$0.810611\pi$
$884$		0			0
$885$	1.14714e6	−	1.14714e6i	0.0492331	−	0.0492331i
$886$		0			0
$887$			1.72290e7i			0.735277i	0.929969	+	0.367639i	$0.119834\pi$
$887$			1.72290e7i			0.735277i	−0.929969	+	0.367639i	$0.880166\pi$
$888$		0			0
$889$			252151.i			0.0107006i
$890$		0			0
$891$	−1.02679e7	+	1.02679e7i	−0.433299	+	0.433299i
$892$		0			0
$893$	174217.	+	174217.i	0.00731074	+	0.00731074i
$894$		0			0
$895$	5.07586e6			0.211813
$896$		0			0
$897$	1.73210e7			0.718771
$898$		0			0
$899$	−6.14478e7	−	6.14478e7i	−2.53575	−	2.53575i
$900$		0			0
$901$	1.24294e7	−	1.24294e7i	0.510078	−	0.510078i
$902$		0			0
$903$		−	1.11782e6i		−	0.0456195i
$904$		0			0
$905$			6.69219e6i			0.271611i
$906$		0			0
$907$	−1.85362e7	+	1.85362e7i	−0.748176	+	0.748176i	−0.974136	−	0.225961i	$-0.927448\pi$
$907$	−1.85362e7	+	1.85362e7i	−0.748176	+	0.748176i	0.225961	+	0.974136i	$0.427448\pi$
$908$		0			0
$909$	−1.39052e6	−	1.39052e6i	−0.0558171	−	0.0558171i
$910$		0			0
$911$	4.80052e7			1.91643			0.958213	−	0.286055i	$-0.0923440\pi$
$911$	4.80052e7			1.91643			0.958213	+	0.286055i	$0.0923440\pi$
$912$		0			0
$913$	1.16385e7			0.462083
$914$		0			0
$915$	−3.75957e6	−	3.75957e6i	−0.148452	−	0.148452i
$916$		0			0
$917$	2.16651e6	−	2.16651e6i	0.0850821	−	0.0850821i
$918$		0			0
$919$			3.31202e7i			1.29361i	0.762655	+	0.646806i	$0.223896\pi$
$919$			3.31202e7i			1.29361i	−0.762655	+	0.646806i	$0.776104\pi$
$920$		0			0
$921$			1.15026e7i			0.446834i
$922$		0			0
$923$	4.36629e7	−	4.36629e7i	1.68697	−	1.68697i
$924$		0			0
$925$	−1.76893e6	−	1.76893e6i	−0.0679762	−	0.0679762i
$926$		0			0
$927$	−2.95020e7			−1.12759
$928$		0			0
$929$	−2.03319e7			−0.772929			−0.386464	−	0.922304i	$-0.626304\pi$
$929$	−2.03319e7			−0.772929			−0.386464	+	0.922304i	$0.626304\pi$
$930$		0			0
$931$	6.07026e6	+	6.07026e6i	0.229527	+	0.229527i
$932$		0			0
$933$	−1.66548e6	+	1.66548e6i	−0.0626378	+	0.0626378i
$934$		0			0
$935$		−	1.98981e7i		−	0.744360i
$936$		0			0
$937$		−	2.10197e7i		−	0.782129i	−0.920363	−	0.391064i	$-0.872107\pi$
$937$		−	2.10197e7i		−	0.782129i	0.920363	−	0.391064i	$-0.127893\pi$
$938$		0			0
$939$	7.01028e6	−	7.01028e6i	0.259461	−	0.259461i
$940$		0			0
$941$	−2.85949e7	−	2.85949e7i	−1.05272	−	1.05272i	−0.998531	−	0.0541926i	$-0.982742\pi$
$941$	−2.85949e7	−	2.85949e7i	−1.05272	−	1.05272i	−0.0541926	−	0.998531i	$-0.517258\pi$
$942$		0			0
$943$	1.05490e7			0.386306
$944$		0			0
$945$	1.26825e6			0.0461983
$946$		0			0
$947$	−2.63221e7	−	2.63221e7i	−0.953775	−	0.953775i	0.0452028	−	0.998978i	$-0.485607\pi$
$947$	−2.63221e7	−	2.63221e7i	−0.953775	−	0.953775i	−0.998978	+	0.0452028i	$0.985607\pi$
$948$		0			0
$949$	3.38747e7	−	3.38747e7i	1.22099	−	1.22099i
$950$		0			0
$951$		−	5.67808e6i		−	0.203587i
$952$		0			0
$953$			4.10495e7i			1.46412i	0.681241	+	0.732059i	$0.261440\pi$
$953$			4.10495e7i			1.46412i	−0.681241	+	0.732059i	$0.738560\pi$
$954$		0			0
$955$	−3.86150e6	+	3.86150e6i	−0.137009	+	0.137009i
$956$		0			0
$957$	1.23586e7	+	1.23586e7i	0.436204	+	0.436204i
$958$		0			0
$959$	−258781.			−0.00908626
$960$		0			0
$961$	7.77500e7			2.71576
$962$		0			0
$963$	−1.18288e7	−	1.18288e7i	−0.411032	−	0.411032i
$964$		0			0
$965$	1.10957e7	−	1.10957e7i	0.383563	−	0.383563i
$966$		0			0
$967$		−	2.06634e7i		−	0.710615i	−0.934749	−	0.355308i	$-0.884376\pi$
$967$		−	2.06634e7i		−	0.710615i	0.934749	−	0.355308i	$-0.115624\pi$
$968$		0			0
$969$			5.98801e6i			0.204867i
$970$		0			0
$971$	−1.81660e7	+	1.81660e7i	−0.618318	+	0.618318i	−0.945100	−	0.326782i	$-0.894036\pi$
$971$	−1.81660e7	+	1.81660e7i	−0.618318	+	0.618318i	0.326782	+	0.945100i	$0.394036\pi$
$972$		0			0
$973$	−1.93212e6	−	1.93212e6i	−0.0654261	−	0.0654261i
$974$		0			0
$975$	−3.00020e6			−0.101074
$976$		0			0
$977$	−2.83398e7			−0.949863			−0.474931	−	0.880023i	$-0.657527\pi$
$977$	−2.83398e7			−0.949863			−0.474931	+	0.880023i	$0.657527\pi$
$978$		0			0
$979$	894395.	+	894395.i	0.0298245	+	0.0298245i
$980$		0			0
$981$	−1.52587e7	+	1.52587e7i	−0.506225	+	0.506225i
$982$		0			0
$983$		−	4.37123e7i		−	1.44285i	−0.692494	−	0.721423i	$-0.743488\pi$
$983$		−	4.37123e7i		−	1.44285i	0.692494	−	0.721423i	$-0.256512\pi$
$984$		0			0
$985$		−	5.15364e6i		−	0.169248i
$986$		0			0
$987$	36992.2	−	36992.2i	0.00120870	−	0.00120870i
$988$		0			0
$989$	2.56476e7	+	2.56476e7i	0.833789	+	0.833789i
$990$		0			0
$991$	4.34267e7			1.40467			0.702333	−	0.711849i	$-0.252142\pi$
$991$	4.34267e7			1.40467			0.702333	+	0.711849i	$0.252142\pi$
$992$		0			0
$993$	−8.83146e6			−0.284223
$994$		0			0
$995$	−1.54569e7	−	1.54569e7i	−0.494955	−	0.494955i
$996$		0			0
$997$	2.27464e7	−	2.27464e7i	0.724727	−	0.724727i	−0.244838	−	0.969564i	$-0.578735\pi$
$997$	2.27464e7	−	2.27464e7i	0.724727	−	0.724727i	0.969564	+	0.244838i	$0.0787346\pi$
$998$		0			0
$999$			9.96800e6i			0.316005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.6.l.a.81.17		80
4.3	odd	2		80.6.l.a.61.5	yes	80
16.5	even	4	inner	320.6.l.a.241.17		80
16.11	odd	4		80.6.l.a.21.5	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.5	✓	80	16.11	odd	4
80.6.l.a.61.5	yes	80	4.3	odd	2
320.6.l.a.81.17		80	1.1	even	1	trivial
320.6.l.a.241.17		80	16.5	even	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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	320.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.86003 - 3.86003i) q^{3} +(-17.6777 + 17.6777i) q^{5} +20.3706i q^{7} -213.200i q^{9} +O(q^{10})\)	\(q+(-3.86003 - 3.86003i) q^{3} +(-17.6777 + 17.6777i) q^{5} +20.3706i q^{7} -213.200i q^{9} +(268.702 - 268.702i) q^{11} +(621.797 + 621.797i) q^{13} +136.473 q^{15} -2094.53 q^{17} +(370.318 + 370.318i) q^{19} +(78.6312 - 78.6312i) q^{21} +3608.29i q^{23} -625.000i q^{25} +(-1760.95 + 1760.95i) q^{27} +(-5957.69 - 5957.69i) q^{29} +10314.0 q^{31} -2074.39 q^{33} +(-360.105 - 360.105i) q^{35} +(2830.29 - 2830.29i) q^{37} -4800.32i q^{39} -2923.54i q^{41} +(7107.96 - 7107.96i) q^{43} +(3768.88 + 3768.88i) q^{45} +470.452 q^{47} +16392.0 q^{49} +(8084.96 + 8084.96i) q^{51} +(-5934.20 + 5934.20i) q^{53} +9500.04i q^{55} -2858.88i q^{57} +(8405.61 - 8405.61i) q^{59} +(-27548.1 - 27548.1i) q^{61} +4343.02 q^{63} -21983.9 q^{65} +(-49797.3 - 49797.3i) q^{67} +(13928.1 - 13928.1i) q^{69} -70220.5i q^{71} -54478.8i q^{73} +(-2412.52 + 2412.52i) q^{75} +(5473.61 + 5473.61i) q^{77} +69249.4 q^{79} -38213.0 q^{81} +(21656.9 + 21656.9i) q^{83} +(37026.4 - 37026.4i) q^{85} +45993.8i q^{87} +3328.58i q^{89} +(-12666.4 + 12666.4i) q^{91} +(-39812.5 - 39812.5i) q^{93} -13092.7 q^{95} +128648. q^{97} +(-57287.2 - 57287.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q+O(q^{10}) \) 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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