LMFDB - Embedded newform 320.6.l.a.81.15

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			81.15
Character	$\chi$	$=$	320.81
Dual form			320.6.l.a.241.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.64986 - 5.64986i) q^{3} +(-17.6777 + 17.6777i) q^{5} -143.077i q^{7} -179.158i q^{9} +O(q^{10})$	\(q+(-5.64986 - 5.64986i) q^{3} +(-17.6777 + 17.6777i) q^{5} -143.077i q^{7} -179.158i q^{9} +(291.881 - 291.881i) q^{11} +(181.016 + 181.016i) q^{13} +199.753 q^{15} +1053.85 q^{17} +(421.682 + 421.682i) q^{19} +(-808.365 + 808.365i) q^{21} -340.870i q^{23} -625.000i q^{25} +(-2385.13 + 2385.13i) q^{27} +(1109.53 + 1109.53i) q^{29} -1054.61 q^{31} -3298.18 q^{33} +(2529.27 + 2529.27i) q^{35} +(2300.69 - 2300.69i) q^{37} -2045.43i q^{39} -13456.2i q^{41} +(2038.54 - 2038.54i) q^{43} +(3167.10 + 3167.10i) q^{45} -15149.3 q^{47} -3664.02 q^{49} +(-5954.12 - 5954.12i) q^{51} +(23031.5 - 23031.5i) q^{53} +10319.6i q^{55} -4764.89i q^{57} +(1167.72 - 1167.72i) q^{59} +(-38311.2 - 38311.2i) q^{61} -25633.4 q^{63} -6399.89 q^{65} +(19188.0 + 19188.0i) q^{67} +(-1925.87 + 1925.87i) q^{69} +39132.5i q^{71} -18613.3i q^{73} +(-3531.16 + 3531.16i) q^{75} +(-41761.5 - 41761.5i) q^{77} -89963.6 q^{79} -16584.1 q^{81} +(-50763.5 - 50763.5i) q^{83} +(-18629.6 + 18629.6i) q^{85} -12537.4i q^{87} +23162.0i q^{89} +(25899.3 - 25899.3i) q^{91} +(5958.40 + 5958.40i) q^{93} -14908.7 q^{95} -94202.7 q^{97} +(-52292.9 - 52292.9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−5.64986	−	5.64986i	−0.362439	−	0.362439i	0.502271	−	0.864710i	$-0.332498\pi$
$3$	−5.64986	−	5.64986i	−0.362439	−	0.362439i	−0.864710	+	0.502271i	$0.832498\pi$
$4$		0			0
$5$	−17.6777	+	17.6777i	−0.316228	+	0.316228i
$5$	−17.6777	+	17.6777i	−0.316228	+	0.316228i
$6$		0			0
$7$		−	143.077i		−	1.10363i	−0.833966	−	0.551817i	$-0.813935\pi$
$7$		−	143.077i		−	1.10363i	0.833966	−	0.551817i	$-0.186065\pi$
$8$		0			0
$9$		−	179.158i		−	0.737276i
$10$		0			0
$11$	291.881	−	291.881i	0.727318	−	0.727318i	−0.242766	−	0.970085i	$-0.578055\pi$
$11$	291.881	−	291.881i	0.727318	−	0.727318i	0.970085	+	0.242766i	$0.0780548\pi$
$12$		0			0
$13$	181.016	+	181.016i	0.297070	+	0.297070i	0.839865	−	0.542795i	$-0.182634\pi$
$13$	181.016	+	181.016i	0.297070	+	0.297070i	−0.542795	+	0.839865i	$0.682634\pi$
$14$		0			0
$15$	199.753			0.229226
$16$		0			0
$17$	1053.85			0.884417			0.442209	−	0.896912i	$-0.354195\pi$
$17$	1053.85			0.884417			0.442209	+	0.896912i	$0.354195\pi$
$18$		0			0
$19$	421.682	+	421.682i	0.267979	+	0.267979i	0.828285	−	0.560306i	$-0.189317\pi$
$19$	421.682	+	421.682i	0.267979	+	0.267979i	−0.560306	+	0.828285i	$0.689317\pi$
$20$		0			0
$21$	−808.365	+	808.365i	−0.399999	+	0.399999i
$22$		0			0
$23$		−	340.870i		−	0.134360i	−0.997741	−	0.0671798i	$-0.978600\pi$
$23$		−	340.870i		−	0.134360i	0.997741	−	0.0671798i	$-0.0214001\pi$
$24$		0			0
$25$		−	625.000i		−	0.200000i
$26$		0			0
$27$	−2385.13	+	2385.13i	−0.629656	+	0.629656i
$28$		0			0
$29$	1109.53	+	1109.53i	0.244988	+	0.244988i	0.818910	−	0.573922i	$-0.194579\pi$
$29$	1109.53	+	1109.53i	0.244988	+	0.244988i	−0.573922	+	0.818910i	$0.694579\pi$
$30$		0			0
$31$	−1054.61			−0.197101			−0.0985503	−	0.995132i	$-0.531421\pi$
$31$	−1054.61			−0.197101			−0.0985503	+	0.995132i	$0.531421\pi$
$32$		0			0
$33$	−3298.18			−0.527217
$34$		0			0
$35$	2529.27	+	2529.27i	0.348999	+	0.348999i
$36$		0			0
$37$	2300.69	−	2300.69i	0.276283	−	0.276283i	−0.555340	−	0.831623i	$-0.687412\pi$
$37$	2300.69	−	2300.69i	0.276283	−	0.276283i	0.831623	+	0.555340i	$0.187412\pi$
$38$		0			0
$39$		−	2045.43i		−	0.215340i
$40$		0			0
$41$		−	13456.2i		−	1.25015i	−0.780565	−	0.625074i	$-0.785069\pi$
$41$		−	13456.2i		−	1.25015i	0.780565	−	0.625074i	$-0.214931\pi$
$42$		0			0
$43$	2038.54	−	2038.54i	0.168131	−	0.168131i	−0.618026	−	0.786158i	$-0.712067\pi$
$43$	2038.54	−	2038.54i	0.168131	−	0.168131i	0.786158	+	0.618026i	$0.212067\pi$
$44$		0			0
$45$	3167.10	+	3167.10i	0.233147	+	0.233147i
$46$		0			0
$47$	−15149.3			−1.00034			−0.500169	−	0.865928i	$-0.666729\pi$
$47$	−15149.3			−1.00034			−0.500169	+	0.865928i	$0.666729\pi$
$48$		0			0
$49$	−3664.02			−0.218006
$50$		0			0
$51$	−5954.12	−	5954.12i	−0.320547	−	0.320547i
$52$		0			0
$53$	23031.5	−	23031.5i	1.12624	−	1.12624i	0.135462	−	0.990783i	$-0.456748\pi$
$53$	23031.5	−	23031.5i	1.12624	−	1.12624i	0.990783	−	0.135462i	$-0.0432518\pi$
$54$		0			0
$55$			10319.6i			0.459997i
$56$		0			0
$57$		−	4764.89i		−	0.194252i
$58$		0			0
$59$	1167.72	−	1167.72i	0.0436724	−	0.0436724i	−0.684933	−	0.728606i	$-0.740169\pi$
$59$	1167.72	−	1167.72i	0.0436724	−	0.0436724i	0.728606	+	0.684933i	$0.240169\pi$
$60$		0			0
$61$	−38311.2	−	38311.2i	−1.31826	−	1.31826i	−0.915152	−	0.403109i	$-0.867930\pi$
$61$	−38311.2	−	38311.2i	−1.31826	−	1.31826i	−0.403109	−	0.915152i	$-0.632070\pi$
$62$		0			0
$63$	−25633.4			−0.813682
$64$		0			0
$65$	−6399.89			−0.187884
$66$		0			0
$67$	19188.0	+	19188.0i	0.522206	+	0.522206i	0.918237	−	0.396031i	$-0.129613\pi$
$67$	19188.0	+	19188.0i	0.522206	+	0.522206i	−0.396031	+	0.918237i	$0.629613\pi$
$68$		0			0
$69$	−1925.87	+	1925.87i	−0.0486972	+	0.0486972i
$70$		0			0
$71$			39132.5i			0.921280i	0.887587	+	0.460640i	$0.152380\pi$
$71$			39132.5i			0.921280i	−0.887587	+	0.460640i	$0.847620\pi$
$72$		0			0
$73$		−	18613.3i		−	0.408805i	−0.978887	−	0.204403i	$-0.934475\pi$
$73$		−	18613.3i		−	0.408805i	0.978887	−	0.204403i	$-0.0655252\pi$
$74$		0			0
$75$	−3531.16	+	3531.16i	−0.0724877	+	0.0724877i
$76$		0			0
$77$	−41761.5	−	41761.5i	−0.802693	−	0.802693i
$78$		0			0
$79$	−89963.6			−1.62181			−0.810903	−	0.585180i	$-0.801024\pi$
$79$	−89963.6			−1.62181			−0.810903	+	0.585180i	$0.801024\pi$
$80$		0			0
$81$	−16584.1			−0.280853
$82$		0			0
$83$	−50763.5	−	50763.5i	−0.808828	−	0.808828i	0.175629	−	0.984456i	$-0.443804\pi$
$83$	−50763.5	−	50763.5i	−0.808828	−	0.808828i	−0.984456	+	0.175629i	$0.943804\pi$
$84$		0			0
$85$	−18629.6	+	18629.6i	−0.279677	+	0.279677i
$86$		0			0
$87$		−	12537.4i		−	0.177586i
$88$		0			0
$89$			23162.0i			0.309956i	0.987918	+	0.154978i	$0.0495307\pi$
$89$			23162.0i			0.309956i	−0.987918	+	0.154978i	$0.950469\pi$
$90$		0			0
$91$	25899.3	−	25899.3i	0.327857	−	0.327857i
$92$		0			0
$93$	5958.40	+	5958.40i	0.0714369	+	0.0714369i
$94$		0			0
$95$	−14908.7			−0.169485
$96$		0			0
$97$	−94202.7			−1.01656			−0.508281	−	0.861191i	$-0.669719\pi$
$97$	−94202.7			−1.01656			−0.508281	+	0.861191i	$0.669719\pi$
$98$		0			0
$99$	−52292.9	−	52292.9i	−0.536235	−	0.536235i
$100$		0			0
$101$	−90695.5	+	90695.5i	−0.884672	+	0.884672i	−0.994005	−	0.109333i	$-0.965129\pi$
$101$	−90695.5	+	90695.5i	−0.884672	+	0.884672i	0.109333	+	0.994005i	$0.465129\pi$
$102$		0			0
$103$		−	134854.i		−	1.25248i	−0.779630	−	0.626241i	$-0.784593\pi$
$103$		−	134854.i		−	1.25248i	0.779630	−	0.626241i	$-0.215407\pi$
$104$		0			0
$105$		−	28580.0i		−	0.252982i
$106$		0			0
$107$	95838.7	−	95838.7i	0.809248	−	0.809248i	−0.175272	−	0.984520i	$-0.556081\pi$
$107$	95838.7	−	95838.7i	0.809248	−	0.809248i	0.984520	+	0.175272i	$0.0560806\pi$
$108$		0			0
$109$	141004.	+	141004.i	1.13675	+	1.13675i	0.989028	+	0.147725i	$0.0471951\pi$
$109$	141004.	+	141004.i	1.13675	+	1.13675i	0.147725	+	0.989028i	$0.452805\pi$
$110$		0			0
$111$	−25997.2			−0.200271
$112$		0			0
$113$	−206889.			−1.52420			−0.762099	−	0.647460i	$-0.775831\pi$
$113$	−206889.			−1.52420			−0.762099	+	0.647460i	$0.775831\pi$
$114$		0			0
$115$	6025.78	+	6025.78i	0.0424883	+	0.0424883i
$116$		0			0
$117$	32430.5	−	32430.5i	0.219023	−	0.219023i
$118$		0			0
$119$		−	150782.i		−	0.976072i
$120$		0			0
$121$		−	9338.44i		−	0.0579844i
$122$		0			0
$123$	−76025.5	+	76025.5i	−0.453102	+	0.453102i
$124$		0			0
$125$	11048.5	+	11048.5i	0.0632456	+	0.0632456i
$126$		0			0
$127$	−34606.3			−0.190391			−0.0951955	−	0.995459i	$-0.530348\pi$
$127$	−34606.3			−0.190391			−0.0951955	+	0.995459i	$0.530348\pi$
$128$		0			0
$129$	−23035.0			−0.121875
$130$		0			0
$131$	−207748.	−	207748.i	−1.05769	−	1.05769i	−0.998231	−	0.0594573i	$-0.981063\pi$
$131$	−207748.	−	207748.i	−1.05769	−	1.05769i	−0.0594573	−	0.998231i	$-0.518937\pi$
$132$		0			0
$133$	60333.0	−	60333.0i	0.295751	−	0.295751i
$134$		0			0
$135$		−	84327.2i		−	0.398230i
$136$		0			0
$137$		−	332218.i		−	1.51224i	−0.654430	−	0.756122i	$-0.727091\pi$
$137$		−	332218.i		−	1.51224i	0.654430	−	0.756122i	$-0.272909\pi$
$138$		0			0
$139$	245006.	−	245006.i	1.07557	−	1.07557i	0.0786730	−	0.996900i	$-0.474932\pi$
$139$	245006.	−	245006.i	1.07557	−	1.07557i	0.996900	−	0.0786730i	$-0.0250683\pi$
$140$		0			0
$141$	85591.3	+	85591.3i	0.362562	+	0.362562i
$142$		0			0
$143$	105671.			0.432130
$144$		0			0
$145$	−39227.8			−0.154944
$146$		0			0
$147$	20701.2	+	20701.2i	0.0790138	+	0.0790138i
$148$		0			0
$149$	−184561.	+	184561.i	−0.681041	+	0.681041i	−0.960235	−	0.279194i	$-0.909933\pi$
$149$	−184561.	+	184561.i	−0.681041	+	0.681041i	0.279194	+	0.960235i	$0.409933\pi$
$150$		0			0
$151$			436893.i			1.55931i	0.626208	+	0.779656i	$0.284606\pi$
$151$			436893.i			1.55931i	−0.626208	+	0.779656i	$0.715394\pi$
$152$		0			0
$153$		−	188806.i		−	0.652060i
$154$		0			0
$155$	18643.1	−	18643.1i	0.0623287	−	0.0623287i
$156$		0			0
$157$	−153307.	−	153307.i	−0.496378	−	0.496378i	0.413930	−	0.910309i	$-0.364156\pi$
$157$	−153307.	−	153307.i	−0.496378	−	0.496378i	−0.910309	+	0.413930i	$0.864156\pi$
$158$		0			0
$159$	−260250.			−0.816389
$160$		0			0
$161$	−48770.6			−0.148284
$162$		0			0
$163$	436208.	+	436208.i	1.28595	+	1.28595i	0.937225	+	0.348725i	$0.113385\pi$
$163$	436208.	+	436208.i	1.28595	+	1.28595i	0.348725	+	0.937225i	$0.386615\pi$
$164$		0			0
$165$	58304.1	−	58304.1i	0.166721	−	0.166721i
$166$		0			0
$167$			552844.i			1.53395i	0.641677	+	0.766975i	$0.278239\pi$
$167$			552844.i			1.53395i	−0.641677	+	0.766975i	$0.721761\pi$
$168$		0			0
$169$		−	305759.i		−	0.823498i
$170$		0			0
$171$	75547.8	−	75547.8i	0.197575	−	0.197575i
$172$		0			0
$173$	395062.	+	395062.i	1.00357	+	1.00357i	0.999994	+	0.00358065i	$0.00113976\pi$
$173$	395062.	+	395062.i	1.00357	+	1.00357i	0.00358065	+	0.999994i	$0.498860\pi$
$174$		0			0
$175$	−89423.1			−0.220727
$176$		0			0
$177$	−13194.9			−0.0316572
$178$		0			0
$179$	−290609.	−	290609.i	−0.677918	−	0.677918i	0.281611	−	0.959529i	$-0.409131\pi$
$179$	−290609.	−	290609.i	−0.677918	−	0.677918i	−0.959529	+	0.281611i	$0.909131\pi$
$180$		0			0
$181$	−93004.4	+	93004.4i	−0.211012	+	0.211012i	−0.804697	−	0.593685i	$-0.797672\pi$
$181$	−93004.4	+	93004.4i	−0.211012	+	0.211012i	0.593685	+	0.804697i	$0.297672\pi$
$182$		0			0
$183$			432906.i			0.955578i
$184$		0			0
$185$			81341.7i			0.174737i
$186$		0			0
$187$	307600.	−	307600.i	0.643253	−	0.643253i
$188$		0			0
$189$	341258.	+	341258.i	0.694909	+	0.694909i
$190$		0			0
$191$	−880503.			−1.74642			−0.873208	−	0.487348i	$-0.837964\pi$
$191$	−880503.			−1.74642			−0.873208	+	0.487348i	$0.837964\pi$
$192$		0			0
$193$	75295.8			0.145505			0.0727524	−	0.997350i	$-0.476822\pi$
$193$	75295.8			0.145505			0.0727524	+	0.997350i	$0.476822\pi$
$194$		0			0
$195$	36158.5	+	36158.5i	0.0680964	+	0.0680964i
$196$		0			0
$197$	−118466.	+	118466.i	−0.217484	+	0.217484i	−0.807437	−	0.589953i	$-0.799146\pi$
$197$	−118466.	+	118466.i	−0.217484	+	0.217484i	0.589953	+	0.807437i	$0.299146\pi$
$198$		0			0
$199$		−	342971.i		−	0.613939i	−0.951719	−	0.306970i	$-0.900685\pi$
$199$		−	342971.i		−	0.613939i	0.951719	−	0.306970i	$-0.0993150\pi$
$200$		0			0
$201$		−	216819.i		−	0.378536i
$202$		0			0
$203$	158748.	−	158748.i	0.270376	−	0.270376i
$204$		0			0
$205$	237874.	+	237874.i	0.395332	+	0.395332i
$206$		0			0
$207$	−61069.6			−0.0990602
$208$		0			0
$209$	246162.			0.389812
$210$		0			0
$211$	617232.	+	617232.i	0.954426	+	0.954426i	0.999006	−	0.0445803i	$-0.0141950\pi$
$211$	617232.	+	617232.i	0.954426	+	0.954426i	−0.0445803	+	0.999006i	$0.514195\pi$
$212$		0			0
$213$	221093.	−	221093.i	0.333908	−	0.333908i
$214$		0			0
$215$			72073.4i			0.106336i
$216$		0			0
$217$			150891.i			0.217527i
$218$		0			0
$219$	−105163.	+	105163.i	−0.148167	+	0.148167i
$220$		0			0
$221$	190764.	+	190764.i	0.262734	+	0.262734i
$222$		0			0
$223$	403929.			0.543929			0.271965	−	0.962307i	$-0.412327\pi$
$223$	403929.			0.543929			0.271965	+	0.962307i	$0.412327\pi$
$224$		0			0
$225$	−111974.			−0.147455
$226$		0			0
$227$	−70307.4	−	70307.4i	−0.0905601	−	0.0905601i	0.660375	−	0.750936i	$-0.270397\pi$
$227$	−70307.4	−	70307.4i	−0.0905601	−	0.0905601i	−0.750936	+	0.660375i	$0.770397\pi$
$228$		0			0
$229$	261814.	−	261814.i	0.329916	−	0.329916i	−0.522638	−	0.852554i	$-0.675052\pi$
$229$	261814.	−	261814.i	0.329916	−	0.329916i	0.852554	+	0.522638i	$0.175052\pi$
$230$		0			0
$231$			471893.i			0.581854i
$232$		0			0
$233$		−	1.28860e6i		−	1.55500i	−0.628884	−	0.777499i	$-0.716488\pi$
$233$		−	1.28860e6i		−	1.55500i	0.628884	−	0.777499i	$-0.283512\pi$
$234$		0			0
$235$	267804.	−	267804.i	0.316335	−	0.316335i
$236$		0			0
$237$	508282.	+	508282.i	0.587806	+	0.587806i
$238$		0			0
$239$	366981.			0.415575			0.207787	−	0.978174i	$-0.433374\pi$
$239$	366981.			0.415575			0.207787	+	0.978174i	$0.433374\pi$
$240$		0			0
$241$	−1.37397e6			−1.52383			−0.761913	−	0.647679i	$-0.775740\pi$
$241$	−1.37397e6			−1.52383			−0.761913	+	0.647679i	$0.775740\pi$
$242$		0			0
$243$	673285.	+	673285.i	0.731448	+	0.731448i
$244$		0			0
$245$	64771.4	−	64771.4i	0.0689395	−	0.0689395i
$246$		0			0
$247$			152663.i			0.159217i
$248$		0			0
$249$			573613.i			0.586301i
$250$		0			0
$251$	−278895.	+	278895.i	−0.279420	+	0.279420i	−0.832877	−	0.553458i	$-0.813308\pi$
$251$	−278895.	+	278895.i	−0.279420	+	0.279420i	0.553458	+	0.832877i	$0.313308\pi$
$252$		0			0
$253$	−99493.6	−	99493.6i	−0.0977223	−	0.0977223i
$254$		0			0
$255$	210510.			0.202732
$256$		0			0
$257$	1.28986e6			1.21817			0.609087	−	0.793103i	$-0.291536\pi$
$257$	1.28986e6			1.21817			0.609087	+	0.793103i	$0.291536\pi$
$258$		0			0
$259$	−329176.	−	329176.i	−0.304915	−	0.304915i
$260$		0			0
$261$	198781.	−	198781.i	0.180624	−	0.180624i
$262$		0			0
$263$			1.44346e6i			1.28681i	0.765525	+	0.643406i	$0.222479\pi$
$263$			1.44346e6i			1.28681i	−0.765525	+	0.643406i	$0.777521\pi$
$264$		0			0
$265$			814287.i			0.712300i
$266$		0			0
$267$	130862.	−	130862.i	0.112340	−	0.112340i
$268$		0			0
$269$	1.39652e6	+	1.39652e6i	1.17671	+	1.17671i	0.980578	+	0.196127i	$0.0628366\pi$
$269$	1.39652e6	+	1.39652e6i	1.17671	+	1.17671i	0.196127	+	0.980578i	$0.437163\pi$
$270$		0			0
$271$	487103.			0.402900			0.201450	−	0.979499i	$-0.435435\pi$
$271$	487103.			0.402900			0.201450	+	0.979499i	$0.435435\pi$
$272$		0			0
$273$	−292655.			−0.237656
$274$		0			0
$275$	−182426.	−	182426.i	−0.145464	−	0.145464i
$276$		0			0
$277$	−159684.	+	159684.i	−0.125044	+	0.125044i	−0.766859	−	0.641815i	$-0.778182\pi$
$277$	−159684.	+	159684.i	−0.125044	+	0.125044i	0.641815	+	0.766859i	$0.278182\pi$
$278$		0			0
$279$			188942.i			0.145318i
$280$		0			0
$281$		−	167923.i		−	0.126866i	−0.997986	−	0.0634330i	$-0.979795\pi$
$281$		−	167923.i		−	0.126866i	0.997986	−	0.0634330i	$-0.0202049\pi$
$282$		0			0
$283$	1.45221e6	−	1.45221e6i	1.07786	−	1.07786i	0.0811627	−	0.996701i	$-0.474137\pi$
$283$	1.45221e6	−	1.45221e6i	1.07786	−	1.07786i	0.996701	−	0.0811627i	$-0.0258633\pi$
$284$		0			0
$285$	84232.1	+	84232.1i	0.0614279	+	0.0614279i
$286$		0			0
$287$	−1.92527e6			−1.37971
$288$		0			0
$289$	−309253.			−0.217806
$290$		0			0
$291$	532232.	+	532232.i	0.368442	+	0.368442i
$292$		0			0
$293$	576523.	−	576523.i	0.392327	−	0.392327i	−0.483189	−	0.875516i	$-0.660522\pi$
$293$	576523.	−	576523.i	0.392327	−	0.392327i	0.875516	+	0.483189i	$0.160522\pi$
$294$		0			0
$295$			41285.0i			0.0276209i
$296$		0			0
$297$			1.39235e6i			0.915921i
$298$		0			0
$299$	61703.0	−	61703.0i	0.0399143	−	0.0399143i
$300$		0			0
$301$	−291669.	−	291669.i	−0.185555	−	0.185555i
$302$		0			0
$303$	1.02483e6			0.641279
$304$		0			0
$305$	1.35451e6			0.833741
$306$		0			0
$307$	206791.	+	206791.i	0.125223	+	0.125223i	0.766941	−	0.641718i	$-0.221778\pi$
$307$	206791.	+	206791.i	0.125223	+	0.125223i	−0.641718	+	0.766941i	$0.721778\pi$
$308$		0			0
$309$	−761907.	+	761907.i	−0.453948	+	0.453948i
$310$		0			0
$311$		−	26746.0i		−	0.0156805i	−0.999969	−	0.00784023i	$-0.997504\pi$
$311$		−	26746.0i		−	0.0156805i	0.999969	−	0.00784023i	$-0.00249565\pi$
$312$		0			0
$313$		−	1.26947e6i		−	0.732424i	−0.930531	−	0.366212i	$-0.880655\pi$
$313$		−	1.26947e6i		−	0.732424i	0.930531	−	0.366212i	$-0.119345\pi$
$314$		0			0
$315$	453139.	−	453139.i	0.257309	−	0.257309i
$316$		0			0
$317$	−59452.2	−	59452.2i	−0.0332292	−	0.0332292i	0.690297	−	0.723526i	$-0.257480\pi$
$317$	−59452.2	−	59452.2i	−0.0332292	−	0.0332292i	−0.723526	+	0.690297i	$0.757480\pi$
$318$		0			0
$319$	647702.			0.356368
$320$		0			0
$321$	−1.08295e6			−0.586605
$322$		0			0
$323$	444390.	+	444390.i	0.237005	+	0.237005i
$324$		0			0
$325$	113135.	−	113135.i	0.0594141	−	0.0594141i
$326$		0			0
$327$		−	1.59331e6i		−	0.824007i
$328$		0			0
$329$			2.16751e6i			1.10401i
$330$		0			0
$331$	172444.	−	172444.i	0.0865123	−	0.0865123i	−0.662526	−	0.749039i	$-0.730516\pi$
$331$	172444.	−	172444.i	0.0865123	−	0.0865123i	0.749039	+	0.662526i	$0.230516\pi$
$332$		0			0
$333$	−412188.	−	412188.i	−0.203697	−	0.203697i
$334$		0			0
$335$	−678397.			−0.330272
$336$		0			0
$337$	−1.28102e6			−0.614443			−0.307221	−	0.951638i	$-0.599399\pi$
$337$	−1.28102e6			−0.614443			−0.307221	+	0.951638i	$0.599399\pi$
$338$		0			0
$339$	1.16890e6	+	1.16890e6i	0.552429	+	0.552429i
$340$		0			0
$341$	−307821.	+	307821.i	−0.143355	+	0.143355i
$342$		0			0
$343$		−	1.88046e6i		−	0.863035i
$344$		0			0
$345$		−	68089.7i		−	0.0307988i
$346$		0			0
$347$	241617.	−	241617.i	0.107722	−	0.107722i	−0.651192	−	0.758913i	$-0.725731\pi$
$347$	241617.	−	241617.i	0.107722	−	0.107722i	0.758913	+	0.651192i	$0.225731\pi$
$348$		0			0
$349$	−1.27223e6	−	1.27223e6i	−0.559117	−	0.559117i	0.369939	−	0.929056i	$-0.379379\pi$
$349$	−1.27223e6	−	1.27223e6i	−0.559117	−	0.559117i	−0.929056	+	0.369939i	$0.879379\pi$
$350$		0			0
$351$	−863497.			−0.374104
$352$		0			0
$353$	4.07045e6			1.73863			0.869313	−	0.494263i	$-0.164562\pi$
$353$	4.07045e6			1.73863			0.869313	+	0.494263i	$0.164562\pi$
$354$		0			0
$355$	−691771.	−	691771.i	−0.291334	−	0.291334i
$356$		0			0
$357$	−851897.	+	851897.i	−0.353766	+	0.353766i
$358$		0			0
$359$		−	1.13485e6i		−	0.464731i	−0.972629	−	0.232366i	$-0.925353\pi$
$359$		−	1.13485e6i		−	0.464731i	0.972629	−	0.232366i	$-0.0746466\pi$
$360$		0			0
$361$		−	2.12047e6i		−	0.856374i
$362$		0			0
$363$	−52760.9	+	52760.9i	−0.0210158	+	0.0210158i
$364$		0			0
$365$	329040.	+	329040.i	0.129276	+	0.129276i
$366$		0			0
$367$	−1.81372e6			−0.702920			−0.351460	−	0.936203i	$-0.614315\pi$
$367$	−1.81372e6			−0.702920			−0.351460	+	0.936203i	$0.614315\pi$
$368$		0			0
$369$	−2.41078e6			−0.921705
$370$		0			0
$371$	−3.29528e6	−	3.29528e6i	−1.24296	−	1.24296i
$372$		0			0
$373$	−13302.2	+	13302.2i	−0.00495053	+	0.00495053i	−0.709578	−	0.704627i	$-0.751114\pi$
$373$	−13302.2	+	13302.2i	−0.00495053	+	0.00495053i	0.704627	+	0.709578i	$0.251114\pi$
$374$		0			0
$375$		−	124845.i		−	0.0458453i
$376$		0			0
$377$			401686.i			0.145557i
$378$		0			0
$379$	−2.23507e6	+	2.23507e6i	−0.799269	+	0.799269i	−0.982980	−	0.183712i	$-0.941189\pi$
$379$	−2.23507e6	+	2.23507e6i	−0.799269	+	0.799269i	0.183712	+	0.982980i	$0.441189\pi$
$380$		0			0
$381$	195521.	+	195521.i	0.0690051	+	0.0690051i
$382$		0			0
$383$	1.73637e6			0.604846			0.302423	−	0.953174i	$-0.402204\pi$
$383$	1.73637e6			0.604846			0.302423	+	0.953174i	$0.402204\pi$
$384$		0			0
$385$	1.47649e6			0.507667
$386$		0			0
$387$	−365222.	−	365222.i	−0.123959	−	0.123959i
$388$		0			0
$389$	−1.03858e6	+	1.03858e6i	−0.347991	+	0.347991i	−0.859361	−	0.511370i	$-0.829138\pi$
$389$	−1.03858e6	+	1.03858e6i	−0.347991	+	0.347991i	0.511370	+	0.859361i	$0.329138\pi$
$390$		0			0
$391$		−	359226.i		−	0.118830i
$392$		0			0
$393$			2.34749e6i			0.766694i
$394$		0			0
$395$	1.59035e6	−	1.59035e6i	0.512860	−	0.512860i
$396$		0			0
$397$	−4.36652e6	−	4.36652e6i	−1.39046	−	1.39046i	−0.824279	−	0.566184i	$-0.808419\pi$
$397$	−4.36652e6	−	4.36652e6i	−1.39046	−	1.39046i	−0.566184	−	0.824279i	$-0.691581\pi$
$398$		0			0
$399$	−681746.			−0.214383
$400$		0			0
$401$	−5.50255e6			−1.70885			−0.854423	−	0.519578i	$-0.826089\pi$
$401$	−5.50255e6			−1.70885			−0.854423	+	0.519578i	$0.826089\pi$
$402$		0			0
$403$	−190902.	−	190902.i	−0.0585527	−	0.0585527i
$404$		0			0
$405$	293168.	−	293168.i	0.0888134	−	0.0888134i
$406$		0			0
$407$		−	1.34306e6i		−	0.401891i
$408$		0			0
$409$		−	3.91372e6i		−	1.15686i	−0.815731	−	0.578431i	$-0.803665\pi$
$409$		−	3.91372e6i		−	1.15686i	0.815731	−	0.578431i	$-0.196335\pi$
$410$		0			0
$411$	−1.87699e6	+	1.87699e6i	−0.548096	+	0.548096i
$412$		0			0
$413$	−167073.	−	167073.i	−0.0481983	−	0.0481983i
$414$		0			0
$415$	1.79476e6			0.511548
$416$		0			0
$417$	−2.76850e6			−0.779659
$418$		0			0
$419$	−2.90419e6	−	2.90419e6i	−0.808147	−	0.808147i	0.176207	−	0.984353i	$-0.443617\pi$
$419$	−2.90419e6	−	2.90419e6i	−0.808147	−	0.808147i	−0.984353	+	0.176207i	$0.943617\pi$
$420$		0			0
$421$	−936361.	+	936361.i	−0.257477	+	0.257477i	−0.824027	−	0.566550i	$-0.808278\pi$
$421$	−936361.	+	936361.i	−0.257477	+	0.257477i	0.566550	+	0.824027i	$0.308278\pi$
$422$		0			0
$423$			2.71412e6i			0.737526i
$424$		0			0
$425$		−	658657.i		−	0.176883i
$426$		0			0
$427$	−5.48145e6	+	5.48145e6i	−1.45488	+	1.45488i
$428$		0			0
$429$	−597024.	−	597024.i	−0.156620	−	0.156620i
$430$		0			0
$431$	−2.05364e6			−0.532513			−0.266257	−	0.963902i	$-0.585787\pi$
$431$	−2.05364e6			−0.532513			−0.266257	+	0.963902i	$0.585787\pi$
$432$		0			0
$433$	5.19369e6			1.33124			0.665620	−	0.746291i	$-0.268167\pi$
$433$	5.19369e6			1.33124			0.665620	+	0.746291i	$0.268167\pi$
$434$		0			0
$435$	221632.	+	221632.i	0.0561576	+	0.0561576i
$436$		0			0
$437$	143739.	−	143739.i	0.0360056	−	0.0360056i
$438$		0			0
$439$		−	3.92534e6i		−	0.972111i	−0.873928	−	0.486056i	$-0.838435\pi$
$439$		−	3.92534e6i		−	0.972111i	0.873928	−	0.486056i	$-0.161565\pi$
$440$		0			0
$441$			656440.i			0.160731i
$442$		0			0
$443$	−2.44291e6	+	2.44291e6i	−0.591423	+	0.591423i	−0.938016	−	0.346593i	$-0.887339\pi$
$443$	−2.44291e6	+	2.44291e6i	−0.591423	+	0.591423i	0.346593	+	0.938016i	$0.387339\pi$
$444$		0			0
$445$	−409450.	−	409450.i	−0.0980168	−	0.0980168i
$446$		0			0
$447$	2.08548e6			0.493672
$448$		0			0
$449$	1.95234e6			0.457025			0.228513	−	0.973541i	$-0.426614\pi$
$449$	1.95234e6			0.457025			0.228513	+	0.973541i	$0.426614\pi$
$450$		0			0
$451$	−3.92760e6	−	3.92760e6i	−0.909256	−	0.909256i
$452$		0			0
$453$	2.46839e6	−	2.46839e6i	0.565155	−	0.565155i
$454$		0			0
$455$			915677.i			0.207355i
$456$		0			0
$457$			2.27789e6i			0.510201i	0.966915	+	0.255101i	$0.0821086\pi$
$457$			2.27789e6i			0.510201i	−0.966915	+	0.255101i	$0.917891\pi$
$458$		0			0
$459$	−2.51358e6	+	2.51358e6i	−0.556879	+	0.556879i
$460$		0			0
$461$	−2.67379e6	−	2.67379e6i	−0.585969	−	0.585969i	0.350568	−	0.936537i	$-0.385988\pi$
$461$	−2.67379e6	−	2.67379e6i	−0.585969	−	0.585969i	−0.936537	+	0.350568i	$0.885988\pi$
$462$		0			0
$463$	8.69290e6			1.88457			0.942285	−	0.334811i	$-0.108672\pi$
$463$	8.69290e6			1.88457			0.942285	+	0.334811i	$0.108672\pi$
$464$		0			0
$465$	−210661.			−0.0451807
$466$		0			0
$467$	1.82222e6	+	1.82222e6i	0.386642	+	0.386642i	0.873488	−	0.486846i	$-0.161853\pi$
$467$	1.82222e6	+	1.82222e6i	0.386642	+	0.386642i	−0.486846	+	0.873488i	$0.661853\pi$
$468$		0			0
$469$	2.74536e6	−	2.74536e6i	0.576324	−	0.576324i
$470$		0			0
$471$			1.73233e6i			0.359813i
$472$		0			0
$473$		−	1.19003e6i		−	0.244570i
$474$		0			0
$475$	263551.	−	263551.i	0.0535958	−	0.0535958i
$476$		0			0
$477$	−4.12628e6	−	4.12628e6i	−0.830353	−	0.830353i
$478$		0			0
$479$	−483261.			−0.0962371			−0.0481186	−	0.998842i	$-0.515323\pi$
$479$	−483261.			−0.0962371			−0.0481186	+	0.998842i	$0.515323\pi$
$480$		0			0
$481$	832926.			0.164151
$482$		0			0
$483$	275547.	+	275547.i	0.0537438	+	0.0537438i
$484$		0			0
$485$	1.66528e6	−	1.66528e6i	0.321465	−	0.321465i
$486$		0			0
$487$			649701.i			0.124134i	0.998072	+	0.0620671i	$0.0197693\pi$
$487$			649701.i			0.124134i	−0.998072	+	0.0620671i	$0.980231\pi$
$488$		0			0
$489$		−	4.92902e6i		−	0.932156i
$490$		0			0
$491$	−4.42640e6	+	4.42640e6i	−0.828603	+	0.828603i	−0.987324	−	0.158720i	$-0.949263\pi$
$491$	−4.42640e6	+	4.42640e6i	−0.828603	+	0.828603i	0.158720	+	0.987324i	$0.449263\pi$
$492$		0			0
$493$	1.16928e6	+	1.16928e6i	0.216671	+	0.216671i
$494$		0			0
$495$	1.84883e6			0.339145
$496$		0			0
$497$	5.59896e6			1.01676
$498$		0			0
$499$	3.11825e6	+	3.11825e6i	0.560608	+	0.560608i	0.929480	−	0.368872i	$-0.120256\pi$
$499$	3.11825e6	+	3.11825e6i	0.560608	+	0.560608i	−0.368872	+	0.929480i	$0.620256\pi$
$500$		0			0
$501$	3.12349e6	−	3.12349e6i	0.555963	−	0.555963i
$502$		0			0
$503$		−	7.75382e6i		−	1.36646i	−0.730205	−	0.683228i	$-0.760575\pi$
$503$		−	7.75382e6i		−	1.36646i	0.730205	−	0.683228i	$-0.239425\pi$
$504$		0			0
$505$		−	3.20657e6i		−	0.559516i
$506$		0			0
$507$	−1.72750e6	+	1.72750e6i	−0.298468	+	0.298468i
$508$		0			0
$509$	−4.66852e6	−	4.66852e6i	−0.798703	−	0.798703i	0.184188	−	0.982891i	$-0.441034\pi$
$509$	−4.66852e6	−	4.66852e6i	−0.798703	−	0.798703i	−0.982891	+	0.184188i	$0.941034\pi$
$510$		0			0
$511$	−2.66314e6			−0.451171
$512$		0			0
$513$	−2.01154e6			−0.337469
$514$		0			0
$515$	2.38391e6	+	2.38391e6i	0.396069	+	0.396069i
$516$		0			0
$517$	−4.42179e6	+	4.42179e6i	−0.727565	+	0.727565i
$518$		0			0
$519$		−	4.46409e6i		−	0.727468i
$520$		0			0
$521$			8.27536e6i			1.33565i	0.744319	+	0.667825i	$0.232774\pi$
$521$			8.27536e6i			1.33565i	−0.744319	+	0.667825i	$0.767226\pi$
$522$		0			0
$523$	4.72044e6	−	4.72044e6i	0.754620	−	0.754620i	−0.220717	−	0.975338i	$-0.570840\pi$
$523$	4.72044e6	−	4.72044e6i	0.754620	−	0.754620i	0.975338	+	0.220717i	$0.0708399\pi$
$524$		0			0
$525$	505228.	+	505228.i	0.0799999	+	0.0799999i
$526$		0			0
$527$	−1.11140e6			−0.174319
$528$		0			0
$529$	6.32015e6			0.981947
$530$		0			0
$531$	−209206.	−	209206.i	−0.0321986	−	0.0321986i
$532$		0			0
$533$	2.43579e6	−	2.43579e6i	0.371382	−	0.371382i
$534$		0			0
$535$			3.38841e6i			0.511813i
$536$		0			0
$537$			3.28380e6i			0.491407i
$538$		0			0
$539$	−1.06946e6	+	1.06946e6i	−0.158560	+	0.158560i
$540$		0			0
$541$	11776.0	+	11776.0i	0.00172984	+	0.00172984i	0.707971	−	0.706241i	$-0.249611\pi$
$541$	11776.0	+	11776.0i	0.00172984	+	0.00172984i	−0.706241	+	0.707971i	$0.749611\pi$
$542$		0			0
$543$	1.05092e6			0.152958
$544$		0			0
$545$	−4.98526e6			−0.718946
$546$		0			0
$547$	−1.39580e6	−	1.39580e6i	−0.199459	−	0.199459i	0.600309	−	0.799768i	$-0.295044\pi$
$547$	−1.39580e6	−	1.39580e6i	−0.199459	−	0.199459i	−0.799768	+	0.600309i	$0.795044\pi$
$548$		0			0
$549$	−6.86377e6	+	6.86377e6i	−0.971922	+	0.971922i
$550$		0			0
$551$			935738.i			0.131303i
$552$		0			0
$553$			1.28717e7i			1.78988i
$554$		0			0
$555$	459570.	−	459570.i	0.0633314	−	0.0633314i
$556$		0			0
$557$	−2.53880e6	−	2.53880e6i	−0.346730	−	0.346730i	0.512160	−	0.858890i	$-0.328845\pi$
$557$	−2.53880e6	−	2.53880e6i	−0.346730	−	0.346730i	−0.858890	+	0.512160i	$0.828845\pi$
$558$		0			0
$559$	738019.			0.0998937
$560$		0			0
$561$	−3.47579e6			−0.466280
$562$		0			0
$563$	592917.	+	592917.i	0.0788357	+	0.0788357i	0.745425	−	0.666589i	$-0.232247\pi$
$563$	592917.	+	592917.i	0.0788357	+	0.0788357i	−0.666589	+	0.745425i	$0.732247\pi$
$564$		0			0
$565$	3.65732e6	−	3.65732e6i	0.481994	−	0.481994i
$566$		0			0
$567$			2.37280e6i			0.309958i
$568$		0			0
$569$			1.17265e7i			1.51841i	0.650851	+	0.759206i	$0.274412\pi$
$569$			1.17265e7i			1.51841i	−0.650851	+	0.759206i	$0.725588\pi$
$570$		0			0
$571$	8.44620e6	−	8.44620e6i	1.08410	−	1.08410i	0.0879828	−	0.996122i	$-0.471958\pi$
$571$	8.44620e6	−	8.44620e6i	1.08410	−	1.08410i	0.996122	−	0.0879828i	$-0.0280420\pi$
$572$		0			0
$573$	4.97472e6	+	4.97472e6i	0.632969	+	0.632969i
$574$		0			0
$575$	−213044.			−0.0268719
$576$		0			0
$577$	1.04084e7			1.30150			0.650751	−	0.759291i	$-0.274454\pi$
$577$	1.04084e7			1.30150			0.650751	+	0.759291i	$0.274454\pi$
$578$		0			0
$579$	−425411.	−	425411.i	−0.0527366	−	0.0527366i
$580$		0			0
$581$	−7.26308e6	+	7.26308e6i	−0.892649	+	0.892649i
$582$		0			0
$583$		−	1.34449e7i		−	1.63828i
$584$		0			0
$585$			1.14659e6i			0.138522i
$586$		0			0
$587$	−2.10564e6	+	2.10564e6i	−0.252226	+	0.252226i	−0.821883	−	0.569657i	$-0.807076\pi$
$587$	−2.10564e6	+	2.10564e6i	−0.252226	+	0.252226i	0.569657	+	0.821883i	$0.307076\pi$
$588$		0			0
$589$	−444710.	−	444710.i	−0.0528188	−	0.0528188i
$590$		0			0
$591$	1.33863e6			0.157650
$592$		0			0
$593$	8.80654e6			1.02841			0.514207	−	0.857666i	$-0.328086\pi$
$593$	8.80654e6			1.02841			0.514207	+	0.857666i	$0.328086\pi$
$594$		0			0
$595$	2.66547e6	+	2.66547e6i	0.308661	+	0.308661i
$596$		0			0
$597$	−1.93774e6	+	1.93774e6i	−0.222515	+	0.222515i
$598$		0			0
$599$			9.65722e6i			1.09973i	0.835255	+	0.549864i	$0.185320\pi$
$599$			9.65722e6i			1.09973i	−0.835255	+	0.549864i	$0.814680\pi$
$600$		0			0
$601$			3.77039e6i			0.425795i	0.977075	+	0.212897i	$0.0682900\pi$
$601$			3.77039e6i			0.425795i	−0.977075	+	0.212897i	$0.931710\pi$
$602$		0			0
$603$	3.43768e6	−	3.43768e6i	0.385010	−	0.385010i
$604$		0			0
$605$	165082.	+	165082.i	0.0183363	+	0.0183363i
$606$		0			0
$607$	6.18205e6			0.681021			0.340511	−	0.940241i	$-0.389400\pi$
$607$	6.18205e6			0.681021			0.340511	+	0.940241i	$0.389400\pi$
$608$		0			0
$609$	−1.79381e6			−0.195990
$610$		0			0
$611$	−2.74227e6	−	2.74227e6i	−0.297171	−	0.297171i
$612$		0			0
$613$	6.39097e6	−	6.39097e6i	0.686935	−	0.686935i	−0.274618	−	0.961553i	$-0.588552\pi$
$613$	6.39097e6	−	6.39097e6i	0.686935	−	0.686935i	0.961553	+	0.274618i	$0.0885515\pi$
$614$		0			0
$615$		−	2.68791e6i		−	0.286567i
$616$		0			0
$617$		−	538688.i		−	0.0569672i	−0.999594	−	0.0284836i	$-0.990932\pi$
$617$		−	538688.i		−	0.0569672i	0.999594	−	0.0284836i	$-0.00906783\pi$
$618$		0			0
$619$	302602.	−	302602.i	0.0317428	−	0.0317428i	−0.691057	−	0.722800i	$-0.742855\pi$
$619$	302602.	−	302602.i	0.0317428	−	0.0317428i	0.722800	+	0.691057i	$0.242855\pi$
$620$		0			0
$621$	813021.	+	813021.i	0.0846004	+	0.0846004i
$622$		0			0
$623$	3.31395e6			0.342078
$624$		0			0
$625$	−390625.			−0.0400000
$626$		0			0
$627$	−1.39078e6	−	1.39078e6i	−0.141283	−	0.141283i
$628$		0			0
$629$	2.42459e6	−	2.42459e6i	0.244349	−	0.244349i
$630$		0			0
$631$			1.13112e7i			1.13093i	0.824772	+	0.565465i	$0.191303\pi$
$631$			1.13112e7i			1.13093i	−0.824772	+	0.565465i	$0.808697\pi$
$632$		0			0
$633$		−	6.97455e6i		−	0.691842i
$634$		0			0
$635$	611760.	−	611760.i	0.0602069	−	0.0602069i
$636$		0			0
$637$	−663248.	−	663248.i	−0.0647631	−	0.0647631i
$638$		0			0
$639$	7.01091e6			0.679238
$640$		0			0
$641$	−1.42270e7			−1.36763			−0.683814	−	0.729656i	$-0.739680\pi$
$641$	−1.42270e7			−1.36763			−0.683814	+	0.729656i	$0.739680\pi$
$642$		0			0
$643$	3.57817e6	+	3.57817e6i	0.341298	+	0.341298i	0.856855	−	0.515557i	$-0.172415\pi$
$643$	3.57817e6	+	3.57817e6i	0.341298	+	0.341298i	−0.515557	+	0.856855i	$0.672415\pi$
$644$		0			0
$645$	407204.	−	407204.i	0.0385401	−	0.0385401i
$646$		0			0
$647$		−	1.77065e7i		−	1.66292i	−0.555585	−	0.831460i	$-0.687506\pi$
$647$		−	1.77065e7i		−	1.66292i	0.555585	−	0.831460i	$-0.312494\pi$
$648$		0			0
$649$		−	681669.i		−	0.0635275i
$650$		0			0
$651$	852510.	−	852510.i	0.0788401	−	0.0788401i
$652$		0			0
$653$	1.48482e7	+	1.48482e7i	1.36267	+	1.36267i	0.870501	+	0.492166i	$0.163795\pi$
$653$	1.48482e7	+	1.48482e7i	1.36267	+	1.36267i	0.492166	+	0.870501i	$0.336205\pi$
$654$		0			0
$655$	7.34498e6			0.668941
$656$		0			0
$657$	−3.33473e6			−0.301402
$658$		0			0
$659$	1.21574e7	+	1.21574e7i	1.09051	+	1.09051i	0.995474	+	0.0950310i	$0.0302950\pi$
$659$	1.21574e7	+	1.21574e7i	1.09051	+	1.09051i	0.0950310	+	0.995474i	$0.469705\pi$
$660$		0			0
$661$	6.00382e6	−	6.00382e6i	0.534471	−	0.534471i	−0.387429	−	0.921900i	$-0.626637\pi$
$661$	6.00382e6	−	6.00382e6i	0.534471	−	0.534471i	0.921900	+	0.387429i	$0.126637\pi$
$662$		0			0
$663$		−	2.15558e6i		−	0.190450i
$664$		0			0
$665$			2.13309e6i			0.187049i
$666$		0			0
$667$	378205.	−	378205.i	0.0329165	−	0.0329165i
$668$		0			0
$669$	−2.28214e6	−	2.28214e6i	−0.197141	−	0.197141i
$670$		0			0
$671$	−2.23647e7			−1.91759
$672$		0			0
$673$	1.02278e7			0.870451			0.435226	−	0.900321i	$-0.356669\pi$
$673$	1.02278e7			0.870451			0.435226	+	0.900321i	$0.356669\pi$
$674$		0			0
$675$	1.49071e6	+	1.49071e6i	0.125931	+	0.125931i
$676$		0			0
$677$	−8.41995e6	+	8.41995e6i	−0.706054	+	0.706054i	−0.965703	−	0.259649i	$-0.916393\pi$
$677$	−8.41995e6	+	8.41995e6i	−0.706054	+	0.706054i	0.259649	+	0.965703i	$0.416393\pi$
$678$		0			0
$679$			1.34782e7i			1.12191i
$680$		0			0
$681$			794455.i			0.0656449i
$682$		0			0
$683$	−6.71475e6	+	6.71475e6i	−0.550780	+	0.550780i	−0.926666	−	0.375886i	$-0.877338\pi$
$683$	−6.71475e6	+	6.71475e6i	−0.550780	+	0.550780i	0.375886	+	0.926666i	$0.377338\pi$
$684$		0			0
$685$	5.87284e6	+	5.87284e6i	0.478214	+	0.478214i
$686$		0			0
$687$	−2.95842e6			−0.239149
$688$		0			0
$689$	8.33816e6			0.669148
$690$		0			0
$691$	−1.05194e7	−	1.05194e7i	−0.838098	−	0.838098i	0.150510	−	0.988608i	$-0.451908\pi$
$691$	−1.05194e7	−	1.05194e7i	−0.838098	−	0.838098i	−0.988608	+	0.150510i	$0.951908\pi$
$692$		0			0
$693$	−7.48191e6	+	7.48191e6i	−0.591806	+	0.591806i
$694$		0			0
$695$			8.66228e6i			0.680252i
$696$		0			0
$697$		−	1.41808e7i		−	1.10565i
$698$		0			0
$699$	−7.28044e6	+	7.28044e6i	−0.563591	+	0.563591i
$700$		0			0
$701$	1.40028e7	+	1.40028e7i	1.07626	+	1.07626i	0.996841	+	0.0794224i	$0.0253076\pi$
$701$	1.40028e7	+	1.40028e7i	1.07626	+	1.07626i	0.0794224	+	0.996841i	$0.474692\pi$
$702$		0			0
$703$	1.94032e6			0.148076
$704$		0			0
$705$	−3.02611e6			−0.229304
$706$		0			0
$707$	1.29764e7	+	1.29764e7i	0.976354	+	0.976354i
$708$		0			0
$709$	5.58854e6	−	5.58854e6i	0.417525	−	0.417525i	−0.466825	−	0.884350i	$-0.654602\pi$
$709$	5.58854e6	−	5.58854e6i	0.417525	−	0.417525i	0.884350	+	0.466825i	$0.154602\pi$
$710$		0			0
$711$			1.61177e7i			1.19572i
$712$		0			0
$713$			359485.i			0.0264824i
$714$		0			0
$715$	−1.86801e6	+	1.86801e6i	−0.136651	+	0.136651i
$716$		0			0
$717$	−2.07339e6	−	2.07339e6i	−0.150620	−	0.150620i
$718$		0			0
$719$	8.53642e6			0.615820			0.307910	−	0.951416i	$-0.400370\pi$
$719$	8.53642e6			0.615820			0.307910	+	0.951416i	$0.400370\pi$
$720$		0			0
$721$	−1.92945e7			−1.38228
$722$		0			0
$723$	7.76275e6	+	7.76275e6i	0.552294	+	0.552294i
$724$		0			0
$725$	693456.	−	693456.i	0.0489975	−	0.0489975i
$726$		0			0
$727$		−	8.88434e6i		−	0.623432i	−0.950175	−	0.311716i	$-0.899096\pi$
$727$		−	8.88434e6i		−	0.623432i	0.950175	−	0.311716i	$-0.100904\pi$
$728$		0			0
$729$		−	3.57801e6i		−	0.249358i
$730$		0			0
$731$	2.14832e6	−	2.14832e6i	0.148698	−	0.148698i
$732$		0			0
$733$	−7.63896e6	−	7.63896e6i	−0.525139	−	0.525139i	0.393980	−	0.919119i	$-0.371098\pi$
$733$	−7.63896e6	−	7.63896e6i	−0.525139	−	0.525139i	−0.919119	+	0.393980i	$0.871098\pi$
$734$		0			0
$735$	−731899.			−0.0499727
$736$		0			0
$737$	1.12012e7			0.759621
$738$		0			0
$739$	2.83232e6	+	2.83232e6i	0.190779	+	0.190779i	0.796033	−	0.605254i	$-0.206928\pi$
$739$	2.83232e6	+	2.83232e6i	0.190779	+	0.190779i	−0.605254	+	0.796033i	$0.706928\pi$
$740$		0			0
$741$	862523.	−	862523.i	0.0577065	−	0.0577065i
$742$		0			0
$743$			4.95901e6i			0.329551i	0.986331	+	0.164776i	$0.0526900\pi$
$743$			4.95901e6i			0.329551i	−0.986331	+	0.164776i	$0.947310\pi$
$744$		0			0
$745$		−	6.52520e6i		−	0.430728i
$746$		0			0
$747$	−9.09469e6	+	9.09469e6i	−0.596330	+	0.596330i
$748$		0			0
$749$	−1.37123e7	−	1.37123e7i	−0.893112	−	0.893112i
$750$		0			0
$751$	−746560.			−0.0483020			−0.0241510	−	0.999708i	$-0.507688\pi$
$751$	−746560.			−0.0483020			−0.0241510	+	0.999708i	$0.507688\pi$
$752$		0			0
$753$	3.15144e6			0.202545
$754$		0			0
$755$	−7.72325e6	−	7.72325e6i	−0.493098	−	0.493098i
$756$		0			0
$757$	4.70246e6	−	4.70246e6i	0.298254	−	0.298254i	−0.542076	−	0.840330i	$-0.682361\pi$
$757$	4.70246e6	−	4.70246e6i	0.298254	−	0.298254i	0.840330	+	0.542076i	$0.182361\pi$
$758$		0			0
$759$			1.12425e6i			0.0708367i
$760$		0			0
$761$		−	1.17758e7i		−	0.737102i	−0.929607	−	0.368551i	$-0.879854\pi$
$761$		−	1.17758e7i		−	0.737102i	0.929607	−	0.368551i	$-0.120146\pi$
$762$		0			0
$763$	2.01745e7	−	2.01745e7i	1.25456	−	1.25456i
$764$		0			0
$765$	3.33765e6	+	3.33765e6i	0.206199	+	0.206199i
$766$		0			0
$767$	422751.			0.0259476
$768$		0			0
$769$	−5.11272e6			−0.311771			−0.155886	−	0.987775i	$-0.549823\pi$
$769$	−5.11272e6			−0.311771			−0.155886	+	0.987775i	$0.549823\pi$
$770$		0			0
$771$	−7.28752e6	−	7.28752e6i	−0.441513	−	0.441513i
$772$		0			0
$773$	7.11366e6	−	7.11366e6i	0.428198	−	0.428198i	−0.459816	−	0.888014i	$-0.652085\pi$
$773$	7.11366e6	−	7.11366e6i	0.428198	−	0.428198i	0.888014	+	0.459816i	$0.152085\pi$
$774$		0			0
$775$			659132.i			0.0394201i
$776$		0			0
$777$			3.71960e6i			0.221026i
$778$		0			0
$779$	5.67422e6	−	5.67422e6i	0.335014	−	0.335014i
$780$		0			0
$781$	1.14220e7	+	1.14220e7i	0.670064	+	0.670064i
$782$		0			0
$783$	−5.29276e6			−0.308516
$784$		0			0
$785$	5.42022e6			0.313937
$786$		0			0
$787$	−5.13772e6	−	5.13772e6i	−0.295688	−	0.295688i	0.543634	−	0.839322i	$-0.317048\pi$
$787$	−5.13772e6	−	5.13772e6i	−0.295688	−	0.295688i	−0.839322	+	0.543634i	$0.817048\pi$
$788$		0			0
$789$	8.15535e6	−	8.15535e6i	0.466391	−	0.466391i
$790$		0			0
$791$			2.96011e7i			1.68216i
$792$		0			0
$793$		−	1.38699e7i		−	0.783232i
$794$		0			0
$795$	4.60061e6	−	4.60061e6i	0.258165	−	0.258165i
$796$		0			0
$797$	4.23906e6	+	4.23906e6i	0.236387	+	0.236387i	0.815352	−	0.578965i	$-0.196543\pi$
$797$	4.23906e6	+	4.23906e6i	0.236387	+	0.236387i	−0.578965	+	0.815352i	$0.696543\pi$
$798$		0			0
$799$	−1.59651e7			−0.884717
$800$		0			0
$801$	4.14966e6			0.228523
$802$		0			0
$803$	−5.43288e6	−	5.43288e6i	−0.297332	−	0.297332i
$804$		0			0
$805$	862151.	−	862151.i	0.0468915	−	0.0468915i
$806$		0			0
$807$		−	1.57803e7i		−	0.852967i
$808$		0			0
$809$		−	2.24244e7i		−	1.20462i	−0.798264	−	0.602308i	$-0.794248\pi$
$809$		−	2.24244e7i		−	1.20462i	0.798264	−	0.602308i	$-0.205752\pi$
$810$		0			0
$811$	2.35569e7	−	2.35569e7i	1.25767	−	1.25767i	0.305468	−	0.952202i	$-0.401187\pi$
$811$	2.35569e7	−	2.35569e7i	1.25767	−	1.25767i	0.952202	−	0.305468i	$-0.0988129\pi$
$812$		0			0
$813$	−2.75206e6	−	2.75206e6i	−0.146027	−	0.146027i
$814$		0			0
$815$	−1.54223e7			−0.813306
$816$		0			0
$817$	1.71923e6			0.0901114
$818$		0			0
$819$	−4.64007e6	−	4.64007e6i	−0.241721	−	0.241721i
$820$		0			0
$821$	−8.49163e6	+	8.49163e6i	−0.439676	+	0.439676i	−0.891903	−	0.452227i	$-0.850630\pi$
$821$	−8.49163e6	+	8.49163e6i	−0.439676	+	0.439676i	0.452227	+	0.891903i	$0.350630\pi$
$822$		0			0
$823$			2.18933e7i			1.12671i	0.826216	+	0.563354i	$0.190489\pi$
$823$			2.18933e7i			1.12671i	−0.826216	+	0.563354i	$0.809511\pi$
$824$		0			0
$825$			2.06136e6i			0.105443i
$826$		0			0
$827$	−3.55037e6	+	3.55037e6i	−0.180513	+	0.180513i	−0.791580	−	0.611066i	$-0.790741\pi$
$827$	−3.55037e6	+	3.55037e6i	−0.180513	+	0.180513i	0.611066	+	0.791580i	$0.290741\pi$
$828$		0			0
$829$	−1.05693e7	−	1.05693e7i	−0.534145	−	0.534145i	0.387658	−	0.921803i	$-0.373284\pi$
$829$	−1.05693e7	−	1.05693e7i	−0.534145	−	0.534145i	−0.921803	+	0.387658i	$0.873284\pi$
$830$		0			0
$831$	1.80438e6			0.0906414
$832$		0			0
$833$	−3.86134e6			−0.192808
$834$		0			0
$835$	−9.77299e6	−	9.77299e6i	−0.485078	−	0.485078i
$836$		0			0
$837$	2.51539e6	−	2.51539e6i	0.124106	−	0.124106i
$838$		0			0
$839$		−	2.25974e7i		−	1.10829i	−0.832421	−	0.554144i	$-0.813046\pi$
$839$		−	2.25974e7i		−	1.10829i	0.832421	−	0.554144i	$-0.186954\pi$
$840$		0			0
$841$		−	1.80490e7i		−	0.879962i
$842$		0			0
$843$	−948743.	+	948743.i	−0.0459812	+	0.0459812i
$844$		0			0
$845$	5.40511e6	+	5.40511e6i	0.260413	+	0.260413i
$846$		0			0
$847$	−1.33612e6			−0.0639935
$848$		0			0
$849$	−1.64096e7			−0.781319
$850$		0			0
$851$	−784237.	−	784237.i	−0.0371213	−	0.0371213i
$852$		0			0
$853$	−1.38328e7	+	1.38328e7i	−0.650933	+	0.650933i	−0.953218	−	0.302285i	$-0.902251\pi$
$853$	−1.38328e7	+	1.38328e7i	−0.650933	+	0.650933i	0.302285	+	0.953218i	$0.402251\pi$
$854$		0			0
$855$			2.67102e6i			0.124957i
$856$		0			0
$857$			1.07937e7i			0.502018i	0.967985	+	0.251009i	$0.0807624\pi$
$857$			1.07937e7i			0.502018i	−0.967985	+	0.251009i	$0.919238\pi$
$858$		0			0
$859$	1.49105e7	−	1.49105e7i	0.689459	−	0.689459i	−0.272653	−	0.962112i	$-0.587901\pi$
$859$	1.49105e7	−	1.49105e7i	0.689459	−	0.689459i	0.962112	+	0.272653i	$0.0879013\pi$
$860$		0			0
$861$	1.08775e7	+	1.08775e7i	0.500059	+	0.500059i
$862$		0			0
$863$	−2.91804e7			−1.33372			−0.666860	−	0.745183i	$-0.732362\pi$
$863$	−2.91804e7			−1.33372			−0.666860	+	0.745183i	$0.732362\pi$
$864$		0			0
$865$	−1.39675e7			−0.634716
$866$		0			0
$867$	1.74724e6	+	1.74724e6i	0.0789413	+	0.0789413i
$868$		0			0
$869$	−2.62587e7	+	2.62587e7i	−1.17957	+	1.17957i
$870$		0			0
$871$			6.94667e6i			0.310264i
$872$		0			0
$873$			1.68772e7i			0.749487i
$874$		0			0
$875$	1.58079e6	−	1.58079e6i	0.0697999	−	0.0697999i
$876$		0			0
$877$	1.62738e7	+	1.62738e7i	0.714478	+	0.714478i	0.967469	−	0.252991i	$-0.0814142\pi$
$877$	1.62738e7	+	1.62738e7i	0.714478	+	0.714478i	−0.252991	+	0.967469i	$0.581414\pi$
$878$		0			0
$879$	−6.51455e6			−0.284389
$880$		0			0
$881$	−4.45872e7			−1.93540			−0.967699	−	0.252108i	$-0.918876\pi$
$881$	−4.45872e7			−1.93540			−0.967699	+	0.252108i	$0.918876\pi$
$882$		0			0
$883$	−4.28324e6	−	4.28324e6i	−0.184872	−	0.184872i	0.608603	−	0.793475i	$-0.291730\pi$
$883$	−4.28324e6	−	4.28324e6i	−0.184872	−	0.184872i	−0.793475	+	0.608603i	$0.791730\pi$
$884$		0			0
$885$	233255.	−	233255.i	0.0100109	−	0.0100109i
$886$		0			0
$887$		−	1.01943e7i		−	0.435060i	−0.976054	−	0.217530i	$-0.930200\pi$
$887$		−	1.01943e7i		−	0.435060i	0.976054	−	0.217530i	$-0.0697999\pi$
$888$		0			0
$889$			4.95137e6i			0.210122i
$890$		0			0
$891$	−4.84058e6	+	4.84058e6i	−0.204269	+	0.204269i
$892$		0			0
$893$	−6.38817e6	−	6.38817e6i	−0.268070	−	0.268070i
$894$		0			0
$895$	1.02746e7			0.428753
$896$		0			0
$897$	−697227.			−0.0289330
$898$		0			0
$899$	−1.17012e6	−	1.17012e6i	−0.0482872	−	0.0482872i
$900$		0			0
$901$	2.42718e7	−	2.42718e7i	0.996070	−	0.996070i
$902$		0			0
$903$			3.29577e6i			0.134505i
$904$		0			0
$905$		−	3.28820e6i		−	0.133456i
$906$		0			0
$907$	−2.27644e7	+	2.27644e7i	−0.918835	+	0.918835i	−0.996945	−	0.0781097i	$-0.975112\pi$
$907$	−2.27644e7	+	2.27644e7i	−0.918835	+	0.918835i	0.0781097	+	0.996945i	$0.475112\pi$
$908$		0			0
$909$	1.62488e7	+	1.62488e7i	0.652248	+	0.652248i
$910$		0			0
$911$	1.31139e7			0.523523			0.261761	−	0.965133i	$-0.415697\pi$
$911$	1.31139e7			0.523523			0.261761	+	0.965133i	$0.415697\pi$
$912$		0			0
$913$	−2.96338e7			−1.17655
$914$		0			0
$915$	−7.65277e6	−	7.65277e6i	−0.302180	−	0.302180i
$916$		0			0
$917$	−2.97239e7	+	2.97239e7i	−1.16730	+	1.16730i
$918$		0			0
$919$		−	3.26795e7i		−	1.27640i	−0.769870	−	0.638201i	$-0.779679\pi$
$919$		−	3.26795e7i		−	1.27640i	0.769870	−	0.638201i	$-0.220321\pi$
$920$		0			0
$921$		−	2.33668e6i		−	0.0907717i
$922$		0			0
$923$	−7.08362e6	+	7.08362e6i	−0.273685	+	0.273685i
$924$		0			0
$925$	−1.43793e6	−	1.43793e6i	−0.0552566	−	0.0552566i
$926$		0			0
$927$	−2.41602e7			−0.923425
$928$		0			0
$929$	2.00579e7			0.762512			0.381256	−	0.924470i	$-0.375492\pi$
$929$	2.00579e7			0.762512			0.381256	+	0.924470i	$0.375492\pi$
$930$		0			0
$931$	−1.54505e6	−	1.54505e6i	−0.0584210	−	0.0584210i
$932$		0			0
$933$	−151111.	+	151111.i	−0.00568320	+	0.00568320i
$934$		0			0
$935$			1.08753e7i			0.406829i
$936$		0			0
$937$		−	3.89767e7i		−	1.45029i	−0.688594	−	0.725147i	$-0.741772\pi$
$937$		−	3.89767e7i		−	1.45029i	0.688594	−	0.725147i	$-0.258228\pi$
$938$		0			0
$939$	−7.17234e6	+	7.17234e6i	−0.265459	+	0.265459i
$940$		0			0
$941$	674890.	+	674890.i	0.0248461	+	0.0248461i	0.719421	−	0.694575i	$-0.244407\pi$
$941$	674890.	+	674890.i	0.0248461	+	0.0248461i	−0.694575	+	0.719421i	$0.744407\pi$
$942$		0			0
$943$	−4.58680e6			−0.167970
$944$		0			0
$945$	−1.20653e7			−0.439499
$946$		0			0
$947$	2.14572e7	+	2.14572e7i	0.777497	+	0.777497i	0.979405	−	0.201908i	$-0.0647141\pi$
$947$	2.14572e7	+	2.14572e7i	0.777497	+	0.777497i	−0.201908	+	0.979405i	$0.564714\pi$
$948$		0			0
$949$	3.36931e6	−	3.36931e6i	0.121444	−	0.121444i
$950$		0			0
$951$			671793.i			0.0240871i
$952$		0			0
$953$		−	4.22078e7i		−	1.50543i	−0.658347	−	0.752715i	$-0.728744\pi$
$953$		−	4.22078e7i		−	1.50543i	0.658347	−	0.752715i	$-0.271256\pi$
$954$		0			0
$955$	1.55652e7	−	1.55652e7i	0.552265	−	0.552265i
$956$		0			0
$957$	−3.65943e6	−	3.65943e6i	−0.129162	−	0.129162i
$958$		0			0
$959$	−4.75328e7			−1.66896
$960$		0			0
$961$	−2.75169e7			−0.961151
$962$		0			0
$963$	−1.71703e7	−	1.71703e7i	−0.596639	−	0.596639i
$964$		0			0
$965$	−1.33105e6	+	1.33105e6i	−0.0460127	+	0.0460127i
$966$		0			0
$967$		−	4.99103e7i		−	1.71642i	−0.513299	−	0.858210i	$-0.671577\pi$
$967$		−	4.99103e7i		−	1.71642i	0.513299	−	0.858210i	$-0.328423\pi$
$968$		0			0
$969$		−	5.02149e6i		−	0.171800i
$970$		0			0
$971$	1.78401e7	−	1.78401e7i	0.607225	−	0.607225i	−0.334995	−	0.942220i	$-0.608735\pi$
$971$	1.78401e7	−	1.78401e7i	0.607225	−	0.607225i	0.942220	+	0.334995i	$0.108735\pi$
$972$		0			0
$973$	−3.50548e7	−	3.50548e7i	−1.18704	−	1.18704i
$974$		0			0
$975$	−1.27840e6			−0.0430679
$976$		0			0
$977$	−4.05446e6			−0.135893			−0.0679465	−	0.997689i	$-0.521645\pi$
$977$	−4.05446e6			−0.135893			−0.0679465	+	0.997689i	$0.521645\pi$
$978$		0			0
$979$	6.76055e6	+	6.76055e6i	0.225437	+	0.225437i
$980$		0			0
$981$	2.52621e7	−	2.52621e7i	0.838102	−	0.838102i
$982$		0			0
$983$			3.22914e7i			1.06587i	0.846157	+	0.532934i	$0.178911\pi$
$983$			3.22914e7i			1.06587i	−0.846157	+	0.532934i	$0.821089\pi$
$984$		0			0
$985$		−	4.18840e6i		−	0.137549i
$986$		0			0
$987$	1.22461e7	−	1.22461e7i	0.400135	−	0.400135i
$988$		0			0
$989$	−694878.	−	694878.i	−0.0225901	−	0.0225901i
$990$		0			0
$991$	3.22757e6			0.104398			0.0521988	−	0.998637i	$-0.483377\pi$
$991$	3.22757e6			0.104398			0.0521988	+	0.998637i	$0.483377\pi$
$992$		0			0
$993$	−1.94857e6			−0.0627108
$994$		0			0
$995$	6.06294e6	+	6.06294e6i	0.194145	+	0.194145i
$996$		0			0
$997$	1.03574e7	−	1.03574e7i	0.329999	−	0.329999i	−0.522587	−	0.852586i	$-0.675033\pi$
$997$	1.03574e7	−	1.03574e7i	0.329999	−	0.329999i	0.852586	+	0.522587i	$0.175033\pi$
$998$		0			0
$999$			1.09749e7i			0.347927i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.6.l.a.81.15		80
4.3	odd	2		80.6.l.a.61.36	yes	80
16.5	even	4	inner	320.6.l.a.241.15		80
16.11	odd	4		80.6.l.a.21.36	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.36	✓	80	16.11	odd	4
80.6.l.a.61.36	yes	80	4.3	odd	2
320.6.l.a.81.15		80	1.1	even	1	trivial
320.6.l.a.241.15		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)

\(f(q)\)	\(=\)	\(q+(-5.64986 - 5.64986i) q^{3} +(-17.6777 + 17.6777i) q^{5} -143.077i q^{7} -179.158i q^{9} +O(q^{10})\)	\(q+(-5.64986 - 5.64986i) q^{3} +(-17.6777 + 17.6777i) q^{5} -143.077i q^{7} -179.158i q^{9} +(291.881 - 291.881i) q^{11} +(181.016 + 181.016i) q^{13} +199.753 q^{15} +1053.85 q^{17} +(421.682 + 421.682i) q^{19} +(-808.365 + 808.365i) q^{21} -340.870i q^{23} -625.000i q^{25} +(-2385.13 + 2385.13i) q^{27} +(1109.53 + 1109.53i) q^{29} -1054.61 q^{31} -3298.18 q^{33} +(2529.27 + 2529.27i) q^{35} +(2300.69 - 2300.69i) q^{37} -2045.43i q^{39} -13456.2i q^{41} +(2038.54 - 2038.54i) q^{43} +(3167.10 + 3167.10i) q^{45} -15149.3 q^{47} -3664.02 q^{49} +(-5954.12 - 5954.12i) q^{51} +(23031.5 - 23031.5i) q^{53} +10319.6i q^{55} -4764.89i q^{57} +(1167.72 - 1167.72i) q^{59} +(-38311.2 - 38311.2i) q^{61} -25633.4 q^{63} -6399.89 q^{65} +(19188.0 + 19188.0i) q^{67} +(-1925.87 + 1925.87i) q^{69} +39132.5i q^{71} -18613.3i q^{73} +(-3531.16 + 3531.16i) q^{75} +(-41761.5 - 41761.5i) q^{77} -89963.6 q^{79} -16584.1 q^{81} +(-50763.5 - 50763.5i) q^{83} +(-18629.6 + 18629.6i) q^{85} -12537.4i q^{87} +23162.0i q^{89} +(25899.3 - 25899.3i) q^{91} +(5958.40 + 5958.40i) q^{93} -14908.7 q^{95} -94202.7 q^{97} +(-52292.9 - 52292.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q+O(q^{10}) \) 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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