LMFDB - Embedded newform 320.6.l.a.241.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("320.81");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$51.3228223402$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			241.18
Character	$\chi$	$=$	320.241
Dual form			320.6.l.a.81.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.58258 + 3.58258i) q^{3} +(17.6777 + 17.6777i) q^{5} -149.558i q^{7} +217.330i q^{9} +O(q^{10})$	\(q+(-3.58258 + 3.58258i) q^{3} +(17.6777 + 17.6777i) q^{5} -149.558i q^{7} +217.330i q^{9} +(38.8975 + 38.8975i) q^{11} +(683.576 - 683.576i) q^{13} -126.663 q^{15} -929.208 q^{17} +(-900.333 + 900.333i) q^{19} +(535.804 + 535.804i) q^{21} -507.581i q^{23} +625.000i q^{25} +(-1649.17 - 1649.17i) q^{27} +(584.811 - 584.811i) q^{29} +5061.59 q^{31} -278.707 q^{33} +(2643.84 - 2643.84i) q^{35} +(-10345.7 - 10345.7i) q^{37} +4897.93i q^{39} +1291.09i q^{41} +(-3874.63 - 3874.63i) q^{43} +(-3841.89 + 3841.89i) q^{45} +1375.42 q^{47} -5560.57 q^{49} +(3328.96 - 3328.96i) q^{51} +(-8947.98 - 8947.98i) q^{53} +1375.23i q^{55} -6451.03i q^{57} +(32361.6 + 32361.6i) q^{59} +(8808.44 - 8808.44i) q^{61} +32503.5 q^{63} +24168.1 q^{65} +(36446.3 - 36446.3i) q^{67} +(1818.45 + 1818.45i) q^{69} -45094.7i q^{71} -86532.8i q^{73} +(-2239.11 - 2239.11i) q^{75} +(5817.43 - 5817.43i) q^{77} +55508.6 q^{79} -40994.7 q^{81} +(-26808.7 + 26808.7i) q^{83} +(-16426.2 - 16426.2i) q^{85} +4190.27i q^{87} -54453.4i q^{89} +(-102234. - 102234. i) q^{91} +(-18133.6 + 18133.6i) q^{93} -31831.6 q^{95} +110499. q^{97} +(-8453.60 + 8453.60i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q+O(q^{10}) $ 80 * q	$ 80 q - 1208 q^{11} + 1800 q^{15} - 2360 q^{19} + 7464 q^{27} - 8144 q^{29} + 21296 q^{37} - 32072 q^{43} + 88360 q^{47} - 192080 q^{49} + 5920 q^{51} - 49456 q^{53} - 44984 q^{59} + 48080 q^{61} - 158760 q^{63} - 61160 q^{67} - 22320 q^{69} - 14896 q^{77} - 177680 q^{79} - 524880 q^{81} + 329240 q^{83} + 132400 q^{85} - 364832 q^{91} - 362352 q^{93} - 288800 q^{95} - 659000 q^{99}+O(q^{100}) $ 80 * q - 1208 * q^11 + 1800 * q^15 - 2360 * q^19 + 7464 * q^27 - 8144 * q^29 + 21296 * q^37 - 32072 * q^43 + 88360 * q^47 - 192080 * q^49 + 5920 * q^51 - 49456 * q^53 - 44984 * q^59 + 48080 * q^61 - 158760 * q^63 - 61160 * q^67 - 22320 * q^69 - 14896 * q^77 - 177680 * q^79 - 524880 * q^81 + 329240 * q^83 + 132400 * q^85 - 364832 * q^91 - 362352 * q^93 - 288800 * q^95 - 659000 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−3.58258	+	3.58258i	−0.229823	+	0.229823i	−0.812619	−	0.582796i	$-0.801959\pi$
$3$	−3.58258	+	3.58258i	−0.229823	+	0.229823i	0.582796	+	0.812619i	$0.301959\pi$
$4$		0			0
$5$	17.6777	+	17.6777i	0.316228	+	0.316228i
$5$	17.6777	+	17.6777i	0.316228	+	0.316228i
$6$		0			0
$7$		−	149.558i		−	1.15362i	−0.816877	−	0.576812i	$-0.804297\pi$
$7$		−	149.558i		−	1.15362i	0.816877	−	0.576812i	$-0.195703\pi$
$8$		0			0
$9$			217.330i			0.894363i
$10$		0			0
$11$	38.8975	+	38.8975i	0.0969259	+	0.0969259i	0.753907	−	0.656981i	$-0.228167\pi$
$11$	38.8975	+	38.8975i	0.0969259	+	0.0969259i	−0.656981	+	0.753907i	$0.728167\pi$
$12$		0			0
$13$	683.576	−	683.576i	1.12183	−	1.12183i	0.130368	−	0.991466i	$-0.458384\pi$
$13$	683.576	−	683.576i	1.12183	−	1.12183i	0.991466	−	0.130368i	$-0.0416157\pi$
$14$		0			0
$15$	−126.663			−0.145353
$16$		0			0
$17$	−929.208			−0.779813			−0.389907	−	0.920854i	$-0.627493\pi$
$17$	−929.208			−0.779813			−0.389907	+	0.920854i	$0.627493\pi$
$18$		0			0
$19$	−900.333	+	900.333i	−0.572162	+	0.572162i	−0.932732	−	0.360570i	$-0.882582\pi$
$19$	−900.333	+	900.333i	−0.572162	+	0.572162i	0.360570	+	0.932732i	$0.382582\pi$
$20$		0			0
$21$	535.804	+	535.804i	0.265129	+	0.265129i
$22$		0			0
$23$		−	507.581i		−	0.200072i	−0.994984	−	0.100036i	$-0.968104\pi$
$23$		−	507.581i		−	0.200072i	0.994984	−	0.100036i	$-0.0318958\pi$
$24$		0			0
$25$			625.000i			0.200000i
$26$		0			0
$27$	−1649.17	−	1649.17i	−0.435368	−	0.435368i
$28$		0			0
$29$	584.811	−	584.811i	0.129128	−	0.129128i	−0.639589	−	0.768717i	$-0.720895\pi$
$29$	584.811	−	584.811i	0.129128	−	0.129128i	0.768717	+	0.639589i	$0.220895\pi$
$30$		0			0
$31$	5061.59			0.945982			0.472991	−	0.881067i	$-0.343174\pi$
$31$	5061.59			0.945982			0.472991	+	0.881067i	$0.343174\pi$
$32$		0			0
$33$	−278.707			−0.0445516
$34$		0			0
$35$	2643.84	−	2643.84i	0.364808	−	0.364808i
$36$		0			0
$37$	−10345.7	−	10345.7i	−1.24238	−	1.24238i	−0.959009	−	0.283375i	$-0.908546\pi$
$37$	−10345.7	−	10345.7i	−1.24238	−	1.24238i	−0.283375	−	0.959009i	$-0.591454\pi$
$38$		0			0
$39$			4897.93i			0.515646i
$40$		0			0
$41$			1291.09i			0.119949i	0.998200	+	0.0599746i	$0.0191020\pi$
$41$			1291.09i			0.119949i	−0.998200	+	0.0599746i	$0.980898\pi$
$42$		0			0
$43$	−3874.63	−	3874.63i	−0.319565	−	0.319565i	0.529035	−	0.848600i	$-0.322554\pi$
$43$	−3874.63	−	3874.63i	−0.319565	−	0.319565i	−0.848600	+	0.529035i	$0.822554\pi$
$44$		0			0
$45$	−3841.89	+	3841.89i	−0.282822	+	0.282822i
$46$		0			0
$47$	1375.42			0.0908219			0.0454110	−	0.998968i	$-0.485540\pi$
$47$	1375.42			0.0908219			0.0454110	+	0.998968i	$0.485540\pi$
$48$		0			0
$49$	−5560.57			−0.330848
$50$		0			0
$51$	3328.96	−	3328.96i	0.179219	−	0.179219i
$52$		0			0
$53$	−8947.98	−	8947.98i	−0.437558	−	0.437558i	0.453631	−	0.891189i	$-0.350128\pi$
$53$	−8947.98	−	8947.98i	−0.437558	−	0.437558i	−0.891189	+	0.453631i	$0.850128\pi$
$54$		0			0
$55$			1375.23i			0.0613013i
$56$		0			0
$57$		−	6451.03i		−	0.262992i
$58$		0			0
$59$	32361.6	+	32361.6i	1.21032	+	1.21032i	0.970921	+	0.239399i	$0.0769504\pi$
$59$	32361.6	+	32361.6i	1.21032	+	1.21032i	0.239399	+	0.970921i	$0.423050\pi$
$60$		0			0
$61$	8808.44	−	8808.44i	0.303092	−	0.303092i	−0.539130	−	0.842222i	$-0.681247\pi$
$61$	8808.44	−	8808.44i	0.303092	−	0.303092i	0.842222	+	0.539130i	$0.181247\pi$
$62$		0			0
$63$	32503.5			1.03176
$64$		0			0
$65$	24168.1			0.709510
$66$		0			0
$67$	36446.3	−	36446.3i	0.991898	−	0.991898i	−0.00806945	−	0.999967i	$-0.502569\pi$
$67$	36446.3	−	36446.3i	0.991898	−	0.991898i	0.999967	+	0.00806945i	$0.00256861\pi$
$68$		0			0
$69$	1818.45	+	1818.45i	0.0459811	+	0.0459811i
$70$		0			0
$71$		−	45094.7i		−	1.06165i	−0.847483	−	0.530823i	$-0.821883\pi$
$71$		−	45094.7i		−	1.06165i	0.847483	−	0.530823i	$-0.178117\pi$
$72$		0			0
$73$		−	86532.8i		−	1.90053i	−0.311450	−	0.950263i	$-0.600814\pi$
$73$		−	86532.8i		−	1.90053i	0.311450	−	0.950263i	$-0.399186\pi$
$74$		0			0
$75$	−2239.11	−	2239.11i	−0.0459646	−	0.0459646i
$76$		0			0
$77$	5817.43	−	5817.43i	0.111816	−	0.111816i
$78$		0			0
$79$	55508.6			1.00067			0.500337	−	0.865831i	$-0.333209\pi$
$79$	55508.6			1.00067			0.500337	+	0.865831i	$0.333209\pi$
$80$		0			0
$81$	−40994.7			−0.694248
$82$		0			0
$83$	−26808.7	+	26808.7i	−0.427150	+	0.427150i	−0.887656	−	0.460506i	$-0.847668\pi$
$83$	−26808.7	+	26808.7i	−0.427150	+	0.427150i	0.460506	+	0.887656i	$0.347668\pi$
$84$		0			0
$85$	−16426.2	−	16426.2i	−0.246599	−	0.246599i
$86$		0			0
$87$			4190.27i			0.0593531i
$88$		0			0
$89$		−	54453.4i		−	0.728702i	−0.931262	−	0.364351i	$-0.881291\pi$
$89$		−	54453.4i		−	0.728702i	0.931262	−	0.364351i	$-0.118709\pi$
$90$		0			0
$91$	−102234.	−	102234.i	−1.29417	−	1.29417i
$92$		0			0
$93$	−18133.6	+	18133.6i	−0.217408	+	0.217408i
$94$		0			0
$95$	−31831.6			−0.361867
$96$		0			0
$97$	110499.			1.19242			0.596208	−	0.802830i	$-0.296673\pi$
$97$	110499.			1.19242			0.596208	+	0.802830i	$0.296673\pi$
$98$		0			0
$99$	−8453.60	+	8453.60i	−0.0866869	+	0.0866869i
$100$		0			0
$101$	16243.2	+	16243.2i	0.158442	+	0.158442i	0.781876	−	0.623434i	$-0.214263\pi$
$101$	16243.2	+	16243.2i	0.158442	+	0.158442i	−0.623434	+	0.781876i	$0.714263\pi$
$102$		0			0
$103$		−	190349.i		−	1.76790i	−0.467582	−	0.883949i	$-0.654875\pi$
$103$		−	190349.i		−	1.76790i	0.467582	−	0.883949i	$-0.345125\pi$
$104$		0			0
$105$			18943.5i			0.167682i
$106$		0			0
$107$	−148544.	−	148544.i	−1.25428	−	1.25428i	−0.953783	−	0.300497i	$-0.902847\pi$
$107$	−148544.	−	148544.i	−1.25428	−	1.25428i	−0.300497	−	0.953783i	$-0.597153\pi$
$108$		0			0
$109$	97591.1	−	97591.1i	0.786763	−	0.786763i	−0.194199	−	0.980962i	$-0.562211\pi$
$109$	97591.1	−	97591.1i	0.786763	−	0.786763i	0.980962	+	0.194199i	$0.0622107\pi$
$110$		0			0
$111$	74128.7			0.571056
$112$		0			0
$113$	152239.			1.12158			0.560791	−	0.827957i	$-0.310497\pi$
$113$	152239.			1.12158			0.560791	+	0.827957i	$0.310497\pi$
$114$		0			0
$115$	8972.86	−	8972.86i	0.0632683	−	0.0632683i
$116$		0			0
$117$	148562.	+	148562.i	1.00333	+	1.00333i
$118$		0			0
$119$			138970.i			0.899611i
$120$		0			0
$121$		−	158025.i		−	0.981211i
$122$		0			0
$123$	−4625.44	−	4625.44i	−0.0275671	−	0.0275671i
$124$		0			0
$125$	−11048.5	+	11048.5i	−0.0632456	+	0.0632456i
$126$		0			0
$127$	104375.			0.574234			0.287117	−	0.957896i	$-0.407303\pi$
$127$	104375.			0.574234			0.287117	+	0.957896i	$0.407303\pi$
$128$		0			0
$129$	27762.4			0.146887
$130$		0			0
$131$	7019.50	−	7019.50i	0.0357378	−	0.0357378i	−0.689012	−	0.724750i	$-0.741955\pi$
$131$	7019.50	−	7019.50i	0.0357378	−	0.0357378i	0.724750	+	0.689012i	$0.241955\pi$
$132$		0			0
$133$	134652.	+	134652.i	0.660060	+	0.660060i
$134$		0			0
$135$		−	58307.0i		−	0.275351i
$136$		0			0
$137$			80126.5i			0.364733i	0.983231	+	0.182366i	$0.0583757\pi$
$137$			80126.5i			0.364733i	−0.983231	+	0.182366i	$0.941624\pi$
$138$		0			0
$139$	−121893.	−	121893.i	−0.535110	−	0.535110i	0.386979	−	0.922089i	$-0.373519\pi$
$139$	−121893.	−	121893.i	−0.535110	−	0.535110i	−0.922089	+	0.386979i	$0.873519\pi$
$140$		0			0
$141$	−4927.55	+	4927.55i	−0.0208729	+	0.0208729i
$142$		0			0
$143$	53178.8			0.217469
$144$		0			0
$145$	20676.2			0.0816677
$146$		0			0
$147$	19921.2	−	19921.2i	0.0760365	−	0.0760365i
$148$		0			0
$149$	−359884.	−	359884.i	−1.32800	−	1.32800i	−0.907116	−	0.420880i	$-0.861721\pi$
$149$	−359884.	−	359884.i	−1.32800	−	1.32800i	−0.420880	−	0.907116i	$-0.638279\pi$
$150$		0			0
$151$			355270.i			1.26799i	0.773336	+	0.633996i	$0.218586\pi$
$151$			355270.i			1.26799i	−0.773336	+	0.633996i	$0.781414\pi$
$152$		0			0
$153$		−	201945.i		−	0.697436i
$154$		0			0
$155$	89477.2	+	89477.2i	0.299146	+	0.299146i
$156$		0			0
$157$	−237892.	+	237892.i	−0.770248	+	0.770248i	−0.978150	−	0.207901i	$-0.933337\pi$
$157$	−237892.	+	237892.i	−0.770248	+	0.770248i	0.207901	+	0.978150i	$0.433337\pi$
$158$		0			0
$159$	64113.8			0.201122
$160$		0			0
$161$	−75912.8			−0.230808
$162$		0			0
$163$	−7842.29	+	7842.29i	−0.0231193	+	0.0231193i	−0.718572	−	0.695453i	$-0.755204\pi$
$163$	−7842.29	+	7842.29i	−0.0231193	+	0.0231193i	0.695453	+	0.718572i	$0.255204\pi$
$164$		0			0
$165$	−4926.89	−	4926.89i	−0.0140884	−	0.0140884i
$166$		0			0
$167$		−	221862.i		−	0.615590i	−0.951453	−	0.307795i	$-0.900409\pi$
$167$		−	221862.i		−	0.615590i	0.951453	−	0.307795i	$-0.0995910\pi$
$168$		0			0
$169$		−	563259.i		−	1.51702i
$170$		0			0
$171$	−195669.	−	195669.i	−0.511720	−	0.511720i
$172$		0			0
$173$	−407014.	+	407014.i	−1.03394	+	1.03394i	−0.0345330	+	0.999404i	$0.510994\pi$
$173$	−407014.	+	407014.i	−1.03394	+	1.03394i	−0.999404	+	0.0345330i	$0.989006\pi$
$174$		0			0
$175$	93473.7			0.230725
$176$		0			0
$177$	−231876.			−0.556318
$178$		0			0
$179$	109397.	−	109397.i	0.255195	−	0.255195i	−0.567902	−	0.823096i	$-0.692245\pi$
$179$	109397.	−	109397.i	0.255195	−	0.255195i	0.823096	+	0.567902i	$0.192245\pi$
$180$		0			0
$181$	122240.	+	122240.i	0.277342	+	0.277342i	0.832047	−	0.554705i	$-0.187169\pi$
$181$	122240.	+	122240.i	0.277342	+	0.277342i	−0.554705	+	0.832047i	$0.687169\pi$
$182$		0			0
$183$			63113.9i			0.139315i
$184$		0			0
$185$		−	365776.i		−	0.785753i
$186$		0			0
$187$	−36143.9	−	36143.9i	−0.0755841	−	0.0755841i
$188$		0			0
$189$	−246647.	+	246647.i	−0.502251	+	0.502251i
$190$		0			0
$191$	103925.			0.206129			0.103064	−	0.994675i	$-0.467135\pi$
$191$	103925.			0.206129			0.103064	+	0.994675i	$0.467135\pi$
$192$		0			0
$193$	591953.			1.14391			0.571957	−	0.820283i	$-0.306184\pi$
$193$	591953.			1.14391			0.571957	+	0.820283i	$0.306184\pi$
$194$		0			0
$195$	−86584.1	+	86584.1i	−0.163061	+	0.163061i
$196$		0			0
$197$	434216.	+	434216.i	0.797151	+	0.797151i	0.982645	−	0.185494i	$-0.0593886\pi$
$197$	434216.	+	434216.i	0.797151	+	0.797151i	−0.185494	+	0.982645i	$0.559389\pi$
$198$		0			0
$199$			838962.i			1.50179i	0.660421	+	0.750895i	$0.270378\pi$
$199$			838962.i			1.50179i	−0.660421	+	0.750895i	$0.729622\pi$
$200$		0			0
$201$			261144.i			0.455922i
$202$		0			0
$203$	−87463.1	−	87463.1i	−0.148965	−	0.148965i
$204$		0			0
$205$	−22823.5	+	22823.5i	−0.0379313	+	0.0379313i
$206$		0			0
$207$	110313.			0.178937
$208$		0			0
$209$	−70041.3			−0.110915
$210$		0			0
$211$	−403638.	+	403638.i	−0.624145	+	0.624145i	−0.946589	−	0.322443i	$-0.895496\pi$
$211$	−403638.	+	403638.i	−0.624145	+	0.624145i	0.322443	+	0.946589i	$0.395496\pi$
$212$		0			0
$213$	161555.	+	161555.i	0.243990	+	0.243990i
$214$		0			0
$215$		−	136989.i		−	0.202111i
$216$		0			0
$217$		−	757001.i		−	1.09131i
$218$		0			0
$219$	310011.	+	310011.i	0.436784	+	0.436784i
$220$		0			0
$221$	−635184.	+	635184.i	−0.874821	+	0.874821i
$222$		0			0
$223$	771172.			1.03846			0.519229	−	0.854635i	$-0.326219\pi$
$223$	771172.			1.03846			0.519229	+	0.854635i	$0.326219\pi$
$224$		0			0
$225$	−135831.			−0.178873
$226$		0			0
$227$	−651907.	+	651907.i	−0.839694	+	0.839694i	−0.988818	−	0.149125i	$-0.952354\pi$
$227$	−651907.	+	651907.i	−0.839694	+	0.839694i	0.149125	+	0.988818i	$0.452354\pi$
$228$		0			0
$229$	170285.	+	170285.i	0.214579	+	0.214579i	0.806210	−	0.591630i	$-0.201515\pi$
$229$	170285.	+	170285.i	0.214579	+	0.214579i	−0.591630	+	0.806210i	$0.701515\pi$
$230$		0			0
$231$			41682.8i			0.0513957i
$232$		0			0
$233$			1.27649e6i			1.54038i	0.637812	+	0.770192i	$0.279840\pi$
$233$			1.27649e6i			1.54038i	−0.637812	+	0.770192i	$0.720160\pi$
$234$		0			0
$235$	24314.2	+	24314.2i	0.0287204	+	0.0287204i
$236$		0			0
$237$	−198864.	+	198864.i	−0.229978	+	0.229978i
$238$		0			0
$239$	1.40814e6			1.59459			0.797297	−	0.603587i	$-0.206262\pi$
$239$	1.40814e6			1.59459			0.797297	+	0.603587i	$0.206262\pi$
$240$		0			0
$241$	−897800.			−0.995719			−0.497860	−	0.867258i	$-0.665881\pi$
$241$	−897800.			−0.995719			−0.497860	+	0.867258i	$0.665881\pi$
$242$		0			0
$243$	547615.	−	547615.i	0.594922	−	0.594922i
$244$		0			0
$245$	−98297.9	−	98297.9i	−0.104623	−	0.104623i
$246$		0			0
$247$			1.23089e6i			1.28374i
$248$		0			0
$249$		−	192089.i		−	0.196338i
$250$		0			0
$251$	−848905.	−	848905.i	−0.850501	−	0.850501i	0.139694	−	0.990195i	$-0.455388\pi$
$251$	−848905.	−	848905.i	−0.850501	−	0.850501i	−0.990195	+	0.139694i	$0.955388\pi$
$252$		0			0
$253$	19743.6	−	19743.6i	0.0193922	−	0.0193922i
$254$		0			0
$255$	117697.			0.113348
$256$		0			0
$257$	368924.			0.348421			0.174211	−	0.984708i	$-0.444263\pi$
$257$	368924.			0.348421			0.174211	+	0.984708i	$0.444263\pi$
$258$		0			0
$259$	−1.54728e6	+	1.54728e6i	−1.43324	+	1.43324i
$260$		0			0
$261$	127097.	+	127097.i	0.115487	+	0.115487i
$262$		0			0
$263$		−	244595.i		−	0.218051i	−0.994039	−	0.109026i	$-0.965227\pi$
$263$		−	244595.i		−	0.218051i	0.994039	−	0.109026i	$-0.0347731\pi$
$264$		0			0
$265$		−	316359.i		−	0.276736i
$266$		0			0
$267$	195084.	+	195084.i	0.167472	+	0.167472i
$268$		0			0
$269$	−565231.	+	565231.i	−0.476261	+	0.476261i	−0.903934	−	0.427673i	$-0.859334\pi$
$269$	−565231.	+	565231.i	−0.476261	+	0.476261i	0.427673	+	0.903934i	$0.359334\pi$
$270$		0			0
$271$	−1.22976e6			−1.01718			−0.508588	−	0.861010i	$-0.669832\pi$
$271$	−1.22976e6			−1.01718			−0.508588	+	0.861010i	$0.669832\pi$
$272$		0			0
$273$	732525.			0.594861
$274$		0			0
$275$	−24310.9	+	24310.9i	−0.0193852	+	0.0193852i
$276$		0			0
$277$	−1.36759e6	−	1.36759e6i	−1.07092	−	1.07092i	−0.997285	−	0.0736368i	$-0.976539\pi$
$277$	−1.36759e6	−	1.36759e6i	−1.07092	−	1.07092i	−0.0736368	−	0.997285i	$-0.523461\pi$
$278$		0			0
$279$			1.10004e6i			0.846051i
$280$		0			0
$281$			905343.i			0.683986i	0.939702	+	0.341993i	$0.111102\pi$
$281$			905343.i			0.683986i	−0.939702	+	0.341993i	$0.888898\pi$
$282$		0			0
$283$	−1.73786e6	−	1.73786e6i	−1.28988	−	1.28988i	−0.934857	−	0.355024i	$-0.884473\pi$
$283$	−1.73786e6	−	1.73786e6i	−1.28988	−	1.28988i	−0.355024	−	0.934857i	$-0.615527\pi$
$284$		0			0
$285$	114039.	−	114039.i	0.0831653	−	0.0831653i
$286$		0			0
$287$	193093.			0.138376
$288$		0			0
$289$	−556429.			−0.391891
$290$		0			0
$291$	−395871.	+	395871.i	−0.274044	+	0.274044i
$292$		0			0
$293$	1.03306e6	+	1.03306e6i	0.703005	+	0.703005i	0.965054	−	0.262050i	$-0.0843984\pi$
$293$	1.03306e6	+	1.03306e6i	0.703005	+	0.703005i	−0.262050	+	0.965054i	$0.584398\pi$
$294$		0			0
$295$			1.14416e6i			0.765474i
$296$		0			0
$297$		−	128297.i		−	0.0843968i
$298$		0			0
$299$	−346970.	−	346970.i	−0.224447	−	0.224447i
$300$		0			0
$301$	−579481.	+	579481.i	−0.368658	+	0.368658i
$302$		0			0
$303$	−116385.			−0.0728269
$304$		0			0
$305$	311425.			0.191692
$306$		0			0
$307$	433474.	−	433474.i	0.262493	−	0.262493i	−0.563573	−	0.826066i	$-0.690574\pi$
$307$	433474.	−	433474.i	0.262493	−	0.262493i	0.826066	+	0.563573i	$0.190574\pi$
$308$		0			0
$309$	681941.	+	681941.i	0.406303	+	0.406303i
$310$		0			0
$311$		−	2.34286e6i		−	1.37355i	−0.726868	−	0.686777i	$-0.759025\pi$
$311$		−	2.34286e6i		−	1.37355i	0.726868	−	0.686777i	$-0.240975\pi$
$312$		0			0
$313$		−	692967.i		−	0.399808i	−0.979815	−	0.199904i	$-0.935937\pi$
$313$		−	692967.i		−	0.399808i	0.979815	−	0.199904i	$-0.0640631\pi$
$314$		0			0
$315$	574585.	+	574585.i	0.326271	+	0.326271i
$316$		0			0
$317$	−2.00689e6	+	2.00689e6i	−1.12170	+	1.12170i	−0.130211	+	0.991486i	$0.541566\pi$
$317$	−2.00689e6	+	2.00689e6i	−1.12170	+	1.12170i	−0.991486	+	0.130211i	$0.958434\pi$
$318$		0			0
$319$	45495.3			0.0250317
$320$		0			0
$321$	1.06434e6			0.576524
$322$		0			0
$323$	836596.	−	836596.i	0.446180	−	0.446180i
$324$		0			0
$325$	427235.	+	427235.i	0.224367	+	0.224367i
$326$		0			0
$327$			699257.i			0.361632i
$328$		0			0
$329$		−	205705.i		−	0.104774i
$330$		0			0
$331$	1.85751e6	+	1.85751e6i	0.931885	+	0.931885i	0.997824	−	0.0659391i	$-0.0210043\pi$
$331$	1.85751e6	+	1.85751e6i	0.931885	+	0.931885i	−0.0659391	+	0.997824i	$0.521004\pi$
$332$		0			0
$333$	2.24843e6	−	2.24843e6i	1.11114	−	1.11114i
$334$		0			0
$335$	1.28857e6			0.627331
$336$		0			0
$337$	892674.			0.428172			0.214086	−	0.976815i	$-0.431323\pi$
$337$	892674.			0.428172			0.214086	+	0.976815i	$0.431323\pi$
$338$		0			0
$339$	−545410.	+	545410.i	−0.257765	+	0.257765i
$340$		0			0
$341$	196883.	+	196883.i	0.0916902	+	0.0916902i
$342$		0			0
$343$		−	1.68199e6i		−	0.771949i
$344$		0			0
$345$			64292.0i			0.0290810i
$346$		0			0
$347$	50929.3	+	50929.3i	0.0227062	+	0.0227062i	0.718369	−	0.695663i	$-0.244889\pi$
$347$	50929.3	+	50929.3i	0.0227062	+	0.0227062i	−0.695663	+	0.718369i	$0.744889\pi$
$348$		0			0
$349$	1.60405e6	−	1.60405e6i	0.704944	−	0.704944i	−0.260524	−	0.965467i	$-0.583895\pi$
$349$	1.60405e6	−	1.60405e6i	0.704944	−	0.704944i	0.965467	+	0.260524i	$0.0838952\pi$
$350$		0			0
$351$	−2.25467e6			−0.976820
$352$		0			0
$353$	−594017.			−0.253724			−0.126862	−	0.991920i	$-0.540491\pi$
$353$	−594017.			−0.253724			−0.126862	+	0.991920i	$0.540491\pi$
$354$		0			0
$355$	797169.	−	797169.i	0.335722	−	0.335722i
$356$		0			0
$357$	−497873.	−	497873.i	−0.206751	−	0.206751i
$358$		0			0
$359$		−	3.26627e6i		−	1.33757i	−0.743457	−	0.668784i	$-0.766815\pi$
$359$		−	3.26627e6i		−	1.33757i	0.743457	−	0.668784i	$-0.233185\pi$
$360$		0			0
$361$			854901.i			0.345261i
$362$		0			0
$363$	566138.	+	566138.i	0.225505	+	0.225505i
$364$		0			0
$365$	1.52970e6	−	1.52970e6i	0.600999	−	0.600999i
$366$		0			0
$367$	−4.74678e6			−1.83964			−0.919822	−	0.392337i	$-0.871667\pi$
$367$	−4.74678e6			−1.83964			−0.919822	+	0.392337i	$0.871667\pi$
$368$		0			0
$369$	−280593.			−0.107278
$370$		0			0
$371$	−1.33824e6	+	1.33824e6i	−0.504777	+	0.504777i
$372$		0			0
$373$	1.07649e6	+	1.07649e6i	0.400624	+	0.400624i	0.878453	−	0.477829i	$-0.158576\pi$
$373$	1.07649e6	+	1.07649e6i	0.400624	+	0.400624i	−0.477829	+	0.878453i	$0.658576\pi$
$374$		0			0
$375$		−	79164.6i		−	0.0290705i
$376$		0			0
$377$		−	799525.i		−	0.289720i
$378$		0			0
$379$	−1.07695e6	−	1.07695e6i	−0.385122	−	0.385122i	0.487821	−	0.872943i	$-0.337792\pi$
$379$	−1.07695e6	−	1.07695e6i	−0.385122	−	0.385122i	−0.872943	+	0.487821i	$0.837792\pi$
$380$		0			0
$381$	−373933.	+	373933.i	−0.131972	+	0.131972i
$382$		0			0
$383$	1.61998e6			0.564302			0.282151	−	0.959370i	$-0.408952\pi$
$383$	1.61998e6			0.564302			0.282151	+	0.959370i	$0.408952\pi$
$384$		0			0
$385$	205677.			0.0707187
$386$		0			0
$387$	842074.	−	842074.i	0.285807	−	0.285807i
$388$		0			0
$389$	−1.61689e6	−	1.61689e6i	−0.541759	−	0.541759i	0.382285	−	0.924044i	$-0.375137\pi$
$389$	−1.61689e6	−	1.61689e6i	−0.541759	−	0.541759i	−0.924044	+	0.382285i	$0.875137\pi$
$390$		0			0
$391$			471649.i			0.156019i
$392$		0			0
$393$			50295.9i			0.0164267i
$394$		0			0
$395$	981263.	+	981263.i	0.316441	+	0.316441i
$396$		0			0
$397$	−400667.	+	400667.i	−0.127587	+	0.127587i	−0.768017	−	0.640430i	$-0.778756\pi$
$397$	−400667.	+	400667.i	−0.127587	+	0.127587i	0.640430	+	0.768017i	$0.278756\pi$
$398$		0			0
$399$	−964803.			−0.303394
$400$		0			0
$401$	−1.51826e6			−0.471503			−0.235751	−	0.971813i	$-0.575755\pi$
$401$	−1.51826e6			−0.471503			−0.235751	+	0.971813i	$0.575755\pi$
$402$		0			0
$403$	3.45998e6	−	3.45998e6i	1.06123	−	1.06123i
$404$		0			0
$405$	−724690.	−	724690.i	−0.219541	−	0.219541i
$406$		0			0
$407$		−	804844.i		−	0.240838i
$408$		0			0
$409$			1.49322e6i			0.441382i	0.975344	+	0.220691i	$0.0708313\pi$
$409$			1.49322e6i			0.441382i	−0.975344	+	0.220691i	$0.929169\pi$
$410$		0			0
$411$	−287060.	−	287060.i	−0.0838239	−	0.0838239i
$412$		0			0
$413$	4.83994e6	−	4.83994e6i	1.39625	−	1.39625i
$414$		0			0
$415$	−947830.			−0.270153
$416$		0			0
$417$	873386.			0.245961
$418$		0			0
$419$	4.75505e6	−	4.75505e6i	1.32318	−	1.32318i	0.411998	−	0.911185i	$-0.364831\pi$
$419$	4.75505e6	−	4.75505e6i	1.32318	−	1.32318i	0.911185	−	0.411998i	$-0.135169\pi$
$420$		0			0
$421$	−2.48208e6	−	2.48208e6i	−0.682511	−	0.682511i	0.278054	−	0.960565i	$-0.410311\pi$
$421$	−2.48208e6	−	2.48208e6i	−0.682511	−	0.682511i	−0.960565	+	0.278054i	$0.910311\pi$
$422$		0			0
$423$			298920.i			0.0812277i
$424$		0			0
$425$		−	580755.i		−	0.155963i
$426$		0			0
$427$	−1.31737e6	−	1.31737e6i	−0.349654	−	0.349654i
$428$		0			0
$429$	−190517.	+	190517.i	−0.0499794	+	0.0499794i
$430$		0			0
$431$	1.70333e6			0.441677			0.220838	−	0.975310i	$-0.429121\pi$
$431$	1.70333e6			0.441677			0.220838	+	0.975310i	$0.429121\pi$
$432$		0			0
$433$	3.13406e6			0.803319			0.401659	−	0.915789i	$-0.368434\pi$
$433$	3.13406e6			0.803319			0.401659	+	0.915789i	$0.368434\pi$
$434$		0			0
$435$	−74074.2	+	74074.2i	−0.0187691	+	0.0187691i
$436$		0			0
$437$	456992.	+	456992.i	0.114474	+	0.114474i
$438$		0			0
$439$			3.94725e6i			0.977537i	0.872414	+	0.488768i	$0.162554\pi$
$439$			3.94725e6i			0.977537i	−0.872414	+	0.488768i	$0.837446\pi$
$440$		0			0
$441$		−	1.20848e6i		−	0.295899i
$442$		0			0
$443$	2.77891e6	+	2.77891e6i	0.672767	+	0.672767i	0.958353	−	0.285586i	$-0.0921883\pi$
$443$	2.77891e6	+	2.77891e6i	0.672767	+	0.672767i	−0.285586	+	0.958353i	$0.592188\pi$
$444$		0			0
$445$	962610.	−	962610.i	0.230436	−	0.230436i
$446$		0			0
$447$	2.57863e6			0.610408
$448$		0			0
$449$	−666721.			−0.156073			−0.0780366	−	0.996950i	$-0.524865\pi$
$449$	−666721.			−0.156073			−0.0780366	+	0.996950i	$0.524865\pi$
$450$		0			0
$451$	−50220.2	+	50220.2i	−0.0116262	+	0.0116262i
$452$		0			0
$453$	−1.27279e6	−	1.27279e6i	−0.291413	−	0.291413i
$454$		0			0
$455$		−	3.61452e6i		−	0.818507i
$456$		0			0
$457$			687743.i			0.154041i	0.997030	+	0.0770204i	$0.0245407\pi$
$457$			687743.i			0.154041i	−0.997030	+	0.0770204i	$0.975459\pi$
$458$		0			0
$459$	1.53242e6	+	1.53242e6i	0.339506	+	0.339506i
$460$		0			0
$461$	1.34081e6	−	1.34081e6i	0.293843	−	0.293843i	−0.544753	−	0.838596i	$-0.683377\pi$
$461$	1.34081e6	−	1.34081e6i	0.293843	−	0.293843i	0.838596	+	0.544753i	$0.183377\pi$
$462$		0			0
$463$	8.72731e6			1.89203			0.946015	−	0.324124i	$-0.105070\pi$
$463$	8.72731e6			1.89203			0.946015	+	0.324124i	$0.105070\pi$
$464$		0			0
$465$	−641119.			−0.137501
$466$		0			0
$467$	−670605.	+	670605.i	−0.142290	+	0.142290i	−0.774664	−	0.632374i	$-0.782081\pi$
$467$	−670605.	+	670605.i	−0.142290	+	0.142290i	0.632374	+	0.774664i	$0.282081\pi$
$468$		0			0
$469$	−5.45084e6	−	5.45084e6i	−1.14428	−	1.14428i
$470$		0			0
$471$		−	1.70454e6i		−	0.354041i
$472$		0			0
$473$		−	301427.i		−	0.0619482i
$474$		0			0
$475$	−562708.	−	562708.i	−0.114432	−	0.114432i
$476$		0			0
$477$	1.94467e6	−	1.94467e6i	0.391336	−	0.391336i
$478$		0			0
$479$	−4.74802e6			−0.945526			−0.472763	−	0.881190i	$-0.656743\pi$
$479$	−4.74802e6			−0.945526			−0.472763	+	0.881190i	$0.656743\pi$
$480$		0			0
$481$	−1.41442e7			−2.78750
$482$		0			0
$483$	271964.	−	271964.i	0.0530449	−	0.0530449i
$484$		0			0
$485$	1.95336e6	+	1.95336e6i	0.377075	+	0.377075i
$486$		0			0
$487$		−	4.78477e6i		−	0.914195i	−0.889417	−	0.457097i	$-0.848889\pi$
$487$		−	4.78477e6i		−	0.914195i	0.889417	−	0.457097i	$-0.151111\pi$
$488$		0			0
$489$		−	56191.3i		−	0.0106267i
$490$		0			0
$491$	6.20974e6	+	6.20974e6i	1.16244	+	1.16244i	0.983940	+	0.178497i	$0.0571236\pi$
$491$	6.20974e6	+	6.20974e6i	1.16244	+	1.16244i	0.178497	+	0.983940i	$0.442876\pi$
$492$		0			0
$493$	−543411.	+	543411.i	−0.100696	+	0.100696i
$494$		0			0
$495$	−298880.			−0.0548256
$496$		0			0
$497$	−6.74427e6			−1.22474
$498$		0			0
$499$	619633.	−	619633.i	0.111399	−	0.111399i	−0.649210	−	0.760609i	$-0.724900\pi$
$499$	619633.	−	619633.i	0.111399	−	0.111399i	0.760609	+	0.649210i	$0.224900\pi$
$500$		0			0
$501$	794838.	+	794838.i	0.141477	+	0.141477i
$502$		0			0
$503$			786743.i			0.138648i	0.997594	+	0.0693239i	$0.0220842\pi$
$503$			786743.i			0.138648i	−0.997594	+	0.0693239i	$0.977916\pi$
$504$		0			0
$505$			574285.i			0.100207i
$506$		0			0
$507$	2.01792e6	+	2.01792e6i	0.348646	+	0.348646i
$508$		0			0
$509$	1.52004e6	−	1.52004e6i	0.260052	−	0.260052i	−0.565023	−	0.825075i	$-0.691133\pi$
$509$	1.52004e6	−	1.52004e6i	0.260052	−	0.260052i	0.825075	+	0.565023i	$0.191133\pi$
$510$		0			0
$511$	−1.29417e7			−2.19249
$512$		0			0
$513$	2.96960e6			0.498202
$514$		0			0
$515$	3.36493e6	−	3.36493e6i	0.559059	−	0.559059i
$516$		0			0
$517$	53500.4	+	53500.4i	0.00880299	+	0.00880299i
$518$		0			0
$519$		−	2.91632e6i		−	0.475244i
$520$		0			0
$521$			7.53189e6i			1.21565i	0.794070	+	0.607827i	$0.207959\pi$
$521$			7.53189e6i			1.21565i	−0.794070	+	0.607827i	$0.792041\pi$
$522$		0			0
$523$	3.36602e6	+	3.36602e6i	0.538099	+	0.538099i	0.922970	−	0.384871i	$-0.125754\pi$
$523$	3.36602e6	+	3.36602e6i	0.538099	+	0.538099i	−0.384871	+	0.922970i	$0.625754\pi$
$524$		0			0
$525$	−334877.	+	334877.i	−0.0530258	+	0.0530258i
$526$		0			0
$527$	−4.70327e6			−0.737690
$528$		0			0
$529$	6.17870e6			0.959971
$530$		0			0
$531$	−7.03316e6	+	7.03316e6i	−1.08247	+	1.08247i
$532$		0			0
$533$	882559.	+	882559.i	0.134563	+	0.134563i
$534$		0			0
$535$		−	5.25181e6i		−	0.793276i
$536$		0			0
$537$			783845.i			0.117299i
$538$		0			0
$539$	−216292.	−	216292.i	−0.0320678	−	0.0320678i
$540$		0			0
$541$	6.26679e6	−	6.26679e6i	0.920560	−	0.920560i	−0.0765086	−	0.997069i	$-0.524377\pi$
$541$	6.26679e6	−	6.26679e6i	0.920560	−	0.920560i	0.997069	+	0.0765086i	$0.0243773\pi$
$542$		0			0
$543$	−875866.			−0.127479
$544$		0			0
$545$	3.45037e6			0.497593
$546$		0			0
$547$	−1.14604e6	+	1.14604e6i	−0.163770	+	0.163770i	−0.784234	−	0.620465i	$-0.786944\pi$
$547$	−1.14604e6	+	1.14604e6i	−0.163770	+	0.163770i	0.620465	+	0.784234i	$0.286944\pi$
$548$		0			0
$549$	1.91434e6	+	1.91434e6i	0.271074	+	0.271074i
$550$		0			0
$551$			1.05305e6i			0.147764i
$552$		0			0
$553$		−	8.30175e6i		−	1.15440i
$554$		0			0
$555$	1.31042e6	+	1.31042e6i	0.180584	+	0.180584i
$556$		0			0
$557$	−5.80858e6	+	5.80858e6i	−0.793291	+	0.793291i	−0.982028	−	0.188737i	$-0.939561\pi$
$557$	−5.80858e6	+	5.80858e6i	−0.793291	+	0.793291i	0.188737	+	0.982028i	$0.439561\pi$
$558$		0			0
$559$	−5.29720e6			−0.716997
$560$		0			0
$561$	258977.			0.0347419
$562$		0			0
$563$	2.59073e6	−	2.59073e6i	0.344470	−	0.344470i	−0.513575	−	0.858045i	$-0.671679\pi$
$563$	2.59073e6	−	2.59073e6i	0.344470	−	0.344470i	0.858045	+	0.513575i	$0.171679\pi$
$564$		0			0
$565$	2.69124e6	+	2.69124e6i	0.354675	+	0.354675i
$566$		0			0
$567$			6.13108e6i			0.800901i
$568$		0			0
$569$			1.06981e7i			1.38524i	0.721304	+	0.692618i	$0.243543\pi$
$569$			1.06981e7i			1.38524i	−0.721304	+	0.692618i	$0.756457\pi$
$570$		0			0
$571$	−2.78779e6	−	2.78779e6i	−0.357824	−	0.357824i	0.505187	−	0.863010i	$-0.331424\pi$
$571$	−2.78779e6	−	2.78779e6i	−0.357824	−	0.357824i	−0.863010	+	0.505187i	$0.831424\pi$
$572$		0			0
$573$	−372321.	+	372321.i	−0.0473731	+	0.0473731i
$574$		0			0
$575$	317238.			0.0400144
$576$		0			0
$577$	1.25782e6			0.157282			0.0786412	−	0.996903i	$-0.474942\pi$
$577$	1.25782e6			0.157282			0.0786412	+	0.996903i	$0.474942\pi$
$578$		0			0
$579$	−2.12072e6	+	2.12072e6i	−0.262898	+	0.262898i
$580$		0			0
$581$	4.00945e6	+	4.00945e6i	0.492770	+	0.492770i
$582$		0			0
$583$		−	696108.i		−	0.0848214i
$584$		0			0
$585$			5.25245e6i			0.634559i
$586$		0			0
$587$	−1.10160e7	−	1.10160e7i	−1.31956	−	1.31956i	−0.914126	−	0.405430i	$-0.867122\pi$
$587$	−1.10160e7	−	1.10160e7i	−1.31956	−	1.31956i	−0.405430	−	0.914126i	$-0.632878\pi$
$588$		0			0
$589$	−4.55712e6	+	4.55712e6i	−0.541255	+	0.541255i
$590$		0			0
$591$	−3.11123e6			−0.366407
$592$		0			0
$593$	1.26173e7			1.47343			0.736713	−	0.676206i	$-0.236377\pi$
$593$	1.26173e7			1.47343			0.736713	+	0.676206i	$0.236377\pi$
$594$		0			0
$595$	−2.45667e6	+	2.45667e6i	−0.284482	+	0.284482i
$596$		0			0
$597$	−3.00565e6	−	3.00565e6i	−0.345146	−	0.345146i
$598$		0			0
$599$			1.05389e7i			1.20013i	0.799950	+	0.600067i	$0.204859\pi$
$599$			1.05389e7i			1.20013i	−0.799950	+	0.600067i	$0.795141\pi$
$600$		0			0
$601$			1.10876e7i			1.25214i	0.779769	+	0.626068i	$0.215337\pi$
$601$			1.10876e7i			1.25214i	−0.779769	+	0.626068i	$0.784663\pi$
$602$		0			0
$603$	7.92089e6	+	7.92089e6i	0.887117	+	0.887117i
$604$		0			0
$605$	2.79351e6	−	2.79351e6i	0.310286	−	0.310286i
$606$		0			0
$607$	−890974.			−0.0981506			−0.0490753	−	0.998795i	$-0.515627\pi$
$607$	−890974.			−0.0981506			−0.0490753	+	0.998795i	$0.515627\pi$
$608$		0			0
$609$	626688.			0.0684712
$610$		0			0
$611$	940204.	−	940204.i	0.101887	−	0.101887i
$612$		0			0
$613$	−8.88039e6	−	8.88039e6i	−0.954510	−	0.954510i	0.0444991	−	0.999009i	$-0.485831\pi$
$613$	−8.88039e6	−	8.88039e6i	−0.954510	−	0.954510i	−0.999009	+	0.0444991i	$0.985831\pi$
$614$		0			0
$615$		−	163534.i		−	0.0174349i
$616$		0			0
$617$			8.90147e6i			0.941345i	0.882308	+	0.470672i	$0.155989\pi$
$617$			8.90147e6i			0.941345i	−0.882308	+	0.470672i	$0.844011\pi$
$618$		0			0
$619$	−6.71588e6	−	6.71588e6i	−0.704493	−	0.704493i	0.260879	−	0.965372i	$-0.415988\pi$
$619$	−6.71588e6	−	6.71588e6i	−0.704493	−	0.704493i	−0.965372	+	0.260879i	$0.915988\pi$
$620$		0			0
$621$	−837089.	+	837089.i	−0.0871049	+	0.0871049i
$622$		0			0
$623$	−8.14394e6			−0.840648
$624$		0			0
$625$	−390625.			−0.0400000
$626$		0			0
$627$	250929.	−	250929.i	0.0254907	−	0.0254907i
$628$		0			0
$629$	9.61332e6	+	9.61332e6i	0.968828	+	0.968828i
$630$		0			0
$631$		−	5.38492e6i		−	0.538401i	−0.963084	−	0.269201i	$-0.913241\pi$
$631$		−	5.38492e6i		−	0.538401i	0.963084	−	0.269201i	$-0.0867595\pi$
$632$		0			0
$633$		−	2.89213e6i		−	0.286886i
$634$		0			0
$635$	1.84511e6	+	1.84511e6i	0.181589	+	0.181589i
$636$		0			0
$637$	−3.80107e6	+	3.80107e6i	−0.371157	+	0.371157i
$638$		0			0
$639$	9.80044e6			0.949496
$640$		0			0
$641$	−1.79300e7			−1.72359			−0.861796	−	0.507254i	$-0.830661\pi$
$641$	−1.79300e7			−1.72359			−0.861796	+	0.507254i	$0.830661\pi$
$642$		0			0
$643$	−2.14350e6	+	2.14350e6i	−0.204454	+	0.204454i	−0.801905	−	0.597451i	$-0.796180\pi$
$643$	−2.14350e6	+	2.14350e6i	−0.204454	+	0.204454i	0.597451	+	0.801905i	$0.296180\pi$
$644$		0			0
$645$	490774.	+	490774.i	0.0464496	+	0.0464496i
$646$		0			0
$647$			1.97136e7i			1.85143i	0.378227	+	0.925713i	$0.376534\pi$
$647$			1.97136e7i			1.85143i	−0.378227	+	0.925713i	$0.623466\pi$
$648$		0			0
$649$			2.51757e6i			0.234623i
$650$		0			0
$651$	2.71202e6	+	2.71202e6i	0.250807	+	0.250807i
$652$		0			0
$653$	1.07789e7	−	1.07789e7i	0.989216	−	0.989216i	−0.0107266	−	0.999942i	$-0.503414\pi$
$653$	1.07789e7	−	1.07789e7i	0.989216	−	0.989216i	0.999942	+	0.0107266i	$0.00341445\pi$
$654$		0			0
$655$	248177.			0.0226026
$656$		0			0
$657$	1.88062e7			1.69976
$658$		0			0
$659$	−2.31615e6	+	2.31615e6i	−0.207755	+	0.207755i	−0.803313	−	0.595557i	$-0.796931\pi$
$659$	−2.31615e6	+	2.31615e6i	−0.207755	+	0.207755i	0.595557	+	0.803313i	$0.296931\pi$
$660$		0			0
$661$	−5.60044e6	−	5.60044e6i	−0.498561	−	0.498561i	0.412429	−	0.910990i	$-0.364680\pi$
$661$	−5.60044e6	−	5.60044e6i	−0.498561	−	0.498561i	−0.910990	+	0.412429i	$0.864680\pi$
$662$		0			0
$663$		−	4.55120e6i		−	0.402107i
$664$		0			0
$665$			4.76066e6i			0.417458i
$666$		0			0
$667$	−296839.	−	296839.i	−0.0258349	−	0.0258349i
$668$		0			0
$669$	−2.76279e6	+	2.76279e6i	−0.238661	+	0.238661i
$670$		0			0
$671$	685252.			0.0587549
$672$		0			0
$673$	−6.07594e6			−0.517101			−0.258551	−	0.965998i	$-0.583245\pi$
$673$	−6.07594e6			−0.517101			−0.258551	+	0.965998i	$0.583245\pi$
$674$		0			0
$675$	1.03073e6	−	1.03073e6i	0.0870736	−	0.0870736i
$676$		0			0
$677$	−2.38722e6	−	2.38722e6i	−0.200180	−	0.200180i	0.599897	−	0.800077i	$-0.295208\pi$
$677$	−2.38722e6	−	2.38722e6i	−0.200180	−	0.200180i	−0.800077	+	0.599897i	$0.795208\pi$
$678$		0			0
$679$		−	1.65260e7i		−	1.37560i
$680$		0			0
$681$		−	4.67102e6i		−	0.385962i
$682$		0			0
$683$	7.61306e6	+	7.61306e6i	0.624464	+	0.624464i	0.946670	−	0.322206i	$-0.104424\pi$
$683$	7.61306e6	+	7.61306e6i	0.624464	+	0.624464i	−0.322206	+	0.946670i	$0.604424\pi$
$684$		0			0
$685$	−1.41645e6	+	1.41645e6i	−0.115339	+	0.115339i
$686$		0			0
$687$	−1.22012e6			−0.0986305
$688$		0			0
$689$	−1.22333e7			−0.981734
$690$		0			0
$691$	−1.08249e7	+	1.08249e7i	−0.862439	+	0.862439i	−0.991621	−	0.129182i	$-0.958765\pi$
$691$	−1.08249e7	+	1.08249e7i	−0.862439	+	0.862439i	0.129182	+	0.991621i	$0.458765\pi$
$692$		0			0
$693$	1.26430e6	+	1.26430e6i	0.100004	+	0.100004i
$694$		0			0
$695$		−	4.30958e6i		−	0.338433i
$696$		0			0
$697$		−	1.19969e6i		−	0.0935380i
$698$		0			0
$699$	−4.57315e6	−	4.57315e6i	−0.354016	−	0.354016i
$700$		0			0
$701$	2.39524e6	−	2.39524e6i	0.184100	−	0.184100i	−0.609039	−	0.793140i	$-0.708445\pi$
$701$	2.39524e6	−	2.39524e6i	0.184100	−	0.184100i	0.793140	+	0.609039i	$0.208445\pi$
$702$		0			0
$703$	1.86292e7			1.42169
$704$		0			0
$705$	−174215.			−0.0132012
$706$		0			0
$707$	2.42930e6	−	2.42930e6i	0.182782	−	0.182782i
$708$		0			0
$709$	9.09930e6	+	9.09930e6i	0.679817	+	0.679817i	0.959959	−	0.280141i	$-0.0903814\pi$
$709$	9.09930e6	+	9.09930e6i	0.679817	+	0.679817i	−0.280141	+	0.959959i	$0.590381\pi$
$710$		0			0
$711$			1.20637e7i			0.894966i
$712$		0			0
$713$		−	2.56917e6i		−	0.189264i
$714$		0			0
$715$	940077.	+	940077.i	0.0687699	+	0.0687699i
$716$		0			0
$717$	−5.04477e6	+	5.04477e6i	−0.366474	+	0.366474i
$718$		0			0
$719$	6.42870e6			0.463768			0.231884	−	0.972743i	$-0.425511\pi$
$719$	6.42870e6			0.463768			0.231884	+	0.972743i	$0.425511\pi$
$720$		0			0
$721$	−2.84682e7			−2.03949
$722$		0			0
$723$	3.21644e6	−	3.21644e6i	0.228839	−	0.228839i
$724$		0			0
$725$	365507.	+	365507.i	0.0258256	+	0.0258256i
$726$		0			0
$727$			2.68443e7i			1.88372i	0.336006	+	0.941860i	$0.390924\pi$
$727$			2.68443e7i			1.88372i	−0.336006	+	0.941860i	$0.609076\pi$
$728$		0			0
$729$		−	6.03795e6i		−	0.420795i
$730$		0			0
$731$	3.60034e6	+	3.60034e6i	0.249201	+	0.249201i
$732$		0			0
$733$	−1.49935e7	+	1.49935e7i	−1.03072	+	1.03072i	−0.0312110	+	0.999513i	$0.509936\pi$
$733$	−1.49935e7	+	1.49935e7i	−1.03072	+	1.03072i	−0.999513	+	0.0312110i	$0.990064\pi$
$734$		0			0
$735$	704321.			0.0480897
$736$		0			0
$737$	2.83534e6			0.192281
$738$		0			0
$739$	−7.73938e6	+	7.73938e6i	−0.521309	+	0.521309i	−0.917967	−	0.396658i	$-0.870170\pi$
$739$	−7.73938e6	+	7.73938e6i	−0.521309	+	0.521309i	0.396658	+	0.917967i	$0.370170\pi$
$740$		0			0
$741$	−4.40977e6	−	4.40977e6i	−0.295033	−	0.295033i
$742$		0			0
$743$		−	4.27335e6i		−	0.283986i	−0.989868	−	0.141993i	$-0.954649\pi$
$743$		−	4.27335e6i		−	0.283986i	0.989868	−	0.141993i	$-0.0453510\pi$
$744$		0			0
$745$		−	1.27238e7i		−	0.839899i
$746$		0			0
$747$	−5.82634e6	−	5.82634e6i	−0.382027	−	0.382027i
$748$		0			0
$749$	−2.22159e7	+	2.22159e7i	−1.44697	+	1.44697i
$750$		0			0
$751$	−1.71751e7			−1.11122			−0.555609	−	0.831444i	$-0.687515\pi$
$751$	−1.71751e7			−1.11122			−0.555609	+	0.831444i	$0.687515\pi$
$752$		0			0
$753$	6.08255e6			0.390929
$754$		0			0
$755$	−6.28035e6	+	6.28035e6i	−0.400974	+	0.400974i
$756$		0			0
$757$	−5.21393e6	−	5.21393e6i	−0.330694	−	0.330694i	0.522156	−	0.852850i	$-0.325128\pi$
$757$	−5.21393e6	−	5.21393e6i	−0.330694	−	0.330694i	−0.852850	+	0.522156i	$0.825128\pi$
$758$		0			0
$759$			141466.i			0.00891352i
$760$		0			0
$761$		−	1.79653e7i		−	1.12454i	−0.826955	−	0.562268i	$-0.809929\pi$
$761$		−	1.79653e7i		−	1.12454i	0.826955	−	0.562268i	$-0.190071\pi$
$762$		0			0
$763$	−1.45955e7	−	1.45955e7i	−0.907629	−	0.907629i
$764$		0			0
$765$	3.56992e6	−	3.56992e6i	0.220549	−	0.220549i
$766$		0			0
$767$	4.42433e7			2.71556
$768$		0			0
$769$	2.43375e7			1.48409			0.742045	−	0.670350i	$-0.233856\pi$
$769$	2.43375e7			1.48409			0.742045	+	0.670350i	$0.233856\pi$
$770$		0			0
$771$	−1.32170e6	+	1.32170e6i	−0.0800751	+	0.0800751i
$772$		0			0
$773$	9.33938e6	+	9.33938e6i	0.562172	+	0.562172i	0.929924	−	0.367752i	$-0.119872\pi$
$773$	9.33938e6	+	9.33938e6i	0.562172	+	0.562172i	−0.367752	+	0.929924i	$0.619872\pi$
$774$		0			0
$775$			3.16350e6i			0.189196i
$776$		0			0
$777$		−	1.10865e7i		−	0.658784i
$778$		0			0
$779$	−1.16241e6	−	1.16241e6i	−0.0686304	−	0.0686304i
$780$		0			0
$781$	1.75407e6	−	1.75407e6i	0.102901	−	0.102901i
$782$		0			0
$783$	−1.92891e6			−0.112436
$784$		0			0
$785$	−8.41075e6			−0.487148
$786$		0			0
$787$	6.36001e6	−	6.36001e6i	0.366034	−	0.366034i	−0.499995	−	0.866028i	$-0.666665\pi$
$787$	6.36001e6	−	6.36001e6i	0.366034	−	0.366034i	0.866028	+	0.499995i	$0.166665\pi$
$788$		0			0
$789$	876283.	+	876283.i	0.0501131	+	0.0501131i
$790$		0			0
$791$		−	2.27686e7i		−	1.29388i
$792$		0			0
$793$		−	1.20425e7i		−	0.680037i
$794$		0			0
$795$	1.13338e6	+	1.13338e6i	0.0636002	+	0.0636002i
$796$		0			0
$797$	−1.59113e7	+	1.59113e7i	−0.887279	+	0.887279i	−0.994261	−	0.106982i	$-0.965881\pi$
$797$	−1.59113e7	+	1.59113e7i	−0.887279	+	0.887279i	0.106982	+	0.994261i	$0.465881\pi$
$798$		0			0
$799$	−1.27805e6			−0.0708241
$800$		0			0
$801$	1.18344e7			0.651724
$802$		0			0
$803$	3.36591e6	−	3.36591e6i	0.184210	−	0.184210i
$804$		0			0
$805$	−1.34196e6	−	1.34196e6i	−0.0729878	−	0.0729878i
$806$		0			0
$807$		−	4.04997e6i		−	0.218911i
$808$		0			0
$809$		−	2.74820e7i		−	1.47631i	−0.674633	−	0.738153i	$-0.735698\pi$
$809$		−	2.74820e7i		−	1.47631i	0.674633	−	0.738153i	$-0.264302\pi$
$810$		0			0
$811$	1.77957e7	+	1.77957e7i	0.950085	+	0.950085i	0.998812	−	0.0487272i	$-0.0155165\pi$
$811$	1.77957e7	+	1.77957e7i	0.950085	+	0.950085i	−0.0487272	+	0.998812i	$0.515516\pi$
$812$		0			0
$813$	4.40570e6	−	4.40570e6i	0.233770	−	0.233770i
$814$		0			0
$815$	−277267.			−0.0146219
$816$		0			0
$817$	6.97691e6			0.365686
$818$		0			0
$819$	2.22186e7	−	2.22186e7i	1.15746	−	1.15746i
$820$		0			0
$821$	1.57469e7	+	1.57469e7i	0.815336	+	0.815336i	0.985428	−	0.170092i	$-0.0544065\pi$
$821$	1.57469e7	+	1.57469e7i	0.815336	+	0.815336i	−0.170092	+	0.985428i	$0.554406\pi$
$822$		0			0
$823$			3.68026e7i			1.89400i	0.321237	+	0.946999i	$0.395902\pi$
$823$			3.68026e7i			1.89400i	−0.321237	+	0.946999i	$0.604098\pi$
$824$		0			0
$825$		−	174192.i		−	0.00891031i
$826$		0			0
$827$	−9.65869e6	−	9.65869e6i	−0.491083	−	0.491083i	0.417565	−	0.908647i	$-0.362884\pi$
$827$	−9.65869e6	−	9.65869e6i	−0.491083	−	0.491083i	−0.908647	+	0.417565i	$0.862884\pi$
$828$		0			0
$829$	3.10341e6	−	3.10341e6i	0.156838	−	0.156838i	−0.624326	−	0.781164i	$-0.714626\pi$
$829$	3.10341e6	−	3.10341e6i	0.156838	−	0.156838i	0.781164	+	0.624326i	$0.214626\pi$
$830$		0			0
$831$	9.79904e6			0.492245
$832$		0			0
$833$	5.16692e6			0.258000
$834$		0			0
$835$	3.92200e6	−	3.92200e6i	0.194667	−	0.194667i
$836$		0			0
$837$	−8.34743e6	−	8.34743e6i	−0.411850	−	0.411850i
$838$		0			0
$839$			6.43004e6i			0.315362i	0.987490	+	0.157681i	$0.0504017\pi$
$839$			6.43004e6i			0.315362i	−0.987490	+	0.157681i	$0.949598\pi$
$840$		0			0
$841$			1.98271e7i			0.966652i
$842$		0			0
$843$	−3.24347e6	−	3.24347e6i	−0.157196	−	0.157196i
$844$		0			0
$845$	9.95710e6	−	9.95710e6i	0.479724	−	0.479724i
$846$		0			0
$847$	−2.36339e7			−1.13195
$848$		0			0
$849$	1.24521e7			0.592888
$850$		0			0
$851$	−5.25129e6	+	5.25129e6i	−0.248566	+	0.248566i
$852$		0			0
$853$	1.04384e6	+	1.04384e6i	0.0491203	+	0.0491203i	0.731240	−	0.682120i	$-0.238942\pi$
$853$	1.04384e6	+	1.04384e6i	0.0491203	+	0.0491203i	−0.682120	+	0.731240i	$0.738942\pi$
$854$		0			0
$855$		−	6.91796e6i		−	0.323640i
$856$		0			0
$857$		−	3.37311e7i		−	1.56884i	−0.620230	−	0.784420i	$-0.712961\pi$
$857$		−	3.37311e7i		−	1.56884i	0.620230	−	0.784420i	$-0.287039\pi$
$858$		0			0
$859$	−2.22076e7	−	2.22076e7i	−1.02688	−	1.02688i	−0.999629	−	0.0272513i	$-0.991325\pi$
$859$	−2.22076e7	−	2.22076e7i	−1.02688	−	1.02688i	−0.0272513	−	0.999629i	$-0.508675\pi$
$860$		0			0
$861$	−691771.	+	691771.i	−0.0318020	+	0.0318020i
$862$		0			0
$863$	7.38131e6			0.337370			0.168685	−	0.985670i	$-0.446048\pi$
$863$	7.38131e6			0.337370			0.168685	+	0.985670i	$0.446048\pi$
$864$		0			0
$865$	−1.43901e7			−0.653919
$866$		0			0
$867$	1.99345e6	−	1.99345e6i	0.0900655	−	0.0900655i
$868$		0			0
$869$	2.15915e6	+	2.15915e6i	0.0969913	+	0.0969913i
$870$		0			0
$871$		−	4.98277e7i		−	2.22549i
$872$		0			0
$873$			2.40147e7i			1.06645i
$874$		0			0
$875$	1.65240e6	+	1.65240e6i	0.0729616	+	0.0729616i
$876$		0			0
$877$	1.79841e6	−	1.79841e6i	0.0789568	−	0.0789568i	−0.666525	−	0.745482i	$-0.732219\pi$
$877$	1.79841e6	−	1.79841e6i	0.0789568	−	0.0789568i	0.745482	+	0.666525i	$0.232219\pi$
$878$		0			0
$879$	−7.40208e6			−0.323133
$880$		0			0
$881$	1.22025e7			0.529673			0.264836	−	0.964293i	$-0.414682\pi$
$881$	1.22025e7			0.529673			0.264836	+	0.964293i	$0.414682\pi$
$882$		0			0
$883$	−6.92584e6	+	6.92584e6i	−0.298931	+	0.298931i	−0.840595	−	0.541664i	$-0.817794\pi$
$883$	−6.92584e6	+	6.92584e6i	−0.298931	+	0.298931i	0.541664	+	0.840595i	$0.317794\pi$
$884$		0			0
$885$	−4.09903e6	−	4.09903e6i	−0.175923	−	0.175923i
$886$		0			0
$887$		−	1.12492e7i		−	0.480077i	−0.970763	−	0.240039i	$-0.922840\pi$
$887$		−	1.12492e7i		−	0.480077i	0.970763	−	0.240039i	$-0.0771601\pi$
$888$		0			0
$889$		−	1.56102e7i		−	0.662450i
$890$		0			0
$891$	−1.59459e6	−	1.59459e6i	−0.0672906	−	0.0672906i
$892$		0			0
$893$	−1.23834e6	+	1.23834e6i	−0.0519648	+	0.0519648i
$894$		0			0
$895$	3.86776e6			0.161399
$896$		0			0
$897$	2.48610e6			0.103166
$898$		0			0
$899$	2.96007e6	−	2.96007e6i	0.122153	−	0.122153i
$900$		0			0
$901$	8.31454e6	+	8.31454e6i	0.341213	+	0.341213i
$902$		0			0
$903$		−	4.15208e6i		−	0.169452i
$904$		0			0
$905$			4.32182e6i			0.175406i
$906$		0			0
$907$	−2.74626e7	−	2.74626e7i	−1.10847	−	1.10847i	−0.993352	−	0.115118i	$-0.963276\pi$
$907$	−2.74626e7	−	2.74626e7i	−1.10847	−	1.10847i	−0.115118	−	0.993352i	$-0.536724\pi$
$908$		0			0
$909$	−3.53014e6	+	3.53014e6i	−0.141704	+	0.141704i
$910$		0			0
$911$	2.65106e7			1.05834			0.529168	−	0.848517i	$-0.322504\pi$
$911$	2.65106e7			1.05834			0.529168	+	0.848517i	$0.322504\pi$
$912$		0			0
$913$	−2.08558e6			−0.0828038
$914$		0			0
$915$	−1.11571e6	+	1.11571e6i	−0.0440552	+	0.0440552i
$916$		0			0
$917$	−1.04982e6	−	1.04982e6i	−0.0412280	−	0.0412280i
$918$		0			0
$919$			1.72867e7i			0.675186i	0.941292	+	0.337593i	$0.109613\pi$
$919$			1.72867e7i			0.675186i	−0.941292	+	0.337593i	$0.890387\pi$
$920$		0			0
$921$			3.10591e6i			0.120654i
$922$		0			0
$923$	−3.08256e7	−	3.08256e7i	−1.19099	−	1.19099i
$924$		0			0
$925$	6.46607e6	−	6.46607e6i	0.248477	−	0.248477i
$926$		0			0
$927$	4.13686e7			1.58114
$928$		0			0
$929$	3.27082e7			1.24342			0.621709	−	0.783248i	$-0.286438\pi$
$929$	3.27082e7			1.24342			0.621709	+	0.783248i	$0.286438\pi$
$930$		0			0
$931$	5.00636e6	−	5.00636e6i	0.189299	−	0.189299i
$932$		0			0
$933$	8.39349e6	+	8.39349e6i	0.315674	+	0.315674i
$934$		0			0
$935$		−	1.27788e6i		−	0.0478036i
$936$		0			0
$937$		−	3.76305e7i		−	1.40020i	−0.714044	−	0.700101i	$-0.753138\pi$
$937$		−	3.76305e7i		−	1.40020i	0.714044	−	0.700101i	$-0.246862\pi$
$938$		0			0
$939$	2.48261e6	+	2.48261e6i	0.0918851	+	0.0918851i
$940$		0			0
$941$	3.52025e7	−	3.52025e7i	1.29598	−	1.29598i	0.364959	−	0.931024i	$-0.381083\pi$
$941$	3.52025e7	−	3.52025e7i	1.29598	−	1.29598i	0.931024	−	0.364959i	$-0.118917\pi$
$942$		0			0
$943$	655334.			0.0239985
$944$		0			0
$945$	−8.72027e6			−0.317651
$946$		0			0
$947$	−2.86727e7	+	2.86727e7i	−1.03895	+	1.03895i	−0.0397356	+	0.999210i	$0.512652\pi$
$947$	−2.86727e7	+	2.86727e7i	−1.03895	+	1.03895i	−0.999210	+	0.0397356i	$0.987348\pi$
$948$		0			0
$949$	−5.91517e7	−	5.91517e7i	−2.13207	−	2.13207i
$950$		0			0
$951$		−	1.43797e7i		−	0.515583i
$952$		0			0
$953$		−	1.94903e7i		−	0.695161i	−0.937650	−	0.347581i	$-0.887003\pi$
$953$		−	1.94903e7i		−	0.695161i	0.937650	−	0.347581i	$-0.112997\pi$
$954$		0			0
$955$	1.83716e6	+	1.83716e6i	0.0651836	+	0.0651836i
$956$		0			0
$957$	−162991.	+	162991.i	−0.00575285	+	0.00575285i
$958$		0			0
$959$	1.19836e7			0.420764
$960$		0			0
$961$	−3.00943e6			−0.105118
$962$		0			0
$963$	3.22830e7	−	3.22830e7i	1.12178	−	1.12178i
$964$		0			0
$965$	1.04643e7	+	1.04643e7i	0.361738	+	0.361738i
$966$		0			0
$967$			2.28442e7i			0.785616i	0.919621	+	0.392808i	$0.128496\pi$
$967$			2.28442e7i			0.785616i	−0.919621	+	0.392808i	$0.871504\pi$
$968$		0			0
$969$			5.99435e6i			0.205084i
$970$		0			0
$971$	2.76612e7	+	2.76612e7i	0.941506	+	0.941506i	0.998381	−	0.0568757i	$-0.0181139\pi$
$971$	2.76612e7	+	2.76612e7i	0.941506	+	0.941506i	−0.0568757	+	0.998381i	$0.518114\pi$
$972$		0			0
$973$	−1.82301e7	+	1.82301e7i	−0.617315	+	0.617315i
$974$		0			0
$975$	−3.06121e6			−0.103129
$976$		0			0
$977$	3.48396e7			1.16771			0.583857	−	0.811856i	$-0.301543\pi$
$977$	3.48396e7			1.16771			0.583857	+	0.811856i	$0.301543\pi$
$978$		0			0
$979$	2.11810e6	−	2.11810e6i	0.0706301	−	0.0706301i
$980$		0			0
$981$	2.12095e7	+	2.12095e7i	0.703652	+	0.703652i
$982$		0			0
$983$			7.78926e6i			0.257106i	0.991703	+	0.128553i	$0.0410333\pi$
$983$			7.78926e6i			0.257106i	−0.991703	+	0.128553i	$0.958967\pi$
$984$		0			0
$985$			1.53519e7i			0.504163i
$986$		0			0
$987$	736955.	+	736955.i	0.0240795	+	0.0240795i
$988$		0			0
$989$	−1.96669e6	+	1.96669e6i	−0.0639359	+	0.0639359i
$990$		0			0
$991$	−2.76782e7			−0.895268			−0.447634	−	0.894217i	$-0.647733\pi$
$991$	−2.76782e7			−0.895268			−0.447634	+	0.894217i	$0.647733\pi$
$992$		0			0
$993$	−1.33094e7			−0.428337
$994$		0			0
$995$	−1.48309e7	+	1.48309e7i	−0.474908	+	0.474908i
$996$		0			0
$997$	7.78540e6	+	7.78540e6i	0.248052	+	0.248052i	0.820171	−	0.572119i	$-0.193878\pi$
$997$	7.78540e6	+	7.78540e6i	0.248052	+	0.248052i	−0.572119	+	0.820171i	$0.693878\pi$
$998$		0			0
$999$			3.41237e7i			1.08179i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.6.l.a.241.18		80
4.3	odd	2		80.6.l.a.21.40	✓	80
16.3	odd	4		80.6.l.a.61.40	yes	80
16.13	even	4	inner	320.6.l.a.81.18		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.40	✓	80	4.3	odd	2
80.6.l.a.61.40	yes	80	16.3	odd	4
320.6.l.a.81.18		80	16.13	even	4	inner
320.6.l.a.241.18		80	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-3.58258 + 3.58258i) q^{3} +(17.6777 + 17.6777i) q^{5} -149.558i q^{7} +217.330i q^{9} +O(q^{10})\)	\(q+(-3.58258 + 3.58258i) q^{3} +(17.6777 + 17.6777i) q^{5} -149.558i q^{7} +217.330i q^{9} +(38.8975 + 38.8975i) q^{11} +(683.576 - 683.576i) q^{13} -126.663 q^{15} -929.208 q^{17} +(-900.333 + 900.333i) q^{19} +(535.804 + 535.804i) q^{21} -507.581i q^{23} +625.000i q^{25} +(-1649.17 - 1649.17i) q^{27} +(584.811 - 584.811i) q^{29} +5061.59 q^{31} -278.707 q^{33} +(2643.84 - 2643.84i) q^{35} +(-10345.7 - 10345.7i) q^{37} +4897.93i q^{39} +1291.09i q^{41} +(-3874.63 - 3874.63i) q^{43} +(-3841.89 + 3841.89i) q^{45} +1375.42 q^{47} -5560.57 q^{49} +(3328.96 - 3328.96i) q^{51} +(-8947.98 - 8947.98i) q^{53} +1375.23i q^{55} -6451.03i q^{57} +(32361.6 + 32361.6i) q^{59} +(8808.44 - 8808.44i) q^{61} +32503.5 q^{63} +24168.1 q^{65} +(36446.3 - 36446.3i) q^{67} +(1818.45 + 1818.45i) q^{69} -45094.7i q^{71} -86532.8i q^{73} +(-2239.11 - 2239.11i) q^{75} +(5817.43 - 5817.43i) q^{77} +55508.6 q^{79} -40994.7 q^{81} +(-26808.7 + 26808.7i) q^{83} +(-16426.2 - 16426.2i) q^{85} +4190.27i q^{87} -54453.4i q^{89} +(-102234. - 102234. i) q^{91} +(-18133.6 + 18133.6i) q^{93} -31831.6 q^{95} +110499. q^{97} +(-8453.60 + 8453.60i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q+O(q^{10}) \) 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

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Representations

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Database

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