LMFDB - Embedded newform 320.6.l.a.81.18

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			81.18
Character	$\chi$	$=$	320.81
Dual form			320.6.l.a.241.18

$q$-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 $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−3.58258	−	3.58258i	−0.229823	−	0.229823i	0.582796	−	0.812619i	$-0.301959\pi$
$3$	−3.58258	−	3.58258i	−0.229823	−	0.229823i	−0.812619	+	0.582796i	$0.801959\pi$
$4$		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	$0.195703\pi$
$7$			149.558i			1.15362i	−0.816877	+	0.576812i	$0.804297\pi$
$8$		0			0
$9$		−	217.330i		−	0.894363i
$10$		0			0
$11$	38.8975	−	38.8975i	0.0969259	−	0.0969259i	−0.656981	−	0.753907i	$-0.728167\pi$
$11$	38.8975	−	38.8975i	0.0969259	−	0.0969259i	0.753907	+	0.656981i	$0.228167\pi$
$12$		0			0
$13$	683.576	+	683.576i	1.12183	+	1.12183i	0.991466	+	0.130368i	$0.0416157\pi$
$13$	683.576	+	683.576i	1.12183	+	1.12183i	0.130368	+	0.991466i	$0.458384\pi$
$14$		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	0.360570	−	0.932732i	$-0.382582\pi$
$19$	−900.333	−	900.333i	−0.572162	−	0.572162i	−0.932732	+	0.360570i	$0.882582\pi$
$20$		0			0
$21$	535.804	−	535.804i	0.265129	−	0.265129i
$22$		0			0
$23$			507.581i			0.200072i	0.994984	+	0.100036i	$0.0318958\pi$
$23$			507.581i			0.200072i	−0.994984	+	0.100036i	$0.968104\pi$
$24$		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	0.768717	−	0.639589i	$-0.220895\pi$
$29$	584.811	+	584.811i	0.129128	+	0.129128i	−0.639589	+	0.768717i	$0.720895\pi$
$30$		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	−0.283375	+	0.959009i	$0.591454\pi$
$37$	−10345.7	+	10345.7i	−1.24238	+	1.24238i	−0.959009	+	0.283375i	$0.908546\pi$
$38$		0			0
$39$		−	4897.93i		−	0.515646i
$40$		0			0
$41$		−	1291.09i		−	0.119949i	−0.998200	−	0.0599746i	$-0.980898\pi$
$41$		−	1291.09i		−	0.119949i	0.998200	−	0.0599746i	$-0.0191020\pi$
$42$		0			0
$43$	−3874.63	+	3874.63i	−0.319565	+	0.319565i	−0.848600	−	0.529035i	$-0.822554\pi$
$43$	−3874.63	+	3874.63i	−0.319565	+	0.319565i	0.529035	+	0.848600i	$0.322554\pi$
$44$		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	−0.891189	−	0.453631i	$-0.850128\pi$
$53$	−8947.98	+	8947.98i	−0.437558	+	0.437558i	0.453631	+	0.891189i	$0.350128\pi$
$54$		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	0.239399	−	0.970921i	$-0.423050\pi$
$59$	32361.6	−	32361.6i	1.21032	−	1.21032i	0.970921	−	0.239399i	$-0.0769504\pi$
$60$		0			0
$61$	8808.44	+	8808.44i	0.303092	+	0.303092i	0.842222	−	0.539130i	$-0.181247\pi$
$61$	8808.44	+	8808.44i	0.303092	+	0.303092i	−0.539130	+	0.842222i	$0.681247\pi$
$62$		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	0.999967	−	0.00806945i	$-0.00256861\pi$
$67$	36446.3	+	36446.3i	0.991898	+	0.991898i	−0.00806945	+	0.999967i	$0.502569\pi$
$68$		0			0
$69$	1818.45	−	1818.45i	0.0459811	−	0.0459811i
$70$		0			0
$71$			45094.7i			1.06165i	0.847483	+	0.530823i	$0.178117\pi$
$71$			45094.7i			1.06165i	−0.847483	+	0.530823i	$0.821883\pi$
$72$		0			0
$73$			86532.8i			1.90053i	0.311450	+	0.950263i	$0.399186\pi$
$73$			86532.8i			1.90053i	−0.311450	+	0.950263i	$0.600814\pi$
$74$		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	0.460506	−	0.887656i	$-0.347668\pi$
$83$	−26808.7	−	26808.7i	−0.427150	−	0.427150i	−0.887656	+	0.460506i	$0.847668\pi$
$84$		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	$0.118709\pi$
$89$			54453.4i			0.728702i	−0.931262	+	0.364351i	$0.881291\pi$
$90$		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	−0.623434	−	0.781876i	$-0.714263\pi$
$101$	16243.2	−	16243.2i	0.158442	−	0.158442i	0.781876	+	0.623434i	$0.214263\pi$
$102$		0			0
$103$			190349.i			1.76790i	0.467582	+	0.883949i	$0.345125\pi$
$103$			190349.i			1.76790i	−0.467582	+	0.883949i	$0.654875\pi$
$104$		0			0
$105$		−	18943.5i		−	0.167682i
$106$		0			0
$107$	−148544.	+	148544.i	−1.25428	+	1.25428i	−0.300497	+	0.953783i	$0.597153\pi$
$107$	−148544.	+	148544.i	−1.25428	+	1.25428i	−0.953783	+	0.300497i	$0.902847\pi$
$108$		0			0
$109$	97591.1	+	97591.1i	0.786763	+	0.786763i	0.980962	−	0.194199i	$-0.0622107\pi$
$109$	97591.1	+	97591.1i	0.786763	+	0.786763i	−0.194199	+	0.980962i	$0.562211\pi$
$110$		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	0.724750	−	0.689012i	$-0.241955\pi$
$131$	7019.50	+	7019.50i	0.0357378	+	0.0357378i	−0.689012	+	0.724750i	$0.741955\pi$
$132$		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	$-0.941624\pi$
$137$		−	80126.5i		−	0.364733i	0.983231	−	0.182366i	$-0.0583757\pi$
$138$		0			0
$139$	−121893.	+	121893.i	−0.535110	+	0.535110i	−0.922089	−	0.386979i	$-0.873519\pi$
$139$	−121893.	+	121893.i	−0.535110	+	0.535110i	0.386979	+	0.922089i	$0.373519\pi$
$140$		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	−0.420880	+	0.907116i	$0.638279\pi$
$149$	−359884.	+	359884.i	−1.32800	+	1.32800i	−0.907116	+	0.420880i	$0.861721\pi$
$150$		0			0
$151$		−	355270.i		−	1.26799i	−0.773336	−	0.633996i	$-0.781414\pi$
$151$		−	355270.i		−	1.26799i	0.773336	−	0.633996i	$-0.218586\pi$
$152$		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	0.207901	−	0.978150i	$-0.433337\pi$
$157$	−237892.	−	237892.i	−0.770248	−	0.770248i	−0.978150	+	0.207901i	$0.933337\pi$
$158$		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	0.695453	−	0.718572i	$-0.255204\pi$
$163$	−7842.29	−	7842.29i	−0.0231193	−	0.0231193i	−0.718572	+	0.695453i	$0.755204\pi$
$164$		0			0
$165$	−4926.89	+	4926.89i	−0.0140884	+	0.0140884i
$166$		0			0
$167$			221862.i			0.615590i	0.951453	+	0.307795i	$0.0995910\pi$
$167$			221862.i			0.615590i	−0.951453	+	0.307795i	$0.900409\pi$
$168$		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	−0.999404	−	0.0345330i	$-0.989006\pi$
$173$	−407014.	−	407014.i	−1.03394	−	1.03394i	−0.0345330	−	0.999404i	$-0.510994\pi$
$174$		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	0.823096	−	0.567902i	$-0.192245\pi$
$179$	109397.	+	109397.i	0.255195	+	0.255195i	−0.567902	+	0.823096i	$0.692245\pi$
$180$		0			0
$181$	122240.	−	122240.i	0.277342	−	0.277342i	−0.554705	−	0.832047i	$-0.687169\pi$
$181$	122240.	−	122240.i	0.277342	−	0.277342i	0.832047	+	0.554705i	$0.187169\pi$
$182$		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	−0.185494	−	0.982645i	$-0.559389\pi$
$197$	434216.	−	434216.i	0.797151	−	0.797151i	0.982645	+	0.185494i	$0.0593886\pi$
$198$		0			0
$199$		−	838962.i		−	1.50179i	−0.660421	−	0.750895i	$-0.729622\pi$
$199$		−	838962.i		−	1.50179i	0.660421	−	0.750895i	$-0.270378\pi$
$200$		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	0.322443	−	0.946589i	$-0.395496\pi$
$211$	−403638.	−	403638.i	−0.624145	−	0.624145i	−0.946589	+	0.322443i	$0.895496\pi$
$212$		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	0.149125	−	0.988818i	$-0.452354\pi$
$227$	−651907.	−	651907.i	−0.839694	−	0.839694i	−0.988818	+	0.149125i	$0.952354\pi$
$228$		0			0
$229$	170285.	−	170285.i	0.214579	−	0.214579i	−0.591630	−	0.806210i	$-0.701515\pi$
$229$	170285.	−	170285.i	0.214579	−	0.214579i	0.806210	+	0.591630i	$0.201515\pi$
$230$		0			0
$231$		−	41682.8i		−	0.0513957i
$232$		0			0
$233$		−	1.27649e6i		−	1.54038i	−0.637812	−	0.770192i	$-0.720160\pi$
$233$		−	1.27649e6i		−	1.54038i	0.637812	−	0.770192i	$-0.279840\pi$
$234$		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	−0.990195	−	0.139694i	$-0.955388\pi$
$251$	−848905.	+	848905.i	−0.850501	+	0.850501i	0.139694	+	0.990195i	$0.455388\pi$
$252$		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	$0.0347731\pi$
$263$			244595.i			0.218051i	−0.994039	+	0.109026i	$0.965227\pi$
$264$		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	0.427673	−	0.903934i	$-0.359334\pi$
$269$	−565231.	−	565231.i	−0.476261	−	0.476261i	−0.903934	+	0.427673i	$0.859334\pi$
$270$		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	−0.0736368	+	0.997285i	$0.523461\pi$
$277$	−1.36759e6	+	1.36759e6i	−1.07092	+	1.07092i	−0.997285	+	0.0736368i	$0.976539\pi$
$278$		0			0
$279$		−	1.10004e6i		−	0.846051i
$280$		0			0
$281$		−	905343.i		−	0.683986i	−0.939702	−	0.341993i	$-0.888898\pi$
$281$		−	905343.i		−	0.683986i	0.939702	−	0.341993i	$-0.111102\pi$
$282$		0			0
$283$	−1.73786e6	+	1.73786e6i	−1.28988	+	1.28988i	−0.355024	+	0.934857i	$0.615527\pi$
$283$	−1.73786e6	+	1.73786e6i	−1.28988	+	1.28988i	−0.934857	+	0.355024i	$0.884473\pi$
$284$		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	−0.262050	−	0.965054i	$-0.584398\pi$
$293$	1.03306e6	−	1.03306e6i	0.703005	−	0.703005i	0.965054	+	0.262050i	$0.0843984\pi$
$294$		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	0.826066	−	0.563573i	$-0.190574\pi$
$307$	433474.	+	433474.i	0.262493	+	0.262493i	−0.563573	+	0.826066i	$0.690574\pi$
$308$		0			0
$309$	681941.	−	681941.i	0.406303	−	0.406303i
$310$		0			0
$311$			2.34286e6i			1.37355i	0.726868	+	0.686777i	$0.240975\pi$
$311$			2.34286e6i			1.37355i	−0.726868	+	0.686777i	$0.759025\pi$
$312$		0			0
$313$			692967.i			0.399808i	0.979815	+	0.199904i	$0.0640631\pi$
$313$			692967.i			0.399808i	−0.979815	+	0.199904i	$0.935937\pi$
$314$		0			0
$315$	574585.	−	574585.i	0.326271	−	0.326271i
$316$		0			0
$317$	−2.00689e6	−	2.00689e6i	−1.12170	−	1.12170i	−0.991486	−	0.130211i	$-0.958434\pi$
$317$	−2.00689e6	−	2.00689e6i	−1.12170	−	1.12170i	−0.130211	−	0.991486i	$-0.541566\pi$
$318$		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	−0.0659391	−	0.997824i	$-0.521004\pi$
$331$	1.85751e6	−	1.85751e6i	0.931885	−	0.931885i	0.997824	+	0.0659391i	$0.0210043\pi$
$332$		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	−0.695663	−	0.718369i	$-0.744889\pi$
$347$	50929.3	−	50929.3i	0.0227062	−	0.0227062i	0.718369	+	0.695663i	$0.244889\pi$
$348$		0			0
$349$	1.60405e6	+	1.60405e6i	0.704944	+	0.704944i	0.965467	−	0.260524i	$-0.0838952\pi$
$349$	1.60405e6	+	1.60405e6i	0.704944	+	0.704944i	−0.260524	+	0.965467i	$0.583895\pi$
$350$		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	$0.233185\pi$
$359$			3.26627e6i			1.33757i	−0.743457	+	0.668784i	$0.766815\pi$
$360$		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	−0.477829	−	0.878453i	$-0.658576\pi$
$373$	1.07649e6	−	1.07649e6i	0.400624	−	0.400624i	0.878453	+	0.477829i	$0.158576\pi$
$374$		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	−0.872943	−	0.487821i	$-0.837792\pi$
$379$	−1.07695e6	+	1.07695e6i	−0.385122	+	0.385122i	0.487821	+	0.872943i	$0.337792\pi$
$380$		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	−0.924044	−	0.382285i	$-0.875137\pi$
$389$	−1.61689e6	+	1.61689e6i	−0.541759	+	0.541759i	0.382285	+	0.924044i	$0.375137\pi$
$390$		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	0.640430	−	0.768017i	$-0.278756\pi$
$397$	−400667.	−	400667.i	−0.127587	−	0.127587i	−0.768017	+	0.640430i	$0.778756\pi$
$398$		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	$-0.929169\pi$
$409$		−	1.49322e6i		−	0.441382i	0.975344	−	0.220691i	$-0.0708313\pi$
$410$		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	0.911185	+	0.411998i	$0.135169\pi$
$419$	4.75505e6	+	4.75505e6i	1.32318	+	1.32318i	0.411998	+	0.911185i	$0.364831\pi$
$420$		0			0
$421$	−2.48208e6	+	2.48208e6i	−0.682511	+	0.682511i	−0.960565	−	0.278054i	$-0.910311\pi$
$421$	−2.48208e6	+	2.48208e6i	−0.682511	+	0.682511i	0.278054	+	0.960565i	$0.410311\pi$
$422$		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	$-0.837446\pi$
$439$		−	3.94725e6i		−	0.977537i	0.872414	−	0.488768i	$-0.162554\pi$
$440$		0			0
$441$			1.20848e6i			0.295899i
$442$		0			0
$443$	2.77891e6	−	2.77891e6i	0.672767	−	0.672767i	−0.285586	−	0.958353i	$-0.592188\pi$
$443$	2.77891e6	−	2.77891e6i	0.672767	−	0.672767i	0.958353	+	0.285586i	$0.0921883\pi$
$444$		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	$-0.975459\pi$
$457$		−	687743.i		−	0.154041i	0.997030	−	0.0770204i	$-0.0245407\pi$
$458$		0			0
$459$	1.53242e6	−	1.53242e6i	0.339506	−	0.339506i
$460$		0			0
$461$	1.34081e6	+	1.34081e6i	0.293843	+	0.293843i	0.838596	−	0.544753i	$-0.183377\pi$
$461$	1.34081e6	+	1.34081e6i	0.293843	+	0.293843i	−0.544753	+	0.838596i	$0.683377\pi$
$462$		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	0.632374	−	0.774664i	$-0.282081\pi$
$467$	−670605.	−	670605.i	−0.142290	−	0.142290i	−0.774664	+	0.632374i	$0.782081\pi$
$468$		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	$0.151111\pi$
$487$			4.78477e6i			0.914195i	−0.889417	+	0.457097i	$0.848889\pi$
$488$		0			0
$489$			56191.3i			0.0106267i
$490$		0			0
$491$	6.20974e6	−	6.20974e6i	1.16244	−	1.16244i	0.178497	−	0.983940i	$-0.442876\pi$
$491$	6.20974e6	−	6.20974e6i	1.16244	−	1.16244i	0.983940	−	0.178497i	$-0.0571236\pi$
$492$		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	0.760609	−	0.649210i	$-0.224900\pi$
$499$	619633.	+	619633.i	0.111399	+	0.111399i	−0.649210	+	0.760609i	$0.724900\pi$
$500$		0			0
$501$	794838.	−	794838.i	0.141477	−	0.141477i
$502$		0			0
$503$		−	786743.i		−	0.138648i	−0.997594	−	0.0693239i	$-0.977916\pi$
$503$		−	786743.i		−	0.138648i	0.997594	−	0.0693239i	$-0.0220842\pi$
$504$		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	0.825075	−	0.565023i	$-0.191133\pi$
$509$	1.52004e6	+	1.52004e6i	0.260052	+	0.260052i	−0.565023	+	0.825075i	$0.691133\pi$
$510$		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	$-0.792041\pi$
$521$		−	7.53189e6i		−	1.21565i	0.794070	−	0.607827i	$-0.207959\pi$
$522$		0			0
$523$	3.36602e6	−	3.36602e6i	0.538099	−	0.538099i	−0.384871	−	0.922970i	$-0.625754\pi$
$523$	3.36602e6	−	3.36602e6i	0.538099	−	0.538099i	0.922970	+	0.384871i	$0.125754\pi$
$524$		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	0.997069	−	0.0765086i	$-0.0243773\pi$
$541$	6.26679e6	+	6.26679e6i	0.920560	+	0.920560i	−0.0765086	+	0.997069i	$0.524377\pi$
$542$		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	0.620465	−	0.784234i	$-0.286944\pi$
$547$	−1.14604e6	−	1.14604e6i	−0.163770	−	0.163770i	−0.784234	+	0.620465i	$0.786944\pi$
$548$		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	0.188737	−	0.982028i	$-0.439561\pi$
$557$	−5.80858e6	−	5.80858e6i	−0.793291	−	0.793291i	−0.982028	+	0.188737i	$0.939561\pi$
$558$		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	0.858045	−	0.513575i	$-0.171679\pi$
$563$	2.59073e6	+	2.59073e6i	0.344470	+	0.344470i	−0.513575	+	0.858045i	$0.671679\pi$
$564$		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	$-0.756457\pi$
$569$		−	1.06981e7i		−	1.38524i	0.721304	−	0.692618i	$-0.243543\pi$
$570$		0			0
$571$	−2.78779e6	+	2.78779e6i	−0.357824	+	0.357824i	−0.863010	−	0.505187i	$-0.831424\pi$
$571$	−2.78779e6	+	2.78779e6i	−0.357824	+	0.357824i	0.505187	+	0.863010i	$0.331424\pi$
$572$		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	−0.405430	+	0.914126i	$0.632878\pi$
$587$	−1.10160e7	+	1.10160e7i	−1.31956	+	1.31956i	−0.914126	+	0.405430i	$0.867122\pi$
$588$		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	$-0.795141\pi$
$599$		−	1.05389e7i		−	1.20013i	0.799950	−	0.600067i	$-0.204859\pi$
$600$		0			0
$601$		−	1.10876e7i		−	1.25214i	−0.779769	−	0.626068i	$-0.784663\pi$
$601$		−	1.10876e7i		−	1.25214i	0.779769	−	0.626068i	$-0.215337\pi$
$602$		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	−0.999009	−	0.0444991i	$-0.985831\pi$
$613$	−8.88039e6	+	8.88039e6i	−0.954510	+	0.954510i	0.0444991	+	0.999009i	$0.485831\pi$
$614$		0			0
$615$			163534.i			0.0174349i
$616$		0			0
$617$		−	8.90147e6i		−	0.941345i	−0.882308	−	0.470672i	$-0.844011\pi$
$617$		−	8.90147e6i		−	0.941345i	0.882308	−	0.470672i	$-0.155989\pi$
$618$		0			0
$619$	−6.71588e6	+	6.71588e6i	−0.704493	+	0.704493i	−0.965372	−	0.260879i	$-0.915988\pi$
$619$	−6.71588e6	+	6.71588e6i	−0.704493	+	0.704493i	0.260879	+	0.965372i	$0.415988\pi$
$620$		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	$0.0867595\pi$
$631$			5.38492e6i			0.538401i	−0.963084	+	0.269201i	$0.913241\pi$
$632$		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	0.597451	−	0.801905i	$-0.296180\pi$
$643$	−2.14350e6	−	2.14350e6i	−0.204454	−	0.204454i	−0.801905	+	0.597451i	$0.796180\pi$
$644$		0			0
$645$	490774.	−	490774.i	0.0464496	−	0.0464496i
$646$		0			0
$647$		−	1.97136e7i		−	1.85143i	−0.378227	−	0.925713i	$-0.623466\pi$
$647$		−	1.97136e7i		−	1.85143i	0.378227	−	0.925713i	$-0.376534\pi$
$648$		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	0.999942	−	0.0107266i	$-0.00341445\pi$
$653$	1.07789e7	+	1.07789e7i	0.989216	+	0.989216i	−0.0107266	+	0.999942i	$0.503414\pi$
$654$		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	0.595557	−	0.803313i	$-0.296931\pi$
$659$	−2.31615e6	−	2.31615e6i	−0.207755	−	0.207755i	−0.803313	+	0.595557i	$0.796931\pi$
$660$		0			0
$661$	−5.60044e6	+	5.60044e6i	−0.498561	+	0.498561i	−0.910990	−	0.412429i	$-0.864680\pi$
$661$	−5.60044e6	+	5.60044e6i	−0.498561	+	0.498561i	0.412429	+	0.910990i	$0.364680\pi$
$662$		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	−0.800077	−	0.599897i	$-0.795208\pi$
$677$	−2.38722e6	+	2.38722e6i	−0.200180	+	0.200180i	0.599897	+	0.800077i	$0.295208\pi$
$678$		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	−0.322206	−	0.946670i	$-0.604424\pi$
$683$	7.61306e6	−	7.61306e6i	0.624464	−	0.624464i	0.946670	+	0.322206i	$0.104424\pi$
$684$		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	0.129182	−	0.991621i	$-0.458765\pi$
$691$	−1.08249e7	−	1.08249e7i	−0.862439	−	0.862439i	−0.991621	+	0.129182i	$0.958765\pi$
$692$		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	0.793140	−	0.609039i	$-0.208445\pi$
$701$	2.39524e6	+	2.39524e6i	0.184100	+	0.184100i	−0.609039	+	0.793140i	$0.708445\pi$
$702$		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	−0.280141	−	0.959959i	$-0.590381\pi$
$709$	9.09930e6	−	9.09930e6i	0.679817	−	0.679817i	0.959959	+	0.280141i	$0.0903814\pi$
$710$		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	$-0.609076\pi$
$727$		−	2.68443e7i		−	1.88372i	0.336006	−	0.941860i	$-0.390924\pi$
$728$		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	−0.999513	−	0.0312110i	$-0.990064\pi$
$733$	−1.49935e7	−	1.49935e7i	−1.03072	−	1.03072i	−0.0312110	−	0.999513i	$-0.509936\pi$
$734$		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	0.396658	−	0.917967i	$-0.370170\pi$
$739$	−7.73938e6	−	7.73938e6i	−0.521309	−	0.521309i	−0.917967	+	0.396658i	$0.870170\pi$
$740$		0			0
$741$	−4.40977e6	+	4.40977e6i	−0.295033	+	0.295033i
$742$		0			0
$743$			4.27335e6i			0.283986i	0.989868	+	0.141993i	$0.0453510\pi$
$743$			4.27335e6i			0.283986i	−0.989868	+	0.141993i	$0.954649\pi$
$744$		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	−0.852850	−	0.522156i	$-0.825128\pi$
$757$	−5.21393e6	+	5.21393e6i	−0.330694	+	0.330694i	0.522156	+	0.852850i	$0.325128\pi$
$758$		0			0
$759$		−	141466.i		−	0.00891352i
$760$		0			0
$761$			1.79653e7i			1.12454i	0.826955	+	0.562268i	$0.190071\pi$
$761$			1.79653e7i			1.12454i	−0.826955	+	0.562268i	$0.809929\pi$
$762$		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	−0.367752	−	0.929924i	$-0.619872\pi$
$773$	9.33938e6	−	9.33938e6i	0.562172	−	0.562172i	0.929924	+	0.367752i	$0.119872\pi$
$774$		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	0.866028	−	0.499995i	$-0.166665\pi$
$787$	6.36001e6	+	6.36001e6i	0.366034	+	0.366034i	−0.499995	+	0.866028i	$0.666665\pi$
$788$		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	0.106982	−	0.994261i	$-0.465881\pi$
$797$	−1.59113e7	−	1.59113e7i	−0.887279	−	0.887279i	−0.994261	+	0.106982i	$0.965881\pi$
$798$		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	$0.264302\pi$
$809$			2.74820e7i			1.47631i	−0.674633	+	0.738153i	$0.735698\pi$
$810$		0			0
$811$	1.77957e7	−	1.77957e7i	0.950085	−	0.950085i	−0.0487272	−	0.998812i	$-0.515516\pi$
$811$	1.77957e7	−	1.77957e7i	0.950085	−	0.950085i	0.998812	+	0.0487272i	$0.0155165\pi$
$812$		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	−0.170092	−	0.985428i	$-0.554406\pi$
$821$	1.57469e7	−	1.57469e7i	0.815336	−	0.815336i	0.985428	+	0.170092i	$0.0544065\pi$
$822$		0			0
$823$		−	3.68026e7i		−	1.89400i	−0.321237	−	0.946999i	$-0.604098\pi$
$823$		−	3.68026e7i		−	1.89400i	0.321237	−	0.946999i	$-0.395902\pi$
$824$		0			0
$825$			174192.i			0.00891031i
$826$		0			0
$827$	−9.65869e6	+	9.65869e6i	−0.491083	+	0.491083i	−0.908647	−	0.417565i	$-0.862884\pi$
$827$	−9.65869e6	+	9.65869e6i	−0.491083	+	0.491083i	0.417565	+	0.908647i	$0.362884\pi$
$828$		0			0
$829$	3.10341e6	+	3.10341e6i	0.156838	+	0.156838i	0.781164	−	0.624326i	$-0.214626\pi$
$829$	3.10341e6	+	3.10341e6i	0.156838	+	0.156838i	−0.624326	+	0.781164i	$0.714626\pi$
$830$		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	$-0.949598\pi$
$839$		−	6.43004e6i		−	0.315362i	0.987490	−	0.157681i	$-0.0504017\pi$
$840$		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	−0.682120	−	0.731240i	$-0.738942\pi$
$853$	1.04384e6	−	1.04384e6i	0.0491203	−	0.0491203i	0.731240	+	0.682120i	$0.238942\pi$
$854$		0			0
$855$			6.91796e6i			0.323640i
$856$		0			0
$857$			3.37311e7i			1.56884i	0.620230	+	0.784420i	$0.287039\pi$
$857$			3.37311e7i			1.56884i	−0.620230	+	0.784420i	$0.712961\pi$
$858$		0			0
$859$	−2.22076e7	+	2.22076e7i	−1.02688	+	1.02688i	−0.0272513	+	0.999629i	$0.508675\pi$
$859$	−2.22076e7	+	2.22076e7i	−1.02688	+	1.02688i	−0.999629	+	0.0272513i	$0.991325\pi$
$860$		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	0.745482	−	0.666525i	$-0.232219\pi$
$877$	1.79841e6	+	1.79841e6i	0.0789568	+	0.0789568i	−0.666525	+	0.745482i	$0.732219\pi$
$878$		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	0.541664	−	0.840595i	$-0.317794\pi$
$883$	−6.92584e6	−	6.92584e6i	−0.298931	−	0.298931i	−0.840595	+	0.541664i	$0.817794\pi$
$884$		0			0
$885$	−4.09903e6	+	4.09903e6i	−0.175923	+	0.175923i
$886$		0			0
$887$			1.12492e7i			0.480077i	0.970763	+	0.240039i	$0.0771601\pi$
$887$			1.12492e7i			0.480077i	−0.970763	+	0.240039i	$0.922840\pi$
$888$		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	−0.115118	+	0.993352i	$0.536724\pi$
$907$	−2.74626e7	+	2.74626e7i	−1.10847	+	1.10847i	−0.993352	+	0.115118i	$0.963276\pi$
$908$		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	$-0.890387\pi$
$919$		−	1.72867e7i		−	0.675186i	0.941292	−	0.337593i	$-0.109613\pi$
$920$		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	$0.246862\pi$
$937$			3.76305e7i			1.40020i	−0.714044	+	0.700101i	$0.753138\pi$
$938$		0			0
$939$	2.48261e6	−	2.48261e6i	0.0918851	−	0.0918851i
$940$		0			0
$941$	3.52025e7	+	3.52025e7i	1.29598	+	1.29598i	0.931024	+	0.364959i	$0.118917\pi$
$941$	3.52025e7	+	3.52025e7i	1.29598	+	1.29598i	0.364959	+	0.931024i	$0.381083\pi$
$942$		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	−0.999210	−	0.0397356i	$-0.987348\pi$
$947$	−2.86727e7	−	2.86727e7i	−1.03895	−	1.03895i	−0.0397356	−	0.999210i	$-0.512652\pi$
$948$		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	$0.112997\pi$
$953$			1.94903e7i			0.695161i	−0.937650	+	0.347581i	$0.887003\pi$
$954$		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	$-0.871504\pi$
$967$		−	2.28442e7i		−	0.785616i	0.919621	−	0.392808i	$-0.128496\pi$
$968$		0			0
$969$		−	5.99435e6i		−	0.205084i
$970$		0			0
$971$	2.76612e7	−	2.76612e7i	0.941506	−	0.941506i	−0.0568757	−	0.998381i	$-0.518114\pi$
$971$	2.76612e7	−	2.76612e7i	0.941506	−	0.941506i	0.998381	+	0.0568757i	$0.0181139\pi$
$972$		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	$-0.958967\pi$
$983$		−	7.78926e6i		−	0.257106i	0.991703	−	0.128553i	$-0.0410333\pi$
$984$		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	−0.572119	−	0.820171i	$-0.693878\pi$
$997$	7.78540e6	−	7.78540e6i	0.248052	−	0.248052i	0.820171	+	0.572119i	$0.193878\pi$
$998$		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.81.18		80
4.3	odd	2		80.6.l.a.61.40	yes	80
16.5	even	4	inner	320.6.l.a.241.18		80
16.11	odd	4		80.6.l.a.21.40	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.40	✓	80	16.11	odd	4
80.6.l.a.61.40	yes	80	4.3	odd	2
320.6.l.a.81.18		80	1.1	even	1	trivial
320.6.l.a.241.18		80	16.5	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

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Database

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