LMFDB - Embedded newform 320.6.l.a.81.13

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			81.13
Character	$\chi$	$=$	320.81
Dual form			320.6.l.a.241.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.88400 - 7.88400i) q^{3} +(17.6777 - 17.6777i) q^{5} +208.047i q^{7} -118.685i q^{9} +O(q^{10})$	\(q+(-7.88400 - 7.88400i) q^{3} +(17.6777 - 17.6777i) q^{5} +208.047i q^{7} -118.685i q^{9} +(-117.724 + 117.724i) q^{11} +(-192.926 - 192.926i) q^{13} -278.742 q^{15} -961.739 q^{17} +(1107.22 + 1107.22i) q^{19} +(1640.24 - 1640.24i) q^{21} -2636.65i q^{23} -625.000i q^{25} +(-2851.53 + 2851.53i) q^{27} +(3437.64 + 3437.64i) q^{29} +2302.12 q^{31} +1856.27 q^{33} +(3677.78 + 3677.78i) q^{35} +(10541.5 - 10541.5i) q^{37} +3042.06i q^{39} -8634.65i q^{41} +(5912.40 - 5912.40i) q^{43} +(-2098.08 - 2098.08i) q^{45} -5889.22 q^{47} -26476.4 q^{49} +(7582.35 + 7582.35i) q^{51} +(-12424.3 + 12424.3i) q^{53} +4162.17i q^{55} -17458.7i q^{57} +(-12930.4 + 12930.4i) q^{59} +(-24417.8 - 24417.8i) q^{61} +24692.0 q^{63} -6820.96 q^{65} +(-13983.9 - 13983.9i) q^{67} +(-20787.4 + 20787.4i) q^{69} -48733.1i q^{71} -88373.4i q^{73} +(-4927.50 + 4927.50i) q^{75} +(-24492.0 - 24492.0i) q^{77} -39883.7 q^{79} +16122.4 q^{81} +(-45453.5 - 45453.5i) q^{83} +(-17001.3 + 17001.3i) q^{85} -54204.8i q^{87} +19622.1i q^{89} +(40137.6 - 40137.6i) q^{91} +(-18149.9 - 18149.9i) q^{93} +39146.2 q^{95} +51026.8 q^{97} +(13972.1 + 13972.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−7.88400	−	7.88400i	−0.505759	−	0.505759i	0.407463	−	0.913222i	$-0.366414\pi$
$3$	−7.88400	−	7.88400i	−0.505759	−	0.505759i	−0.913222	+	0.407463i	$0.866414\pi$
$4$		0			0
$5$	17.6777	−	17.6777i	0.316228	−	0.316228i
$5$	17.6777	−	17.6777i	0.316228	−	0.316228i
$6$		0			0
$7$			208.047i			1.60478i	0.596800	+	0.802390i	$0.296438\pi$
$7$			208.047i			1.60478i	−0.596800	+	0.802390i	$0.703562\pi$
$8$		0			0
$9$		−	118.685i		−	0.488416i
$10$		0			0
$11$	−117.724	+	117.724i	−0.293348	+	0.293348i	−0.838401	−	0.545054i	$-0.816509\pi$
$11$	−117.724	+	117.724i	−0.293348	+	0.293348i	0.545054	+	0.838401i	$0.316509\pi$
$12$		0			0
$13$	−192.926	−	192.926i	−0.316616	−	0.316616i	0.530850	−	0.847466i	$-0.321873\pi$
$13$	−192.926	−	192.926i	−0.316616	−	0.316616i	−0.847466	+	0.530850i	$0.821873\pi$
$14$		0			0
$15$	−278.742			−0.319870
$16$		0			0
$17$	−961.739			−0.807114			−0.403557	−	0.914954i	$-0.632226\pi$
$17$	−961.739			−0.807114			−0.403557	+	0.914954i	$0.632226\pi$
$18$		0			0
$19$	1107.22	+	1107.22i	0.703639	+	0.703639i	0.965190	−	0.261550i	$-0.0842338\pi$
$19$	1107.22	+	1107.22i	0.703639	+	0.703639i	−0.261550	+	0.965190i	$0.584234\pi$
$20$		0			0
$21$	1640.24	−	1640.24i	0.811632	−	0.811632i
$22$		0			0
$23$		−	2636.65i		−	1.03928i	−0.854385	−	0.519641i	$-0.826066\pi$
$23$		−	2636.65i		−	1.03928i	0.854385	−	0.519641i	$-0.173934\pi$
$24$		0			0
$25$		−	625.000i		−	0.200000i
$26$		0			0
$27$	−2851.53	+	2851.53i	−0.752780	+	0.752780i
$28$		0			0
$29$	3437.64	+	3437.64i	0.759042	+	0.759042i	0.976148	−	0.217106i	$-0.0696617\pi$
$29$	3437.64	+	3437.64i	0.759042	+	0.759042i	−0.217106	+	0.976148i	$0.569662\pi$
$30$		0			0
$31$	2302.12			0.430253			0.215126	−	0.976586i	$-0.430984\pi$
$31$	2302.12			0.430253			0.215126	+	0.976586i	$0.430984\pi$
$32$		0			0
$33$	1856.27			0.296726
$34$		0			0
$35$	3677.78	+	3677.78i	0.507476	+	0.507476i
$36$		0			0
$37$	10541.5	−	10541.5i	1.26590	−	1.26590i	0.317710	−	0.948188i	$-0.397086\pi$
$37$	10541.5	−	10541.5i	1.26590	−	1.26590i	0.948188	−	0.317710i	$-0.102914\pi$
$38$		0			0
$39$			3042.06i			0.320262i
$40$		0			0
$41$		−	8634.65i		−	0.802204i	−0.916033	−	0.401102i	$-0.868627\pi$
$41$		−	8634.65i		−	0.802204i	0.916033	−	0.401102i	$-0.131373\pi$
$42$		0			0
$43$	5912.40	−	5912.40i	0.487633	−	0.487633i	−0.419926	−	0.907558i	$-0.637944\pi$
$43$	5912.40	−	5912.40i	0.487633	−	0.487633i	0.907558	+	0.419926i	$0.137944\pi$
$44$		0			0
$45$	−2098.08	−	2098.08i	−0.154451	−	0.154451i
$46$		0			0
$47$	−5889.22			−0.388878			−0.194439	−	0.980915i	$-0.562289\pi$
$47$	−5889.22			−0.388878			−0.194439	+	0.980915i	$0.562289\pi$
$48$		0			0
$49$	−26476.4			−1.57532
$50$		0			0
$51$	7582.35	+	7582.35i	0.408205	+	0.408205i
$52$		0			0
$53$	−12424.3	+	12424.3i	−0.607552	+	0.607552i	−0.942306	−	0.334754i	$-0.891347\pi$
$53$	−12424.3	+	12424.3i	−0.607552	+	0.607552i	0.334754	+	0.942306i	$0.391347\pi$
$54$		0			0
$55$			4162.17i			0.185529i
$56$		0			0
$57$		−	17458.7i		−	0.711744i
$58$		0			0
$59$	−12930.4	+	12930.4i	−0.483595	+	0.483595i	−0.906278	−	0.422683i	$-0.861088\pi$
$59$	−12930.4	+	12930.4i	−0.483595	+	0.483595i	0.422683	+	0.906278i	$0.361088\pi$
$60$		0			0
$61$	−24417.8	−	24417.8i	−0.840197	−	0.840197i	0.148687	−	0.988884i	$-0.452495\pi$
$61$	−24417.8	−	24417.8i	−0.840197	−	0.840197i	−0.988884	+	0.148687i	$0.952495\pi$
$62$		0			0
$63$	24692.0			0.783800
$64$		0			0
$65$	−6820.96			−0.200245
$66$		0			0
$67$	−13983.9	−	13983.9i	−0.380576	−	0.380576i	0.490734	−	0.871310i	$-0.336729\pi$
$67$	−13983.9	−	13983.9i	−0.380576	−	0.380576i	−0.871310	+	0.490734i	$0.836729\pi$
$68$		0			0
$69$	−20787.4	+	20787.4i	−0.525626	+	0.525626i
$70$		0			0
$71$		−	48733.1i		−	1.14730i	−0.819099	−	0.573652i	$-0.805526\pi$
$71$		−	48733.1i		−	1.14730i	0.819099	−	0.573652i	$-0.194474\pi$
$72$		0			0
$73$		−	88373.4i		−	1.94095i	−0.241203	−	0.970475i	$-0.577542\pi$
$73$		−	88373.4i		−	1.94095i	0.241203	−	0.970475i	$-0.422458\pi$
$74$		0			0
$75$	−4927.50	+	4927.50i	−0.101152	+	0.101152i
$76$		0			0
$77$	−24492.0	−	24492.0i	−0.470758	−	0.470758i
$78$		0			0
$79$	−39883.7			−0.718998			−0.359499	−	0.933145i	$-0.617052\pi$
$79$	−39883.7			−0.718998			−0.359499	+	0.933145i	$0.617052\pi$
$80$		0			0
$81$	16122.4			0.273034
$82$		0			0
$83$	−45453.5	−	45453.5i	−0.724222	−	0.724222i	0.245240	−	0.969462i	$-0.421133\pi$
$83$	−45453.5	−	45453.5i	−0.724222	−	0.724222i	−0.969462	+	0.245240i	$0.921133\pi$
$84$		0			0
$85$	−17001.3	+	17001.3i	−0.255232	+	0.255232i
$86$		0			0
$87$		−	54204.8i		−	0.767785i
$88$		0			0
$89$			19622.1i			0.262585i	0.991344	+	0.131293i	$0.0419128\pi$
$89$			19622.1i			0.262585i	−0.991344	+	0.131293i	$0.958087\pi$
$90$		0			0
$91$	40137.6	−	40137.6i	0.508098	−	0.508098i
$92$		0			0
$93$	−18149.9	−	18149.9i	−0.217604	−	0.217604i
$94$		0			0
$95$	39146.2			0.445021
$96$		0			0
$97$	51026.8			0.550642			0.275321	−	0.961352i	$-0.411216\pi$
$97$	51026.8			0.550642			0.275321	+	0.961352i	$0.411216\pi$
$98$		0			0
$99$	13972.1	+	13972.1i	0.143276	+	0.143276i
$100$		0			0
$101$	123045.	−	123045.i	1.20022	−	1.20022i	0.226120	−	0.974100i	$-0.427396\pi$
$101$	123045.	−	123045.i	1.20022	−	1.20022i	0.974100	−	0.226120i	$-0.0726040\pi$
$102$		0			0
$103$		−	212680.i		−	1.97530i	−0.156683	−	0.987649i	$-0.550080\pi$
$103$		−	212680.i		−	1.97530i	0.156683	−	0.987649i	$-0.449920\pi$
$104$		0			0
$105$		−	57991.2i		−	0.513321i
$106$		0			0
$107$	−106075.	+	106075.i	−0.895678	+	0.895678i	−0.995050	−	0.0993727i	$-0.968316\pi$
$107$	−106075.	+	106075.i	−0.895678	+	0.895678i	0.0993727	+	0.995050i	$0.468316\pi$
$108$		0			0
$109$	−17617.5	−	17617.5i	−0.142029	−	0.142029i	0.632517	−	0.774546i	$-0.282022\pi$
$109$	−17617.5	−	17617.5i	−0.142029	−	0.142029i	−0.774546	+	0.632517i	$0.782022\pi$
$110$		0			0
$111$	−166219.			−1.28048
$112$		0			0
$113$	71983.2			0.530317			0.265158	−	0.964205i	$-0.414576\pi$
$113$	71983.2			0.530317			0.265158	+	0.964205i	$0.414576\pi$
$114$		0			0
$115$	−46609.9	−	46609.9i	−0.328650	−	0.328650i
$116$		0			0
$117$	−22897.4	+	22897.4i	−0.154640	+	0.154640i
$118$		0			0
$119$		−	200087.i		−	1.29524i
$120$		0			0
$121$			133333.i			0.827894i
$122$		0			0
$123$	−68075.6	+	68075.6i	−0.405722	+	0.405722i
$124$		0			0
$125$	−11048.5	−	11048.5i	−0.0632456	−	0.0632456i
$126$		0			0
$127$	−239532.			−1.31781			−0.658906	−	0.752225i	$-0.728980\pi$
$127$	−239532.			−1.31781			−0.658906	+	0.752225i	$0.728980\pi$
$128$		0			0
$129$	−93226.7			−0.493249
$130$		0			0
$131$	132808.	+	132808.i	0.676155	+	0.676155i	0.959128	−	0.282973i	$-0.0913206\pi$
$131$	132808.	+	132808.i	0.676155	+	0.676155i	−0.282973	+	0.959128i	$0.591321\pi$
$132$		0			0
$133$	−230353.	+	230353.i	−1.12919	+	1.12919i
$134$		0			0
$135$			100817.i			0.476100i
$136$		0			0
$137$		−	155055.i		−	0.705802i	−0.935661	−	0.352901i	$-0.885195\pi$
$137$		−	155055.i		−	0.705802i	0.935661	−	0.352901i	$-0.114805\pi$
$138$		0			0
$139$	262037.	−	262037.i	1.15034	−	1.15034i	0.163851	−	0.986485i	$-0.447608\pi$
$139$	262037.	−	262037.i	1.15034	−	1.15034i	0.986485	−	0.163851i	$-0.0523917\pi$
$140$		0			0
$141$	46430.6	+	46430.6i	0.196678	+	0.196678i
$142$		0			0
$143$	45424.0			0.185757
$144$		0			0
$145$	121539.			0.480060
$146$		0			0
$147$	208740.	+	208740.i	0.796731	+	0.796731i
$148$		0			0
$149$	−192042.	+	192042.i	−0.708646	+	0.708646i	−0.966250	−	0.257604i	$-0.917067\pi$
$149$	−192042.	+	192042.i	−0.708646	+	0.708646i	0.257604	+	0.966250i	$0.417067\pi$
$150$		0			0
$151$		−	427260.i		−	1.52493i	−0.647029	−	0.762466i	$-0.723989\pi$
$151$		−	427260.i		−	1.52493i	0.647029	−	0.762466i	$-0.276011\pi$
$152$		0			0
$153$			114144.i			0.394207i
$154$		0			0
$155$	40696.1	−	40696.1i	0.136058	−	0.136058i
$156$		0			0
$157$	−229660.	−	229660.i	−0.743595	−	0.743595i	0.229673	−	0.973268i	$-0.426234\pi$
$157$	−229660.	−	229660.i	−0.743595	−	0.743595i	−0.973268	+	0.229673i	$0.926234\pi$
$158$		0			0
$159$	195907.			0.614549
$160$		0			0
$161$	548547.			1.66782
$162$		0			0
$163$	−336280.	−	336280.i	−0.991363	−	0.991363i	0.00860016	−	0.999963i	$-0.497262\pi$
$163$	−336280.	−	336280.i	−0.991363	−	0.991363i	−0.999963	+	0.00860016i	$0.997262\pi$
$164$		0			0
$165$	32814.5	−	32814.5i	0.0938332	−	0.0938332i
$166$		0			0
$167$			338007.i			0.937852i	0.883237	+	0.468926i	$0.155359\pi$
$167$			338007.i			0.937852i	−0.883237	+	0.468926i	$0.844641\pi$
$168$		0			0
$169$		−	296852.i		−	0.799509i
$170$		0			0
$171$	131411.	−	131411.i	0.343669	−	0.343669i
$172$		0			0
$173$	144268.	+	144268.i	0.366485	+	0.366485i	0.866194	−	0.499709i	$-0.166560\pi$
$173$	144268.	+	144268.i	0.366485	+	0.366485i	−0.499709	+	0.866194i	$0.666560\pi$
$174$		0			0
$175$	130029.			0.320956
$176$		0			0
$177$	203886.			0.489165
$178$		0			0
$179$	385415.	+	385415.i	0.899075	+	0.899075i	0.995354	−	0.0962793i	$-0.0306942\pi$
$179$	385415.	+	385415.i	0.899075	+	0.899075i	−0.0962793	+	0.995354i	$0.530694\pi$
$180$		0			0
$181$	−135597.	+	135597.i	−0.307647	+	0.307647i	−0.843996	−	0.536349i	$-0.819803\pi$
$181$	−135597.	+	135597.i	−0.307647	+	0.307647i	0.536349	+	0.843996i	$0.319803\pi$
$182$		0			0
$183$			385019.i			0.849875i
$184$		0			0
$185$		−	372699.i		−	0.800624i
$186$		0			0
$187$	113220.	−	113220.i	0.236765	−	0.236765i
$188$		0			0
$189$	−593250.	−	593250.i	−1.20805	−	1.20805i
$190$		0			0
$191$	70124.0			0.139086			0.0695430	−	0.997579i	$-0.477846\pi$
$191$	70124.0			0.139086			0.0695430	+	0.997579i	$0.477846\pi$
$192$		0			0
$193$	714068.			1.37990			0.689948	−	0.723859i	$-0.257633\pi$
$193$	714068.			1.37990			0.689948	+	0.723859i	$0.257633\pi$
$194$		0			0
$195$	53776.5	+	53776.5i	0.101276	+	0.101276i
$196$		0			0
$197$	−441131.	+	441131.i	−0.809845	+	0.809845i	−0.984610	−	0.174765i	$-0.944083\pi$
$197$	−441131.	+	441131.i	−0.809845	+	0.809845i	0.174765	+	0.984610i	$0.444083\pi$
$198$		0			0
$199$		−	135153.i		−	0.241931i	−0.992657	−	0.120966i	$-0.961401\pi$
$199$		−	135153.i		−	0.241931i	0.992657	−	0.120966i	$-0.0385991\pi$
$200$		0			0
$201$			220498.i			0.384960i
$202$		0			0
$203$	−715190.	+	715190.i	−1.21810	+	1.21810i
$204$		0			0
$205$	−152640.	−	152640.i	−0.253679	−	0.253679i
$206$		0			0
$207$	−312931.			−0.507602
$208$		0			0
$209$	−260693.			−0.412822
$210$		0			0
$211$	672860.	+	672860.i	1.04044	+	1.04044i	0.999147	+	0.0412971i	$0.0131490\pi$
$211$	672860.	+	672860.i	1.04044	+	1.04044i	0.0412971	+	0.999147i	$0.486851\pi$
$212$		0			0
$213$	−384212.	+	384212.i	−0.580259	+	0.580259i
$214$		0			0
$215$		−	209035.i		−	0.308406i
$216$		0			0
$217$			478948.i			0.690461i
$218$		0			0
$219$	−696736.	+	696736.i	−0.981652	+	0.981652i
$220$		0			0
$221$	185545.	+	185545.i	0.255545	+	0.255545i
$222$		0			0
$223$	−1.33714e6			−1.80059			−0.900293	−	0.435285i	$-0.856648\pi$
$223$	−1.33714e6			−1.80059			−0.900293	+	0.435285i	$0.856648\pi$
$224$		0			0
$225$	−74178.2			−0.0976832
$226$		0			0
$227$	24080.3	+	24080.3i	0.0310168	+	0.0310168i	0.722445	−	0.691428i	$-0.243018\pi$
$227$	24080.3	+	24080.3i	0.0310168	+	0.0310168i	−0.691428	+	0.722445i	$0.743018\pi$
$228$		0			0
$229$	332429.	−	332429.i	0.418900	−	0.418900i	−0.465925	−	0.884824i	$-0.654278\pi$
$229$	332429.	−	332429.i	0.418900	−	0.418900i	0.884824	+	0.465925i	$0.154278\pi$
$230$		0			0
$231$			386191.i			0.476181i
$232$		0			0
$233$		−	909342.i		−	1.09733i	−0.836042	−	0.548665i	$-0.815136\pi$
$233$		−	909342.i		−	1.09733i	0.836042	−	0.548665i	$-0.184864\pi$
$234$		0			0
$235$	−104108.	+	104108.i	−0.122974	+	0.122974i
$236$		0			0
$237$	314443.	+	314443.i	0.363640	+	0.363640i
$238$		0			0
$239$	259767.			0.294164			0.147082	−	0.989124i	$-0.453012\pi$
$239$	259767.			0.294164			0.147082	+	0.989124i	$0.453012\pi$
$240$		0			0
$241$	199206.			0.220932			0.110466	−	0.993880i	$-0.464766\pi$
$241$	199206.			0.220932			0.110466	+	0.993880i	$0.464766\pi$
$242$		0			0
$243$	565812.	+	565812.i	0.614690	+	0.614690i
$244$		0			0
$245$	−468040.	+	468040.i	−0.498159	+	0.498159i
$246$		0			0
$247$		−	427223.i		−	0.445567i
$248$		0			0
$249$			716711.i			0.732564i
$250$		0			0
$251$	−522423.	+	522423.i	−0.523405	+	0.523405i	−0.918598	−	0.395193i	$-0.870678\pi$
$251$	−522423.	+	522423.i	−0.523405	+	0.523405i	0.395193	+	0.918598i	$0.370678\pi$
$252$		0			0
$253$	310397.	+	310397.i	0.304871	+	0.304871i
$254$		0			0
$255$	268077.			0.258172
$256$		0			0
$257$	1.24541e6			1.17620			0.588099	−	0.808789i	$-0.299877\pi$
$257$	1.24541e6			1.17620			0.588099	+	0.808789i	$0.299877\pi$
$258$		0			0
$259$	2.19312e6	+	2.19312e6i	2.03149	+	2.03149i
$260$		0			0
$261$	407997.	−	407997.i	0.370728	−	0.370728i
$262$		0			0
$263$		−	1.93577e6i		−	1.72570i	−0.505462	−	0.862849i	$-0.668678\pi$
$263$		−	1.93577e6i		−	1.72570i	0.505462	−	0.862849i	$-0.331322\pi$
$264$		0			0
$265$			439266.i			0.384249i
$266$		0			0
$267$	154701.	−	154701.i	0.132805	−	0.132805i
$268$		0			0
$269$	629021.	+	629021.i	0.530010	+	0.530010i	0.920575	−	0.390565i	$-0.127720\pi$
$269$	629021.	+	629021.i	0.530010	+	0.530010i	−0.390565	+	0.920575i	$0.627720\pi$
$270$		0			0
$271$	1.61018e6			1.33184			0.665921	−	0.746023i	$-0.268039\pi$
$271$	1.61018e6			1.33184			0.665921	+	0.746023i	$0.268039\pi$
$272$		0			0
$273$	−632890.			−0.513951
$274$		0			0
$275$	73577.4	+	73577.4i	0.0586696	+	0.0586696i
$276$		0			0
$277$	−1.05351e6	+	1.05351e6i	−0.824974	+	0.824974i	−0.986817	−	0.161842i	$-0.948256\pi$
$277$	−1.05351e6	+	1.05351e6i	−0.824974	+	0.824974i	0.161842	+	0.986817i	$0.448256\pi$
$278$		0			0
$279$		−	273227.i		−	0.210142i
$280$		0			0
$281$			14414.9i			0.0108904i	0.999985	+	0.00544522i	$0.00173328\pi$
$281$			14414.9i			0.0108904i	−0.999985	+	0.00544522i	$0.998267\pi$
$282$		0			0
$283$	328025.	−	328025.i	0.243468	−	0.243468i	−0.574815	−	0.818283i	$-0.694926\pi$
$283$	328025.	−	328025.i	0.243468	−	0.243468i	0.818283	+	0.574815i	$0.194926\pi$
$284$		0			0
$285$	−308628.	−	308628.i	−0.225073	−	0.225073i
$286$		0			0
$287$	1.79641e6			1.28736
$288$		0			0
$289$	−494914.			−0.348566
$290$		0			0
$291$	−402296.	−	402296.i	−0.278492	−	0.278492i
$292$		0			0
$293$	1.52796e6	−	1.52796e6i	1.03978	−	1.03978i	0.0406088	−	0.999175i	$-0.487070\pi$
$293$	1.52796e6	−	1.52796e6i	1.03978	−	1.03978i	0.999175	−	0.0406088i	$-0.0129297\pi$
$294$		0			0
$295$			457158.i			0.305852i
$296$		0			0
$297$		−	671385.i		−	0.441652i
$298$		0			0
$299$	−508679.	+	508679.i	−0.329053	+	0.329053i
$300$		0			0
$301$	1.23005e6	+	1.23005e6i	0.782543	+	0.782543i
$302$		0			0
$303$	−1.94017e6			−1.21404
$304$		0			0
$305$	−863298.			−0.531387
$306$		0			0
$307$	−588349.	−	588349.i	−0.356278	−	0.356278i	0.506161	−	0.862439i	$-0.331064\pi$
$307$	−588349.	−	588349.i	−0.356278	−	0.356278i	−0.862439	+	0.506161i	$0.831064\pi$
$308$		0			0
$309$	−1.67677e6	+	1.67677e6i	−0.999025	+	0.999025i
$310$		0			0
$311$			133732.i			0.0784036i	0.999231	+	0.0392018i	$0.0124815\pi$
$311$			133732.i			0.0784036i	−0.999231	+	0.0392018i	$0.987518\pi$
$312$		0			0
$313$			2.56615e6i			1.48054i	0.672307	+	0.740272i	$0.265303\pi$
$313$			2.56615e6i			1.48054i	−0.672307	+	0.740272i	$0.734697\pi$
$314$		0			0
$315$	436497.	−	436497.i	0.247859	−	0.247859i
$316$		0			0
$317$	1.19775e6	+	1.19775e6i	0.669448	+	0.669448i	0.957588	−	0.288140i	$-0.0930370\pi$
$317$	1.19775e6	+	1.19775e6i	0.669448	+	0.669448i	−0.288140	+	0.957588i	$0.593037\pi$
$318$		0			0
$319$	−809385.			−0.445327
$320$		0			0
$321$	1.67258e6			0.905994
$322$		0			0
$323$	−1.06486e6	−	1.06486e6i	−0.567917	−	0.567917i
$324$		0			0
$325$	−120579.	+	120579.i	−0.0633231	+	0.0633231i
$326$		0			0
$327$			277793.i			0.143665i
$328$		0			0
$329$		−	1.22523e6i		−	0.624063i
$330$		0			0
$331$	174005.	−	174005.i	0.0872955	−	0.0872955i	−0.662111	−	0.749406i	$-0.730339\pi$
$331$	174005.	−	174005.i	0.0872955	−	0.0872955i	0.749406	+	0.662111i	$0.230339\pi$
$332$		0			0
$333$	−1.25112e6	−	1.25112e6i	−0.618284	−	0.618284i
$334$		0			0
$335$	−494406.			−0.240697
$336$		0			0
$337$	3.44408e6			1.65196			0.825978	−	0.563703i	$-0.190624\pi$
$337$	3.44408e6			1.65196			0.825978	+	0.563703i	$0.190624\pi$
$338$		0			0
$339$	−567516.	−	567516.i	−0.268212	−	0.268212i
$340$		0			0
$341$	−271014.	+	271014.i	−0.126214	+	0.126214i
$342$		0			0
$343$		−	2.01168e6i		−	0.923257i
$344$		0			0
$345$			734945.i			0.332435i
$346$		0			0
$347$	315686.	−	315686.i	0.140745	−	0.140745i	−0.633224	−	0.773969i	$-0.718269\pi$
$347$	315686.	−	315686.i	0.140745	−	0.140745i	0.773969	+	0.633224i	$0.218269\pi$
$348$		0			0
$349$	−623357.	−	623357.i	−0.273951	−	0.273951i	0.556737	−	0.830689i	$-0.312053\pi$
$349$	−623357.	−	623357.i	−0.273951	−	0.273951i	−0.830689	+	0.556737i	$0.812053\pi$
$350$		0			0
$351$	1.10027e6			0.476684
$352$		0			0
$353$	−3.20077e6			−1.36716			−0.683578	−	0.729878i	$-0.739577\pi$
$353$	−3.20077e6			−1.36716			−0.683578	+	0.729878i	$0.739577\pi$
$354$		0			0
$355$	−861488.	−	861488.i	−0.362809	−	0.362809i
$356$		0			0
$357$	−1.57748e6	+	1.57748e6i	−0.655079	+	0.655079i
$358$		0			0
$359$			1.76174e6i			0.721449i	0.932672	+	0.360724i	$0.117471\pi$
$359$			1.76174e6i			0.721449i	−0.932672	+	0.360724i	$0.882529\pi$
$360$		0			0
$361$		−	24224.3i		−	0.00978323i
$362$		0			0
$363$	1.05120e6	−	1.05120e6i	0.418715	−	0.418715i
$364$		0			0
$365$	−1.56224e6	−	1.56224e6i	−0.613782	−	0.613782i
$366$		0			0
$367$	322537.			0.125001			0.0625006	−	0.998045i	$-0.480092\pi$
$367$	322537.			0.125001			0.0625006	+	0.998045i	$0.480092\pi$
$368$		0			0
$369$	−1.02480e6			−0.391809
$370$		0			0
$371$	−2.58484e6	−	2.58484e6i	−0.974987	−	0.974987i
$372$		0			0
$373$	1.70422e6	−	1.70422e6i	0.634238	−	0.634238i	−0.314890	−	0.949128i	$-0.601968\pi$
$373$	1.70422e6	−	1.70422e6i	0.634238	−	0.634238i	0.949128	+	0.314890i	$0.101968\pi$
$374$		0			0
$375$			174213.i			0.0639740i
$376$		0			0
$377$		−	1.32642e6i		−	0.480649i
$378$		0			0
$379$	1.11070e6	−	1.11070e6i	0.397191	−	0.397191i	−0.480050	−	0.877241i	$-0.659381\pi$
$379$	1.11070e6	−	1.11070e6i	0.397191	−	0.397191i	0.877241	+	0.480050i	$0.159381\pi$
$380$		0			0
$381$	1.88847e6	+	1.88847e6i	0.666495	+	0.666495i
$382$		0			0
$383$	−4.30045e6			−1.49802			−0.749009	−	0.662559i	$-0.769470\pi$
$383$	−4.30045e6			−1.49802			−0.749009	+	0.662559i	$0.769470\pi$
$384$		0			0
$385$	−865924.			−0.297734
$386$		0			0
$387$	−701714.	−	701714.i	−0.238167	−	0.238167i
$388$		0			0
$389$	4.14998e6	−	4.14998e6i	1.39050	−	1.39050i	0.566313	−	0.824190i	$-0.308369\pi$
$389$	4.14998e6	−	4.14998e6i	1.39050	−	1.39050i	0.824190	−	0.566313i	$-0.191631\pi$
$390$		0			0
$391$			2.53577e6i			0.838820i
$392$		0			0
$393$		−	2.09412e6i		−	0.683943i
$394$		0			0
$395$	−705051.	+	705051.i	−0.227367	+	0.227367i
$396$		0			0
$397$	−1.05760e6	−	1.05760e6i	−0.336781	−	0.336781i	0.518374	−	0.855154i	$-0.326538\pi$
$397$	−1.05760e6	−	1.05760e6i	−0.336781	−	0.336781i	−0.855154	+	0.518374i	$0.826538\pi$
$398$		0			0
$399$	3.63221e6			1.14219
$400$		0			0
$401$	653994.			0.203101			0.101551	−	0.994830i	$-0.467620\pi$
$401$	653994.			0.203101			0.101551	+	0.994830i	$0.467620\pi$
$402$		0			0
$403$	−444139.	−	444139.i	−0.136225	−	0.136225i
$404$		0			0
$405$	285006.	−	285006.i	0.0863410	−	0.0863410i
$406$		0			0
$407$			2.48197e6i			0.742696i
$408$		0			0
$409$		−	3.75150e6i		−	1.10891i	−0.832214	−	0.554455i	$-0.812927\pi$
$409$		−	3.75150e6i		−	1.10891i	0.832214	−	0.554455i	$-0.187073\pi$
$410$		0			0
$411$	−1.22245e6	+	1.22245e6i	−0.356966	+	0.356966i
$412$		0			0
$413$	−2.69012e6	−	2.69012e6i	−0.776063	−	0.776063i
$414$		0			0
$415$	−1.60702e6			−0.458039
$416$		0			0
$417$	−4.13179e6			−1.16359
$418$		0			0
$419$	−191869.	−	191869.i	−0.0533913	−	0.0533913i	0.679907	−	0.733298i	$-0.262020\pi$
$419$	−191869.	−	191869.i	−0.0533913	−	0.0533913i	−0.733298	+	0.679907i	$0.762020\pi$
$420$		0			0
$421$	1.78024e6	−	1.78024e6i	0.489523	−	0.489523i	−0.418633	−	0.908156i	$-0.637491\pi$
$421$	1.78024e6	−	1.78024e6i	0.489523	−	0.489523i	0.908156	+	0.418633i	$0.137491\pi$
$422$		0			0
$423$			698962.i			0.189934i
$424$		0			0
$425$			601087.i			0.161423i
$426$		0			0
$427$	5.08003e6	−	5.08003e6i	1.34833	−	1.34833i
$428$		0			0
$429$	−358123.	−	358123.i	−0.0939483	−	0.0939483i
$430$		0			0
$431$	−2.05116e6			−0.531871			−0.265936	−	0.963991i	$-0.585681\pi$
$431$	−2.05116e6			−0.531871			−0.265936	+	0.963991i	$0.585681\pi$
$432$		0			0
$433$	−4.88523e6			−1.25217			−0.626087	−	0.779753i	$-0.715345\pi$
$433$	−4.88523e6			−1.25217			−0.626087	+	0.779753i	$0.715345\pi$
$434$		0			0
$435$	−958214.	−	958214.i	−0.242795	−	0.242795i
$436$		0			0
$437$	2.91936e6	−	2.91936e6i	0.731280	−	0.731280i
$438$		0			0
$439$		−	4.22642e6i		−	1.04667i	−0.852126	−	0.523337i	$-0.824687\pi$
$439$		−	4.22642e6i		−	1.04667i	0.852126	−	0.523337i	$-0.175313\pi$
$440$		0			0
$441$			3.14235e6i			0.769410i
$442$		0			0
$443$	−3.63313e6	+	3.63313e6i	−0.879573	+	0.879573i	−0.993490	−	0.113918i	$-0.963660\pi$
$443$	−3.63313e6	+	3.63313e6i	−0.879573	+	0.879573i	0.113918	+	0.993490i	$0.463660\pi$
$444$		0			0
$445$	346873.	+	346873.i	0.0830368	+	0.0830368i
$446$		0			0
$447$	3.02811e6			0.716808
$448$		0			0
$449$	−1.68435e6			−0.394291			−0.197145	−	0.980374i	$-0.563167\pi$
$449$	−1.68435e6			−0.394291			−0.197145	+	0.980374i	$0.563167\pi$
$450$		0			0
$451$	1.01650e6	+	1.01650e6i	0.235325	+	0.235325i
$452$		0			0
$453$	−3.36852e6	+	3.36852e6i	−0.771248	+	0.771248i
$454$		0			0
$455$		−	1.41908e6i		−	0.321350i
$456$		0			0
$457$		−	3.26840e6i		−	0.732056i	−0.930604	−	0.366028i	$-0.880717\pi$
$457$		−	3.26840e6i		−	0.732056i	0.930604	−	0.366028i	$-0.119283\pi$
$458$		0			0
$459$	2.74242e6	−	2.74242e6i	0.607579	−	0.607579i
$460$		0			0
$461$	−5.01159e6	−	5.01159e6i	−1.09831	−	1.09831i	−0.994609	−	0.103697i	$-0.966933\pi$
$461$	−5.01159e6	−	5.01159e6i	−1.09831	−	1.09831i	−0.103697	−	0.994609i	$-0.533067\pi$
$462$		0			0
$463$	455834.			0.0988221			0.0494110	−	0.998779i	$-0.484266\pi$
$463$	455834.			0.0988221			0.0494110	+	0.998779i	$0.484266\pi$
$464$		0			0
$465$	−641696.			−0.137625
$466$		0			0
$467$	277375.	+	277375.i	0.0588539	+	0.0588539i	0.735921	−	0.677067i	$-0.236749\pi$
$467$	277375.	+	277375.i	0.0588539	+	0.0588539i	−0.677067	+	0.735921i	$0.736749\pi$
$468$		0			0
$469$	2.90930e6	−	2.90930e6i	0.610741	−	0.610741i
$470$		0			0
$471$			3.62128e6i			0.752160i
$472$		0			0
$473$			1.39206e6i			0.286092i
$474$		0			0
$475$	692013.	−	692013.i	0.140728	−	0.140728i
$476$		0			0
$477$	1.47458e6	+	1.47458e6i	0.296738	+	0.296738i
$478$		0			0
$479$	−5.13891e6			−1.02337			−0.511684	−	0.859173i	$-0.670978\pi$
$479$	−5.13891e6			−1.02337			−0.511684	+	0.859173i	$0.670978\pi$
$480$		0			0
$481$	−4.06746e6			−0.801606
$482$		0			0
$483$	−4.32474e6	−	4.32474e6i	−0.843514	−	0.843514i
$484$		0			0
$485$	902035.	−	902035.i	0.174128	−	0.174128i
$486$		0			0
$487$			3.67637e6i			0.702420i	0.936297	+	0.351210i	$0.114230\pi$
$487$			3.67637e6i			0.702420i	−0.936297	+	0.351210i	$0.885770\pi$
$488$		0			0
$489$			5.30247e6i			1.00278i
$490$		0			0
$491$	1.38862e6	−	1.38862e6i	0.259943	−	0.259943i	−0.565088	−	0.825031i	$-0.691158\pi$
$491$	1.38862e6	−	1.38862e6i	0.259943	−	0.259943i	0.825031	+	0.565088i	$0.191158\pi$
$492$		0			0
$493$	−3.30612e6	−	3.30612e6i	−0.612634	−	0.612634i
$494$		0			0
$495$	493987.			0.0906155
$496$		0			0
$497$	1.01388e7			1.84117
$498$		0			0
$499$	−1.15528e6	−	1.15528e6i	−0.207699	−	0.207699i	0.595590	−	0.803289i	$-0.296918\pi$
$499$	−1.15528e6	−	1.15528e6i	−0.207699	−	0.207699i	−0.803289	+	0.595590i	$0.796918\pi$
$500$		0			0
$501$	2.66485e6	−	2.66485e6i	0.474327	−	0.474327i
$502$		0			0
$503$			3.23595e6i			0.570271i	0.958487	+	0.285135i	$0.0920386\pi$
$503$			3.23595e6i			0.570271i	−0.958487	+	0.285135i	$0.907961\pi$
$504$		0			0
$505$		−	4.35030e6i		−	0.759085i
$506$		0			0
$507$	−2.34038e6	+	2.34038e6i	−0.404359	+	0.404359i
$508$		0			0
$509$	7.03415e6	+	7.03415e6i	1.20342	+	1.20342i	0.973120	+	0.230301i	$0.0739709\pi$
$509$	7.03415e6	+	7.03415e6i	1.20342	+	1.20342i	0.230301	+	0.973120i	$0.426029\pi$
$510$		0			0
$511$	1.83858e7			3.11480
$512$		0			0
$513$	−6.31454e6			−1.05937
$514$		0			0
$515$	−3.75968e6	−	3.75968e6i	−0.624644	−	0.624644i
$516$		0			0
$517$	693302.	−	693302.i	0.114076	−	0.114076i
$518$		0			0
$519$		−	2.27483e6i		−	0.370706i
$520$		0			0
$521$			1.02322e7i			1.65149i	0.564042	+	0.825746i	$0.309246\pi$
$521$			1.02322e7i			1.65149i	−0.564042	+	0.825746i	$0.690754\pi$
$522$		0			0
$523$	1.85939e6	−	1.85939e6i	0.297246	−	0.297246i	−0.542688	−	0.839934i	$-0.682593\pi$
$523$	1.85939e6	−	1.85939e6i	0.297246	−	0.297246i	0.839934	+	0.542688i	$0.182593\pi$
$524$		0			0
$525$	−1.02515e6	−	1.02515e6i	−0.162326	−	0.162326i
$526$		0			0
$527$	−2.21404e6			−0.347263
$528$		0			0
$529$	−515597.			−0.0801072
$530$		0			0
$531$	1.53464e6	+	1.53464e6i	0.236195	+	0.236195i
$532$		0			0
$533$	−1.66585e6	+	1.66585e6i	−0.253990	+	0.253990i
$534$		0			0
$535$			3.75030e6i			0.566476i
$536$		0			0
$537$		−	6.07722e6i		−	0.909430i
$538$		0			0
$539$	3.11690e6	−	3.11690e6i	0.462116	−	0.462116i
$540$		0			0
$541$	5.40070e6	+	5.40070e6i	0.793336	+	0.793336i	0.982035	−	0.188699i	$-0.0604271\pi$
$541$	5.40070e6	+	5.40070e6i	0.793336	+	0.793336i	−0.188699	+	0.982035i	$0.560427\pi$
$542$		0			0
$543$	2.13809e6			0.311191
$544$		0			0
$545$	−622873.			−0.0898273
$546$		0			0
$547$	7.23243e6	+	7.23243e6i	1.03351	+	1.03351i	0.999419	+	0.0340941i	$0.0108546\pi$
$547$	7.23243e6	+	7.23243e6i	1.03351	+	1.03351i	0.0340941	+	0.999419i	$0.489145\pi$
$548$		0			0
$549$	−2.89802e6	+	2.89802e6i	−0.410366	+	0.410366i
$550$		0			0
$551$			7.61246e6i			1.06818i
$552$		0			0
$553$		−	8.29767e6i		−	1.15383i
$554$		0			0
$555$	−2.93836e6	+	2.93836e6i	−0.404923	+	0.404923i
$556$		0			0
$557$	3.43079e6	+	3.43079e6i	0.468550	+	0.468550i	0.901445	−	0.432894i	$-0.142508\pi$
$557$	3.43079e6	+	3.43079e6i	0.468550	+	0.468550i	−0.432894	+	0.901445i	$0.642508\pi$
$558$		0			0
$559$	−2.28131e6			−0.308784
$560$		0			0
$561$	−1.78525e6			−0.239492
$562$		0			0
$563$	−5.24831e6	−	5.24831e6i	−0.697828	−	0.697828i	0.266114	−	0.963942i	$-0.414260\pi$
$563$	−5.24831e6	−	5.24831e6i	−0.697828	−	0.697828i	−0.963942	+	0.266114i	$0.914260\pi$
$564$		0			0
$565$	1.27250e6	−	1.27250e6i	0.167701	−	0.167701i
$566$		0			0
$567$			3.35421e6i			0.438160i
$568$		0			0
$569$			8.98310e6i			1.16318i	0.813483	+	0.581588i	$0.197569\pi$
$569$			8.98310e6i			1.16318i	−0.813483	+	0.581588i	$0.802431\pi$
$570$		0			0
$571$	2.67366e6	−	2.67366e6i	0.343176	−	0.343176i	−0.514384	−	0.857560i	$-0.671979\pi$
$571$	2.67366e6	−	2.67366e6i	0.343176	−	0.343176i	0.857560	+	0.514384i	$0.171979\pi$
$572$		0			0
$573$	−552858.	−	552858.i	−0.0703439	−	0.0703439i
$574$		0			0
$575$	−1.64791e6			−0.207856
$576$		0			0
$577$	−2.47918e6			−0.310005			−0.155003	−	0.987914i	$-0.549539\pi$
$577$	−2.47918e6			−0.310005			−0.155003	+	0.987914i	$0.549539\pi$
$578$		0			0
$579$	−5.62972e6	−	5.62972e6i	−0.697895	−	0.697895i
$580$		0			0
$581$	9.45644e6	−	9.45644e6i	1.16222	−	1.16222i
$582$		0			0
$583$		−	2.92528e6i		−	0.356448i
$584$		0			0
$585$			809547.i			0.0978030i
$586$		0			0
$587$	−3.20495e6	+	3.20495e6i	−0.383906	+	0.383906i	−0.872507	−	0.488601i	$-0.837507\pi$
$587$	−3.20495e6	+	3.20495e6i	−0.383906	+	0.383906i	0.488601	+	0.872507i	$0.337507\pi$
$588$		0			0
$589$	2.54895e6	+	2.54895e6i	0.302743	+	0.302743i
$590$		0			0
$591$	6.95575e6			0.819172
$592$		0			0
$593$	3.73079e6			0.435677			0.217838	−	0.975985i	$-0.430099\pi$
$593$	3.73079e6			0.435677			0.217838	+	0.975985i	$0.430099\pi$
$594$		0			0
$595$	−3.53706e6	−	3.53706e6i	−0.409591	−	0.409591i
$596$		0			0
$597$	−1.06554e6	+	1.06554e6i	−0.122359	+	0.122359i
$598$		0			0
$599$			2.96317e6i			0.337434i	0.985665	+	0.168717i	$0.0539625\pi$
$599$			2.96317e6i			0.337434i	−0.985665	+	0.168717i	$0.946038\pi$
$600$		0			0
$601$			1.10701e7i			1.25016i	0.780561	+	0.625079i	$0.214933\pi$
$601$			1.10701e7i			1.25016i	−0.780561	+	0.625079i	$0.785067\pi$
$602$		0			0
$603$	−1.65968e6	+	1.65968e6i	−0.185879	+	0.185879i
$604$		0			0
$605$	2.35702e6	+	2.35702e6i	0.261803	+	0.261803i
$606$		0			0
$607$	−1.42525e7			−1.57007			−0.785036	−	0.619450i	$-0.787356\pi$
$607$	−1.42525e7			−1.57007			−0.785036	+	0.619450i	$0.787356\pi$
$608$		0			0
$609$	1.12771e7			1.23212
$610$		0			0
$611$	1.13618e6	+	1.13618e6i	0.123125	+	0.123125i
$612$		0			0
$613$	−5.52901e6	+	5.52901e6i	−0.594287	+	0.594287i	−0.938787	−	0.344499i	$-0.888049\pi$
$613$	−5.52901e6	+	5.52901e6i	−0.594287	+	0.594287i	0.344499	+	0.938787i	$0.388049\pi$
$614$		0			0
$615$			2.40683e6i			0.256601i
$616$		0			0
$617$			1.12751e7i			1.19236i	0.802852	+	0.596178i	$0.203315\pi$
$617$			1.12751e7i			1.19236i	−0.802852	+	0.596178i	$0.796685\pi$
$618$		0			0
$619$	−7.49743e6	+	7.49743e6i	−0.786476	+	0.786476i	−0.980915	−	0.194438i	$-0.937712\pi$
$619$	−7.49743e6	+	7.49743e6i	−0.786476	+	0.786476i	0.194438	+	0.980915i	$0.437712\pi$
$620$		0			0
$621$	7.51848e6	+	7.51848e6i	0.782350	+	0.782350i
$622$		0			0
$623$	−4.08231e6			−0.421392
$624$		0			0
$625$	−390625.			−0.0400000
$626$		0			0
$627$	2.05530e6	+	2.05530e6i	0.208788	+	0.208788i
$628$		0			0
$629$	−1.01382e7	+	1.01382e7i	−1.02172	+	1.02172i
$630$		0			0
$631$		−	7.22894e6i		−	0.722771i	−0.932416	−	0.361386i	$-0.882304\pi$
$631$		−	7.22894e6i		−	0.722771i	0.932416	−	0.361386i	$-0.117696\pi$
$632$		0			0
$633$		−	1.06097e7i		−	1.05243i
$634$		0			0
$635$	−4.23436e6	+	4.23436e6i	−0.416729	+	0.416729i
$636$		0			0
$637$	5.10798e6	+	5.10798e6i	0.498770	+	0.498770i
$638$		0			0
$639$	−5.78389e6			−0.560361
$640$		0			0
$641$	−1.53670e7			−1.47722			−0.738610	−	0.674133i	$-0.764517\pi$
$641$	−1.53670e7			−1.47722			−0.738610	+	0.674133i	$0.764517\pi$
$642$		0			0
$643$	288960.	+	288960.i	0.0275620	+	0.0275620i	0.720753	−	0.693191i	$-0.243796\pi$
$643$	288960.	+	288960.i	0.0275620	+	0.0275620i	−0.693191	+	0.720753i	$0.743796\pi$
$644$		0			0
$645$	−1.64803e6	+	1.64803e6i	−0.155979	+	0.155979i
$646$		0			0
$647$		−	1.39042e7i		−	1.30583i	−0.757432	−	0.652914i	$-0.773546\pi$
$647$		−	1.39042e7i		−	1.30583i	0.757432	−	0.652914i	$-0.226454\pi$
$648$		0			0
$649$		−	3.04443e6i		−	0.283723i
$650$		0			0
$651$	3.77603e6	−	3.77603e6i	0.349207	−	0.349207i
$652$		0			0
$653$	2.44568e6	+	2.44568e6i	0.224449	+	0.224449i	0.810369	−	0.585920i	$-0.199267\pi$
$653$	2.44568e6	+	2.44568e6i	0.224449	+	0.224449i	−0.585920	+	0.810369i	$0.699267\pi$
$654$		0			0
$655$	4.69548e6			0.427638
$656$		0			0
$657$	−1.04886e7			−0.947990
$658$		0			0
$659$	5.00967e6	+	5.00967e6i	0.449361	+	0.449361i	0.895142	−	0.445781i	$-0.147074\pi$
$659$	5.00967e6	+	5.00967e6i	0.449361	+	0.449361i	−0.445781	+	0.895142i	$0.647074\pi$
$660$		0			0
$661$	1.37540e7	−	1.37540e7i	1.22441	−	1.22441i	0.258359	−	0.966049i	$-0.416818\pi$
$661$	1.37540e7	−	1.37540e7i	1.22441	−	1.22441i	0.966049	−	0.258359i	$-0.0831816\pi$
$662$		0			0
$663$		−	2.92567e6i		−	0.258488i
$664$		0			0
$665$			8.14422e6i			0.714160i
$666$		0			0
$667$	9.06387e6	−	9.06387e6i	0.788859	−	0.788859i
$668$		0			0
$669$	1.05420e7	+	1.05420e7i	0.910662	+	0.910662i
$670$		0			0
$671$	5.74911e6			0.492940
$672$		0			0
$673$	−2.01324e7			−1.71339			−0.856696	−	0.515821i	$-0.827487\pi$
$673$	−2.01324e7			−1.71339			−0.856696	+	0.515821i	$0.827487\pi$
$674$		0			0
$675$	1.78220e6	+	1.78220e6i	0.150556	+	0.150556i
$676$		0			0
$677$	−2.09354e6	+	2.09354e6i	−0.175554	+	0.175554i	−0.789414	−	0.613861i	$-0.789616\pi$
$677$	−2.09354e6	+	2.09354e6i	−0.175554	+	0.175554i	0.613861	+	0.789414i	$0.289616\pi$
$678$		0			0
$679$			1.06160e7i			0.883659i
$680$		0			0
$681$		−	379698.i		−	0.0313740i
$682$		0			0
$683$	−73464.0	+	73464.0i	−0.00602591	+	0.00602591i	−0.710113	−	0.704087i	$-0.751356\pi$
$683$	−73464.0	+	73464.0i	−0.00602591	+	0.00602591i	0.704087	+	0.710113i	$0.251356\pi$
$684$		0			0
$685$	−2.74100e6	−	2.74100e6i	−0.223194	−	0.223194i
$686$		0			0
$687$	−5.24174e6			−0.423724
$688$		0			0
$689$	4.79395e6			0.384721
$690$		0			0
$691$	8.05791e6	+	8.05791e6i	0.641989	+	0.641989i	0.951044	−	0.309055i	$-0.100013\pi$
$691$	8.05791e6	+	8.05791e6i	0.641989	+	0.641989i	−0.309055	+	0.951044i	$0.600013\pi$
$692$		0			0
$693$	−2.90684e6	+	2.90684e6i	−0.229926	+	0.229926i
$694$		0			0
$695$		−	9.26439e6i		−	0.727537i
$696$		0			0
$697$			8.30428e6i			0.647470i
$698$		0			0
$699$	−7.16926e6	+	7.16926e6i	−0.554985	+	0.554985i
$700$		0			0
$701$	−1.51961e7	−	1.51961e7i	−1.16799	−	1.16799i	−0.982681	−	0.185307i	$-0.940672\pi$
$701$	−1.51961e7	−	1.51961e7i	−1.16799	−	1.16799i	−0.185307	−	0.982681i	$-0.559328\pi$
$702$		0			0
$703$	2.33436e7			1.78147
$704$		0			0
$705$	1.64157e6			0.124390
$706$		0			0
$707$	2.55991e7	+	2.55991e7i	1.92609	+	1.92609i
$708$		0			0
$709$	3.46603e6	−	3.46603e6i	0.258951	−	0.258951i	−0.565677	−	0.824627i	$-0.691385\pi$
$709$	3.46603e6	−	3.46603e6i	0.258951	−	0.258951i	0.824627	+	0.565677i	$0.191385\pi$
$710$		0			0
$711$			4.73360e6i			0.351170i
$712$		0			0
$713$		−	6.06989e6i		−	0.447154i
$714$		0			0
$715$	802990.	−	802990.i	0.0587415	−	0.0587415i
$716$		0			0
$717$	−2.04801e6	−	2.04801e6i	−0.148776	−	0.148776i
$718$		0			0
$719$	−1.14717e7			−0.827568			−0.413784	−	0.910375i	$-0.635793\pi$
$719$	−1.14717e7			−0.827568			−0.413784	+	0.910375i	$0.635793\pi$
$720$		0			0
$721$	4.42472e7			3.16992
$722$		0			0
$723$	−1.57054e6	−	1.57054e6i	−0.111738	−	0.111738i
$724$		0			0
$725$	2.14853e6	−	2.14853e6i	0.151808	−	0.151808i
$726$		0			0
$727$		−	3.32886e6i		−	0.233593i	−0.993156	−	0.116796i	$-0.962737\pi$
$727$		−	3.32886e6i		−	0.233593i	0.993156	−	0.116796i	$-0.0372625\pi$
$728$		0			0
$729$		−	1.28395e7i		−	0.894804i
$730$		0			0
$731$	−5.68619e6	+	5.68619e6i	−0.393575	+	0.393575i
$732$		0			0
$733$	−1.00193e7	−	1.00193e7i	−0.688772	−	0.688772i	0.273188	−	0.961961i	$-0.411922\pi$
$733$	−1.00193e7	−	1.00193e7i	−0.688772	−	0.688772i	−0.961961	+	0.273188i	$0.911922\pi$
$734$		0			0
$735$	7.38006e6			0.503897
$736$		0			0
$737$	3.29248e6			0.223282
$738$		0			0
$739$	8.02079e6	+	8.02079e6i	0.540264	+	0.540264i	0.923606	−	0.383342i	$-0.125227\pi$
$739$	8.02079e6	+	8.02079e6i	0.540264	+	0.540264i	−0.383342	+	0.923606i	$0.625227\pi$
$740$		0			0
$741$	−3.36823e6	+	3.36823e6i	−0.225349	+	0.225349i
$742$		0			0
$743$			1.92310e7i			1.27800i	0.769207	+	0.639000i	$0.220651\pi$
$743$			1.92310e7i			1.27800i	−0.769207	+	0.639000i	$0.779349\pi$
$744$		0			0
$745$			6.78969e6i			0.448187i
$746$		0			0
$747$	−5.39465e6	+	5.39465e6i	−0.353722	+	0.353722i
$748$		0			0
$749$	−2.20684e7	−	2.20684e7i	−1.43736	−	1.43736i
$750$		0			0
$751$	2.91259e6			0.188443			0.0942214	−	0.995551i	$-0.469964\pi$
$751$	2.91259e6			0.188443			0.0942214	+	0.995551i	$0.469964\pi$
$752$		0			0
$753$	8.23756e6			0.529433
$754$		0			0
$755$	−7.55297e6	−	7.55297e6i	−0.482226	−	0.482226i
$756$		0			0
$757$	−1.75862e7	+	1.75862e7i	−1.11541	+	1.11541i	−0.123001	+	0.992407i	$0.539252\pi$
$757$	−1.75862e7	+	1.75862e7i	−1.11541	+	1.11541i	−0.992407	+	0.123001i	$0.960748\pi$
$758$		0			0
$759$		−	4.89434e6i		−	0.308383i
$760$		0			0
$761$			9.66060e6i			0.604704i	0.953196	+	0.302352i	$0.0977717\pi$
$761$			9.66060e6i			0.604704i	−0.953196	+	0.302352i	$0.902228\pi$
$762$		0			0
$763$	3.66526e6	−	3.66526e6i	0.227926	−	0.227926i
$764$		0			0
$765$	2.01780e6	+	2.01780e6i	0.124659	+	0.124659i
$766$		0			0
$767$	4.98922e6			0.306227
$768$		0			0
$769$	2.46747e7			1.50465			0.752325	−	0.658793i	$-0.228932\pi$
$769$	2.46747e7			1.50465			0.752325	+	0.658793i	$0.228932\pi$
$770$		0			0
$771$	−9.81883e6	−	9.81883e6i	−0.594873	−	0.594873i
$772$		0			0
$773$	−1.25753e7	+	1.25753e7i	−0.756952	+	0.756952i	−0.975766	−	0.218815i	$-0.929781\pi$
$773$	−1.25753e7	+	1.25753e7i	−0.756952	+	0.756952i	0.218815	+	0.975766i	$0.429781\pi$
$774$		0			0
$775$		−	1.43882e6i		−	0.0860505i
$776$		0			0
$777$		−	3.45812e7i		−	2.05488i
$778$		0			0
$779$	9.56046e6	−	9.56046e6i	0.564462	−	0.564462i
$780$		0			0
$781$	5.73705e6	+	5.73705e6i	0.336559	+	0.336559i
$782$		0			0
$783$	−1.96051e7			−1.14278
$784$		0			0
$785$	−8.11972e6			−0.470291
$786$		0			0
$787$	−2.75578e6	−	2.75578e6i	−0.158602	−	0.158602i	0.623345	−	0.781947i	$-0.285773\pi$
$787$	−2.75578e6	−	2.75578e6i	−0.158602	−	0.158602i	−0.781947	+	0.623345i	$0.785773\pi$
$788$		0			0
$789$	−1.52616e7	+	1.52616e7i	−0.872787	+	0.872787i
$790$		0			0
$791$			1.49759e7i			0.851041i
$792$		0			0
$793$			9.42164e6i			0.532039i
$794$		0			0
$795$	3.46318e6	−	3.46318e6i	0.194338	−	0.194338i
$796$		0			0
$797$	409177.	+	409177.i	0.0228173	+	0.0228173i	0.718423	−	0.695606i	$-0.244864\pi$
$797$	409177.	+	409177.i	0.0228173	+	0.0228173i	−0.695606	+	0.718423i	$0.744864\pi$
$798$		0			0
$799$	5.66389e6			0.313869
$800$		0			0
$801$	2.32885e6			0.128251
$802$		0			0
$803$	1.04037e7	+	1.04037e7i	0.569373	+	0.569373i
$804$		0			0
$805$	9.69702e6	−	9.69702e6i	0.527410	−	0.527410i
$806$		0			0
$807$		−	9.91840e6i		−	0.536115i
$808$		0			0
$809$		−	9.46799e6i		−	0.508612i	−0.967124	−	0.254306i	$-0.918153\pi$
$809$		−	9.46799e6i		−	0.508612i	0.967124	−	0.254306i	$-0.0818470\pi$
$810$		0			0
$811$	−9.11567e6	+	9.11567e6i	−0.486672	+	0.486672i	−0.907254	−	0.420582i	$-0.861826\pi$
$811$	−9.11567e6	+	9.11567e6i	−0.486672	+	0.486672i	0.420582	+	0.907254i	$0.361826\pi$
$812$		0			0
$813$	−1.26947e7	−	1.26947e7i	−0.673591	−	0.673591i
$814$		0			0
$815$	−1.18893e7			−0.626993
$816$		0			0
$817$	1.30927e7			0.686235
$818$		0			0
$819$	−4.76373e6	−	4.76373e6i	−0.248163	−	0.248163i
$820$		0			0
$821$	200028.	−	200028.i	0.0103570	−	0.0103570i	−0.701909	−	0.712266i	$-0.747669\pi$
$821$	200028.	−	200028.i	0.0103570	−	0.0103570i	0.712266	+	0.701909i	$0.247669\pi$
$822$		0			0
$823$		−	8.13591e6i		−	0.418703i	−0.977840	−	0.209352i	$-0.932865\pi$
$823$		−	8.13591e6i		−	0.418703i	0.977840	−	0.209352i	$-0.0671353\pi$
$824$		0			0
$825$		−	1.16017e6i		−	0.0593453i
$826$		0			0
$827$	−7.65710e6	+	7.65710e6i	−0.389315	+	0.389315i	−0.874443	−	0.485128i	$-0.838773\pi$
$827$	−7.65710e6	+	7.65710e6i	−0.389315	+	0.389315i	0.485128	+	0.874443i	$0.338773\pi$
$828$		0			0
$829$	7.43206e6	+	7.43206e6i	0.375598	+	0.375598i	0.869511	−	0.493913i	$-0.164434\pi$
$829$	7.43206e6	+	7.43206e6i	0.375598	+	0.375598i	−0.493913	+	0.869511i	$0.664434\pi$
$830$		0			0
$831$	1.66118e7			0.834476
$832$		0			0
$833$	2.54634e7			1.27146
$834$		0			0
$835$	5.97517e6	+	5.97517e6i	0.296575	+	0.296575i
$836$		0			0
$837$	−6.56455e6	+	6.56455e6i	−0.323885	+	0.323885i
$838$		0			0
$839$		−	1.10391e7i		−	0.541411i	−0.962662	−	0.270706i	$-0.912743\pi$
$839$		−	1.10391e7i		−	0.541411i	0.962662	−	0.270706i	$-0.0872570\pi$
$840$		0			0
$841$			3.12364e6i			0.152290i
$842$		0			0
$843$	113647.	−	113647.i	0.00550794	−	0.00550794i
$844$		0			0
$845$	−5.24765e6	−	5.24765e6i	−0.252827	−	0.252827i
$846$		0			0
$847$	−2.77395e7			−1.32859
$848$		0			0
$849$	−5.17230e6			−0.246272
$850$		0			0
$851$	−2.77943e7	−	2.77943e7i	−1.31562	−	1.31562i
$852$		0			0
$853$	8.06632e6	−	8.06632e6i	0.379580	−	0.379580i	−0.491371	−	0.870951i	$-0.663504\pi$
$853$	8.06632e6	−	8.06632e6i	0.379580	−	0.379580i	0.870951	+	0.491371i	$0.163504\pi$
$854$		0			0
$855$		−	4.64606e6i		−	0.217355i
$856$		0			0
$857$		−	1.88879e7i		−	0.878481i	−0.898370	−	0.439240i	$-0.855248\pi$
$857$		−	1.88879e7i		−	0.878481i	0.898370	−	0.439240i	$-0.144752\pi$
$858$		0			0
$859$	883925.	−	883925.i	0.0408726	−	0.0408726i	−0.686375	−	0.727248i	$-0.740799\pi$
$859$	883925.	−	883925.i	0.0408726	−	0.0408726i	0.727248	+	0.686375i	$0.240799\pi$
$860$		0			0
$861$	−1.41629e7	−	1.41629e7i	−0.651094	−	0.651094i
$862$		0			0
$863$	−3.68542e7			−1.68446			−0.842228	−	0.539121i	$-0.818756\pi$
$863$	−3.68542e7			−1.68446			−0.842228	+	0.539121i	$0.818756\pi$
$864$		0			0
$865$	5.10066e6			0.231785
$866$		0			0
$867$	3.90191e6	+	3.90191e6i	0.176291	+	0.176291i
$868$		0			0
$869$	4.69527e6	−	4.69527e6i	0.210917	−	0.210917i
$870$		0			0
$871$			5.39572e6i			0.240993i
$872$		0			0
$873$		−	6.05612e6i		−	0.268942i
$874$		0			0
$875$	2.29861e6	−	2.29861e6i	0.101495	−	0.101495i
$876$		0			0
$877$	8.11374e6	+	8.11374e6i	0.356223	+	0.356223i	0.862419	−	0.506196i	$-0.168949\pi$
$877$	8.11374e6	+	8.11374e6i	0.356223	+	0.356223i	−0.506196	+	0.862419i	$0.668949\pi$
$878$		0			0
$879$	−2.40929e7			−1.05176
$880$		0			0
$881$	−3.60518e7			−1.56490			−0.782452	−	0.622711i	$-0.786031\pi$
$881$	−3.60518e7			−1.56490			−0.782452	+	0.622711i	$0.786031\pi$
$882$		0			0
$883$	1.86543e7	+	1.86543e7i	0.805150	+	0.805150i	0.983895	−	0.178745i	$-0.0572038\pi$
$883$	1.86543e7	+	1.86543e7i	0.805150	+	0.805150i	−0.178745	+	0.983895i	$0.557204\pi$
$884$		0			0
$885$	3.60424e6	−	3.60424e6i	0.154687	−	0.154687i
$886$		0			0
$887$		−	4.04585e7i		−	1.72663i	−0.504662	−	0.863317i	$-0.668383\pi$
$887$		−	4.04585e7i		−	1.72663i	0.504662	−	0.863317i	$-0.331617\pi$
$888$		0			0
$889$		−	4.98337e7i		−	2.11480i
$890$		0			0
$891$	−1.89799e6	+	1.89799e6i	−0.0800940	+	0.0800940i
$892$		0			0
$893$	−6.52066e6	−	6.52066e6i	−0.273630	−	0.273630i
$894$		0			0
$895$	1.36265e7			0.568625
$896$		0			0
$897$	8.02085e6			0.332843
$898$		0			0
$899$	7.91387e6	+	7.91387e6i	0.326580	+	0.326580i
$900$		0			0
$901$	1.19490e7	−	1.19490e7i	0.490364	−	0.490364i
$902$		0			0
$903$		−	1.93955e7i		−	0.791556i
$904$		0			0
$905$			4.79408e6i			0.194573i
$906$		0			0
$907$	2.58435e7	−	2.58435e7i	1.04312	−	1.04312i	0.0440875	−	0.999028i	$-0.485962\pi$
$907$	2.58435e7	−	2.58435e7i	1.04312	−	1.04312i	0.999028	−	0.0440875i	$-0.0140380\pi$
$908$		0			0
$909$	−1.46036e7	−	1.46036e7i	−0.586206	−	0.586206i
$910$		0			0
$911$	4.65222e7			1.85723			0.928613	−	0.371051i	$-0.121002\pi$
$911$	4.65222e7			1.85723			0.928613	+	0.371051i	$0.121002\pi$
$912$		0			0
$913$	1.07019e7			0.424898
$914$		0			0
$915$	6.80625e6	+	6.80625e6i	0.268754	+	0.268754i
$916$		0			0
$917$	−2.76303e7	+	2.76303e7i	−1.08508	+	1.08508i
$918$		0			0
$919$		−	3.79334e7i		−	1.48161i	−0.671721	−	0.740804i	$-0.734445\pi$
$919$		−	3.79334e7i		−	1.48161i	0.671721	−	0.740804i	$-0.265555\pi$
$920$		0			0
$921$			9.27710e6i			0.360382i
$922$		0			0
$923$	−9.40188e6	+	9.40188e6i	−0.363254	+	0.363254i
$924$		0			0
$925$	−6.58845e6	−	6.58845e6i	−0.253180	−	0.253180i
$926$		0			0
$927$	−2.52419e7			−0.964767
$928$		0			0
$929$	2.09742e7			0.797345			0.398673	−	0.917093i	$-0.369471\pi$
$929$	2.09742e7			0.797345			0.398673	+	0.917093i	$0.369471\pi$
$930$		0			0
$931$	−2.93152e7	−	2.93152e7i	−1.10846	−	1.10846i
$932$		0			0
$933$	1.05435e6	−	1.05435e6i	0.0396533	−	0.0396533i
$934$		0			0
$935$		−	4.00292e6i		−	0.149743i
$936$		0			0
$937$		−	8.90174e6i		−	0.331227i	−0.986191	−	0.165614i	$-0.947040\pi$
$937$		−	8.90174e6i		−	0.331227i	0.986191	−	0.165614i	$-0.0529604\pi$
$938$		0			0
$939$	2.02315e7	−	2.02315e7i	0.748799	−	0.748799i
$940$		0			0
$941$	−9.99541e6	−	9.99541e6i	−0.367982	−	0.367982i	0.498759	−	0.866741i	$-0.333789\pi$
$941$	−9.99541e6	−	9.99541e6i	−0.367982	−	0.367982i	−0.866741	+	0.498759i	$0.833789\pi$
$942$		0			0
$943$	−2.27666e7			−0.833716
$944$		0			0
$945$	−2.09746e7			−0.764035
$946$		0			0
$947$	1.56749e7	+	1.56749e7i	0.567975	+	0.567975i	0.931561	−	0.363586i	$-0.118448\pi$
$947$	1.56749e7	+	1.56749e7i	0.567975	+	0.567975i	−0.363586	+	0.931561i	$0.618448\pi$
$948$		0			0
$949$	−1.70495e7	+	1.70495e7i	−0.614535	+	0.614535i
$950$		0			0
$951$		−	1.88861e7i		−	0.677158i
$952$		0			0
$953$			4.61016e7i			1.64431i	0.569264	+	0.822155i	$0.307228\pi$
$953$			4.61016e7i			1.64431i	−0.569264	+	0.822155i	$0.692772\pi$
$954$		0			0
$955$	1.23963e6	−	1.23963e6i	0.0439828	−	0.0439828i
$956$		0			0
$957$	6.38119e6	+	6.38119e6i	0.225228	+	0.225228i
$958$		0			0
$959$	3.22586e7			1.13266
$960$		0			0
$961$	−2.33294e7			−0.814883
$962$		0			0
$963$	1.25895e7	+	1.25895e7i	0.437463	+	0.437463i
$964$		0			0
$965$	1.26231e7	−	1.26231e7i	0.436362	−	0.436362i
$966$		0			0
$967$		−	4.19970e7i		−	1.44428i	−0.691745	−	0.722142i	$-0.743158\pi$
$967$		−	4.19970e7i		−	1.44428i	0.691745	−	0.722142i	$-0.256842\pi$
$968$		0			0
$969$			1.67907e7i			0.574459i
$970$		0			0
$971$	−2.33246e7	+	2.33246e7i	−0.793901	+	0.793901i	−0.982126	−	0.188225i	$-0.939727\pi$
$971$	−2.33246e7	+	2.33246e7i	−0.793901	+	0.793901i	0.188225	+	0.982126i	$0.439727\pi$
$972$		0			0
$973$	5.45158e7	+	5.45158e7i	1.84604	+	1.84604i
$974$		0			0
$975$	1.90129e6			0.0640525
$976$		0			0
$977$	−3.98399e7			−1.33531			−0.667654	−	0.744471i	$-0.732702\pi$
$977$	−3.98399e7			−1.33531			−0.667654	+	0.744471i	$0.732702\pi$
$978$		0			0
$979$	−2.30999e6	−	2.30999e6i	−0.0770288	−	0.0770288i
$980$		0			0
$981$	−2.09093e6	+	2.09093e6i	−0.0693694	+	0.0693694i
$982$		0			0
$983$		−	5.00098e7i		−	1.65071i	−0.564613	−	0.825356i	$-0.690975\pi$
$983$		−	5.00098e7i		−	1.65071i	0.564613	−	0.825356i	$-0.309025\pi$
$984$		0			0
$985$			1.55963e7i			0.512191i
$986$		0			0
$987$	−9.65973e6	+	9.65973e6i	−0.315625	+	0.315625i
$988$		0			0
$989$	−1.55889e7	−	1.55889e7i	−0.506788	−	0.506788i
$990$		0			0
$991$	−1.59025e7			−0.514376			−0.257188	−	0.966361i	$-0.582796\pi$
$991$	−1.59025e7			−0.514376			−0.257188	+	0.966361i	$0.582796\pi$
$992$		0			0
$993$	−2.74371e6			−0.0883010
$994$		0			0
$995$	−2.38919e6	−	2.38919e6i	−0.0765054	−	0.0765054i
$996$		0			0
$997$	7.39010e6	−	7.39010e6i	0.235457	−	0.235457i	−0.579509	−	0.814966i	$-0.696756\pi$
$997$	7.39010e6	−	7.39010e6i	0.235457	−	0.235457i	0.814966	+	0.579509i	$0.196756\pi$
$998$		0			0
$999$			6.01188e7i			1.90588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.6.l.a.81.13		80
4.3	odd	2		80.6.l.a.61.21	yes	80
16.5	even	4	inner	320.6.l.a.241.13		80
16.11	odd	4		80.6.l.a.21.21	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.21	✓	80	16.11	odd	4
80.6.l.a.61.21	yes	80	4.3	odd	2
320.6.l.a.81.13		80	1.1	even	1	trivial
320.6.l.a.241.13		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)

\(f(q)\)	\(=\)	\(q+(-7.88400 - 7.88400i) q^{3} +(17.6777 - 17.6777i) q^{5} +208.047i q^{7} -118.685i q^{9} +O(q^{10})\)	\(q+(-7.88400 - 7.88400i) q^{3} +(17.6777 - 17.6777i) q^{5} +208.047i q^{7} -118.685i q^{9} +(-117.724 + 117.724i) q^{11} +(-192.926 - 192.926i) q^{13} -278.742 q^{15} -961.739 q^{17} +(1107.22 + 1107.22i) q^{19} +(1640.24 - 1640.24i) q^{21} -2636.65i q^{23} -625.000i q^{25} +(-2851.53 + 2851.53i) q^{27} +(3437.64 + 3437.64i) q^{29} +2302.12 q^{31} +1856.27 q^{33} +(3677.78 + 3677.78i) q^{35} +(10541.5 - 10541.5i) q^{37} +3042.06i q^{39} -8634.65i q^{41} +(5912.40 - 5912.40i) q^{43} +(-2098.08 - 2098.08i) q^{45} -5889.22 q^{47} -26476.4 q^{49} +(7582.35 + 7582.35i) q^{51} +(-12424.3 + 12424.3i) q^{53} +4162.17i q^{55} -17458.7i q^{57} +(-12930.4 + 12930.4i) q^{59} +(-24417.8 - 24417.8i) q^{61} +24692.0 q^{63} -6820.96 q^{65} +(-13983.9 - 13983.9i) q^{67} +(-20787.4 + 20787.4i) q^{69} -48733.1i q^{71} -88373.4i q^{73} +(-4927.50 + 4927.50i) q^{75} +(-24492.0 - 24492.0i) q^{77} -39883.7 q^{79} +16122.4 q^{81} +(-45453.5 - 45453.5i) q^{83} +(-17001.3 + 17001.3i) q^{85} -54204.8i q^{87} +19622.1i q^{89} +(40137.6 - 40137.6i) q^{91} +(-18149.9 - 18149.9i) q^{93} +39146.2 q^{95} +51026.8 q^{97} +(13972.1 + 13972.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q+O(q^{10}) \) 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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