LMFDB - Embedded newform 320.6.l.a.81.5

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			81.5
Character	$\chi$	$=$	320.81
Dual form			320.6.l.a.241.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-16.3104 - 16.3104i) q^{3} +(-17.6777 + 17.6777i) q^{5} -214.455i q^{7} +289.056i q^{9} +O(q^{10})$	\(q+(-16.3104 - 16.3104i) q^{3} +(-17.6777 + 17.6777i) q^{5} -214.455i q^{7} +289.056i q^{9} +(-104.396 + 104.396i) q^{11} +(420.156 + 420.156i) q^{13} +576.659 q^{15} -1591.46 q^{17} +(-1661.81 - 1661.81i) q^{19} +(-3497.85 + 3497.85i) q^{21} +2569.14i q^{23} -625.000i q^{25} +(751.198 - 751.198i) q^{27} +(1456.11 + 1456.11i) q^{29} -4060.77 q^{31} +3405.46 q^{33} +(3791.07 + 3791.07i) q^{35} +(184.011 - 184.011i) q^{37} -13705.8i q^{39} -8232.81i q^{41} +(-13460.9 + 13460.9i) q^{43} +(-5109.84 - 5109.84i) q^{45} +12520.4 q^{47} -29184.1 q^{49} +(25957.4 + 25957.4i) q^{51} +(-1026.20 + 1026.20i) q^{53} -3690.94i q^{55} +54209.6i q^{57} +(17001.4 - 17001.4i) q^{59} +(19736.4 + 19736.4i) q^{61} +61989.7 q^{63} -14854.7 q^{65} +(45894.2 + 45894.2i) q^{67} +(41903.6 - 41903.6i) q^{69} -73134.4i q^{71} -36222.2i q^{73} +(-10194.0 + 10194.0i) q^{75} +(22388.2 + 22388.2i) q^{77} -71449.5 q^{79} +45736.1 q^{81} +(71360.9 + 71360.9i) q^{83} +(28133.4 - 28133.4i) q^{85} -47499.4i q^{87} -57058.1i q^{89} +(90104.6 - 90104.6i) q^{91} +(66232.6 + 66232.6i) q^{93} +58754.0 q^{95} +46024.0 q^{97} +(-30176.2 - 30176.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q+O(q^{10}) $ 80 * q	$ 80 q - 1208 q^{11} + 1800 q^{15} - 2360 q^{19} + 7464 q^{27} - 8144 q^{29} + 21296 q^{37} - 32072 q^{43} + 88360 q^{47} - 192080 q^{49} + 5920 q^{51} - 49456 q^{53} - 44984 q^{59} + 48080 q^{61} - 158760 q^{63} - 61160 q^{67} - 22320 q^{69} - 14896 q^{77} - 177680 q^{79} - 524880 q^{81} + 329240 q^{83} + 132400 q^{85} - 364832 q^{91} - 362352 q^{93} - 288800 q^{95} - 659000 q^{99}+O(q^{100}) $ 80 * q - 1208 * q^11 + 1800 * q^15 - 2360 * q^19 + 7464 * q^27 - 8144 * q^29 + 21296 * q^37 - 32072 * q^43 + 88360 * q^47 - 192080 * q^49 + 5920 * q^51 - 49456 * q^53 - 44984 * q^59 + 48080 * q^61 - 158760 * q^63 - 61160 * q^67 - 22320 * q^69 - 14896 * q^77 - 177680 * q^79 - 524880 * q^81 + 329240 * q^83 + 132400 * q^85 - 364832 * q^91 - 362352 * q^93 - 288800 * q^95 - 659000 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−16.3104	−	16.3104i	−1.04631	−	1.04631i	−0.998874	−	0.0474366i	$-0.984895\pi$
$3$	−16.3104	−	16.3104i	−1.04631	−	1.04631i	−0.0474366	−	0.998874i	$-0.515105\pi$
$4$		0			0
$5$	−17.6777	+	17.6777i	−0.316228	+	0.316228i
$5$	−17.6777	+	17.6777i	−0.316228	+	0.316228i
$6$		0			0
$7$		−	214.455i		−	1.65421i	−0.562045	−	0.827107i	$-0.689985\pi$
$7$		−	214.455i		−	1.65421i	0.562045	−	0.827107i	$-0.310015\pi$
$8$		0			0
$9$			289.056i			1.18953i
$10$		0			0
$11$	−104.396	+	104.396i	−0.260136	+	0.260136i	−0.825109	−	0.564973i	$-0.808886\pi$
$11$	−104.396	+	104.396i	−0.260136	+	0.260136i	0.564973	+	0.825109i	$0.308886\pi$
$12$		0			0
$13$	420.156	+	420.156i	0.689528	+	0.689528i	0.962128	−	0.272600i	$-0.0878834\pi$
$13$	420.156	+	420.156i	0.689528	+	0.689528i	−0.272600	+	0.962128i	$0.587883\pi$
$14$		0			0
$15$	576.659			0.661745
$16$		0			0
$17$	−1591.46			−1.33559			−0.667797	−	0.744343i	$-0.732763\pi$
$17$	−1591.46			−1.33559			−0.667797	+	0.744343i	$0.732763\pi$
$18$		0			0
$19$	−1661.81	−	1661.81i	−1.05608	−	1.05608i	−0.998331	−	0.0577529i	$-0.981606\pi$
$19$	−1661.81	−	1661.81i	−1.05608	−	1.05608i	−0.0577529	−	0.998331i	$-0.518394\pi$
$20$		0			0
$21$	−3497.85	+	3497.85i	−1.73082	+	1.73082i
$22$		0			0
$23$			2569.14i			1.01267i	0.862337	+	0.506335i	$0.169000\pi$
$23$			2569.14i			1.01267i	−0.862337	+	0.506335i	$0.831000\pi$
$24$		0			0
$25$		−	625.000i		−	0.200000i
$26$		0			0
$27$	751.198	−	751.198i	0.198310	−	0.198310i
$28$		0			0
$29$	1456.11	+	1456.11i	0.321513	+	0.321513i	0.849347	−	0.527834i	$-0.176996\pi$
$29$	1456.11	+	1456.11i	0.321513	+	0.321513i	−0.527834	+	0.849347i	$0.676996\pi$
$30$		0			0
$31$	−4060.77			−0.758934			−0.379467	−	0.925205i	$-0.623893\pi$
$31$	−4060.77			−0.758934			−0.379467	+	0.925205i	$0.623893\pi$
$32$		0			0
$33$	3405.46			0.544366
$34$		0			0
$35$	3791.07	+	3791.07i	0.523108	+	0.523108i
$36$		0			0
$37$	184.011	−	184.011i	0.0220973	−	0.0220973i	−0.695972	−	0.718069i	$-0.745026\pi$
$37$	184.011	−	184.011i	0.0220973	−	0.0220973i	0.718069	+	0.695972i	$0.245026\pi$
$38$		0			0
$39$		−	13705.8i		−	1.44292i
$40$		0			0
$41$		−	8232.81i		−	0.764871i	−0.923982	−	0.382436i	$-0.875085\pi$
$41$		−	8232.81i		−	0.764871i	0.923982	−	0.382436i	$-0.124915\pi$
$42$		0			0
$43$	−13460.9	+	13460.9i	−1.11020	+	1.11020i	−0.117081	+	0.993122i	$0.537354\pi$
$43$	−13460.9	+	13460.9i	−1.11020	+	1.11020i	−0.993122	+	0.117081i	$0.962646\pi$
$44$		0			0
$45$	−5109.84	−	5109.84i	−0.376163	−	0.376163i
$46$		0			0
$47$	12520.4			0.826750			0.413375	−	0.910561i	$-0.364350\pi$
$47$	12520.4			0.826750			0.413375	+	0.910561i	$0.364350\pi$
$48$		0			0
$49$	−29184.1			−1.73642
$50$		0			0
$51$	25957.4	+	25957.4i	1.39745	+	1.39745i
$52$		0			0
$53$	−1026.20	+	1026.20i	−0.0501815	+	0.0501815i	−0.731752	−	0.681571i	$-0.761297\pi$
$53$	−1026.20	+	1026.20i	−0.0501815	+	0.0501815i	0.681571	+	0.731752i	$0.261297\pi$
$54$		0			0
$55$		−	3690.94i		−	0.164524i
$56$		0			0
$57$			54209.6i			2.20998i
$58$		0			0
$59$	17001.4	−	17001.4i	0.635851	−	0.635851i	−0.313679	−	0.949529i	$-0.601561\pi$
$59$	17001.4	−	17001.4i	0.635851	−	0.635851i	0.949529	+	0.313679i	$0.101561\pi$
$60$		0			0
$61$	19736.4	+	19736.4i	0.679116	+	0.679116i	0.959800	−	0.280685i	$-0.0905615\pi$
$61$	19736.4	+	19736.4i	0.679116	+	0.679116i	−0.280685	+	0.959800i	$0.590561\pi$
$62$		0			0
$63$	61989.7			1.96774
$64$		0			0
$65$	−14854.7			−0.436096
$66$		0			0
$67$	45894.2	+	45894.2i	1.24902	+	1.24902i	0.956152	+	0.292872i	$0.0946111\pi$
$67$	45894.2	+	45894.2i	1.24902	+	1.24902i	0.292872	+	0.956152i	$0.405389\pi$
$68$		0			0
$69$	41903.6	−	41903.6i	1.05957	−	1.05957i
$70$		0			0
$71$		−	73134.4i		−	1.72177i	−0.508798	−	0.860886i	$-0.669910\pi$
$71$		−	73134.4i		−	1.72177i	0.508798	−	0.860886i	$-0.330090\pi$
$72$		0			0
$73$		−	36222.2i		−	0.795551i	−0.917483	−	0.397775i	$-0.869782\pi$
$73$		−	36222.2i		−	0.795551i	0.917483	−	0.397775i	$-0.130218\pi$
$74$		0			0
$75$	−10194.0	+	10194.0i	−0.209262	+	0.209262i
$76$		0			0
$77$	22388.2	+	22388.2i	0.430320	+	0.430320i
$78$		0			0
$79$	−71449.5			−1.28805			−0.644023	−	0.765006i	$-0.722736\pi$
$79$	−71449.5			−1.28805			−0.644023	+	0.765006i	$0.722736\pi$
$80$		0			0
$81$	45736.1			0.774545
$82$		0			0
$83$	71360.9	+	71360.9i	1.13701	+	1.13701i	0.988983	+	0.148030i	$0.0472931\pi$
$83$	71360.9	+	71360.9i	1.13701	+	1.13701i	0.148030	+	0.988983i	$0.452707\pi$
$84$		0			0
$85$	28133.4	−	28133.4i	0.422352	−	0.422352i
$86$		0			0
$87$		−	47499.4i		−	0.672806i
$88$		0			0
$89$		−	57058.1i		−	0.763558i	−0.924254	−	0.381779i	$-0.875311\pi$
$89$		−	57058.1i		−	0.763558i	0.924254	−	0.381779i	$-0.124689\pi$
$90$		0			0
$91$	90104.6	−	90104.6i	1.14063	−	1.14063i
$92$		0			0
$93$	66232.6	+	66232.6i	0.794080	+	0.794080i
$94$		0			0
$95$	58754.0			0.667926
$96$		0			0
$97$	46024.0			0.496655			0.248327	−	0.968676i	$-0.420119\pi$
$97$	46024.0			0.496655			0.248327	+	0.968676i	$0.420119\pi$
$98$		0			0
$99$	−30176.2	−	30176.2i	−0.309440	−	0.309440i
$100$		0			0
$101$	100590.	−	100590.i	0.981183	−	0.981183i	−0.0186427	−	0.999826i	$-0.505935\pi$
$101$	100590.	−	100590.i	0.981183	−	0.981183i	0.999826	+	0.0186427i	$0.00593451\pi$
$102$		0			0
$103$		−	17705.7i		−	0.164445i	−0.996614	−	0.0822224i	$-0.973798\pi$
$103$		−	17705.7i		−	0.164445i	0.996614	−	0.0822224i	$-0.0262018\pi$
$104$		0			0
$105$		−	123668.i		−	1.09467i
$106$		0			0
$107$	13476.2	−	13476.2i	0.113791	−	0.113791i	−0.647918	−	0.761710i	$-0.724360\pi$
$107$	13476.2	−	13476.2i	0.113791	−	0.113791i	0.761710	+	0.647918i	$0.224360\pi$
$108$		0			0
$109$	144159.	+	144159.i	1.16218	+	1.16218i	0.983997	+	0.178186i	$0.0570230\pi$
$109$	144159.	+	144159.i	1.16218	+	1.16218i	0.178186	+	0.983997i	$0.442977\pi$
$110$		0			0
$111$	−6002.59			−0.0462414
$112$		0			0
$113$	149602.			1.10215			0.551077	−	0.834455i	$-0.314217\pi$
$113$	149602.			1.10215			0.551077	+	0.834455i	$0.314217\pi$
$114$		0			0
$115$	−45416.4	−	45416.4i	−0.320234	−	0.320234i
$116$		0			0
$117$	−121449.	+	121449.i	−0.820216	+	0.820216i
$118$		0			0
$119$			341298.i			2.20936i
$120$		0			0
$121$			139254.i			0.864659i
$122$		0			0
$123$	−134280.	+	134280.i	−0.800293	+	0.800293i
$124$		0			0
$125$	11048.5	+	11048.5i	0.0632456	+	0.0632456i
$126$		0			0
$127$	−133065.			−0.732072			−0.366036	−	0.930601i	$-0.619285\pi$
$127$	−133065.			−0.732072			−0.366036	+	0.930601i	$0.619285\pi$
$128$		0			0
$129$	439104.			2.32324
$130$		0			0
$131$	−40448.2	−	40448.2i	−0.205931	−	0.205931i	0.596605	−	0.802535i	$-0.296516\pi$
$131$	−40448.2	−	40448.2i	−0.205931	−	0.205931i	−0.802535	+	0.596605i	$0.796516\pi$
$132$		0			0
$133$	−356385.	+	356385.i	−1.74699	+	1.74699i
$134$		0			0
$135$			26558.9i			0.125422i
$136$		0			0
$137$			113456.i			0.516446i	0.966085	+	0.258223i	$0.0831369\pi$
$137$			113456.i			0.516446i	−0.966085	+	0.258223i	$0.916863\pi$
$138$		0			0
$139$	−164091.	+	164091.i	−0.720358	+	0.720358i	−0.968678	−	0.248320i	$-0.920122\pi$
$139$	−164091.	+	164091.i	−0.720358	+	0.720358i	0.248320	+	0.968678i	$0.420122\pi$
$140$		0			0
$141$	−204213.	−	204213.i	−0.865037	−	0.865037i
$142$		0			0
$143$	−87724.8			−0.358742
$144$		0			0
$145$	−51481.2			−0.203343
$146$		0			0
$147$	476003.	+	476003.i	1.81684	+	1.81684i
$148$		0			0
$149$	−179726.	+	179726.i	−0.663200	+	0.663200i	−0.956133	−	0.292933i	$-0.905369\pi$
$149$	−179726.	+	179726.i	−0.663200	+	0.663200i	0.292933	+	0.956133i	$0.405369\pi$
$150$		0			0
$151$		−	410078.i		−	1.46360i	−0.681517	−	0.731802i	$-0.738680\pi$
$151$		−	410078.i		−	1.46360i	0.681517	−	0.731802i	$-0.261320\pi$
$152$		0			0
$153$		−	460023.i		−	1.58873i
$154$		0			0
$155$	71784.9	−	71784.9i	0.239996	−	0.239996i
$156$		0			0
$157$	−327095.	−	327095.i	−1.05907	−	1.05907i	−0.998142	−	0.0609288i	$-0.980594\pi$
$157$	−327095.	−	327095.i	−1.05907	−	1.05907i	−0.0609288	−	0.998142i	$-0.519406\pi$
$158$		0			0
$159$	33475.5			0.105011
$160$		0			0
$161$	550965.			1.67517
$162$		0			0
$163$	−309189.	−	309189.i	−0.911496	−	0.911496i	0.0848944	−	0.996390i	$-0.472945\pi$
$163$	−309189.	−	309189.i	−0.911496	−	0.911496i	−0.996390	+	0.0848944i	$0.972945\pi$
$164$		0			0
$165$	−60200.6	+	60200.6i	−0.172144	+	0.172144i
$166$		0			0
$167$			337869.i			0.937469i	0.883339	+	0.468734i	$0.155290\pi$
$167$			337869.i			0.937469i	−0.883339	+	0.468734i	$0.844710\pi$
$168$		0			0
$169$		−	18231.4i		−	0.0491024i
$170$		0			0
$171$	480358.	−	480358.i	1.25625	−	1.25625i
$172$		0			0
$173$	163738.	+	163738.i	0.415944	+	0.415944i	0.883803	−	0.467859i	$-0.154974\pi$
$173$	163738.	+	163738.i	0.415944	+	0.415944i	−0.467859	+	0.883803i	$0.654974\pi$
$174$		0			0
$175$	−134035.			−0.330843
$176$		0			0
$177$	−554599.			−1.33059
$178$		0			0
$179$	170326.	+	170326.i	0.397327	+	0.397327i	0.877289	−	0.479962i	$-0.159350\pi$
$179$	170326.	+	170326.i	0.397327	+	0.397327i	−0.479962	+	0.877289i	$0.659350\pi$
$180$		0			0
$181$	−43461.4	+	43461.4i	−0.0986069	+	0.0986069i	−0.754689	−	0.656082i	$-0.772212\pi$
$181$	−43461.4	+	43461.4i	−0.0986069	+	0.0986069i	0.656082	+	0.754689i	$0.272212\pi$
$182$		0			0
$183$		−	643817.i		−	1.42113i
$184$		0			0
$185$			6505.78i			0.0139756i
$186$		0			0
$187$	166142.	−	166142.i	0.347436	−	0.347436i
$188$		0			0
$189$	−161098.	−	161098.i	−0.328047	−	0.328047i
$190$		0			0
$191$	−660656.			−1.31036			−0.655182	−	0.755471i	$-0.727408\pi$
$191$	−660656.			−1.31036			−0.655182	+	0.755471i	$0.727408\pi$
$192$		0			0
$193$	88554.5			0.171127			0.0855633	−	0.996333i	$-0.472731\pi$
$193$	88554.5			0.171127			0.0855633	+	0.996333i	$0.472731\pi$
$194$		0			0
$195$	242286.	+	242286.i	0.456292	+	0.456292i
$196$		0			0
$197$	235846.	−	235846.i	0.432976	−	0.432976i	−0.456664	−	0.889639i	$-0.650956\pi$
$197$	235846.	−	235846.i	0.432976	−	0.432976i	0.889639	+	0.456664i	$0.150956\pi$
$198$		0			0
$199$			438843.i			0.785555i	0.919634	+	0.392777i	$0.128486\pi$
$199$			438843.i			0.785555i	−0.919634	+	0.392777i	$0.871514\pi$
$200$		0			0
$201$		−	1.49710e6i		−	2.61373i
$202$		0			0
$203$	312270.	−	312270.i	0.531852	−	0.531852i
$204$		0			0
$205$	145537.	+	145537.i	0.241874	+	0.241874i
$206$		0			0
$207$	−742626.			−1.20460
$208$		0			0
$209$	346972.			0.549451
$210$		0			0
$211$	532584.	+	532584.i	0.823535	+	0.823535i	0.986613	−	0.163079i	$-0.0521424\pi$
$211$	532584.	+	532584.i	0.823535	+	0.823535i	−0.163079	+	0.986613i	$0.552142\pi$
$212$		0			0
$213$	−1.19285e6	+	1.19285e6i	−1.80151	+	1.80151i
$214$		0			0
$215$		−	475914.i		−	0.702154i
$216$		0			0
$217$			870853.i			1.25544i
$218$		0			0
$219$	−590798.	+	590798.i	−0.832394	+	0.832394i
$220$		0			0
$221$	−668663.	−	668663.i	−0.920930	−	0.920930i
$222$		0			0
$223$	800984.			1.07860			0.539302	−	0.842113i	$-0.318688\pi$
$223$	800984.			1.07860			0.539302	+	0.842113i	$0.318688\pi$
$224$		0			0
$225$	180660.			0.237907
$226$		0			0
$227$	315977.	+	315977.i	0.406996	+	0.406996i	0.880690	−	0.473694i	$-0.157080\pi$
$227$	315977.	+	315977.i	0.406996	+	0.406996i	−0.473694	+	0.880690i	$0.657080\pi$
$228$		0			0
$229$	−506273.	+	506273.i	−0.637964	+	0.637964i	−0.950053	−	0.312089i	$-0.898971\pi$
$229$	−506273.	+	506273.i	−0.637964	+	0.637964i	0.312089	+	0.950053i	$0.398971\pi$
$230$		0			0
$231$		−	730319.i		−	0.900498i
$232$		0			0
$233$			1.06603e6i			1.28641i	0.765695	+	0.643204i	$0.222395\pi$
$233$			1.06603e6i			1.28641i	−0.765695	+	0.643204i	$0.777605\pi$
$234$		0			0
$235$	−221332.	+	221332.i	−0.261441	+	0.261441i
$236$		0			0
$237$	1.16537e6	+	1.16537e6i	1.34770	+	1.34770i
$238$		0			0
$239$	−277079.			−0.313768			−0.156884	−	0.987617i	$-0.550145\pi$
$239$	−277079.			−0.313768			−0.156884	+	0.987617i	$0.550145\pi$
$240$		0			0
$241$	−554591.			−0.615078			−0.307539	−	0.951535i	$-0.599506\pi$
$241$	−554591.			−0.615078			−0.307539	+	0.951535i	$0.599506\pi$
$242$		0			0
$243$	−928514.	−	928514.i	−1.00872	−	1.00872i
$244$		0			0
$245$	515906.	−	515906.i	0.549105	−	0.549105i
$246$		0			0
$247$		−	1.39644e6i		−	1.45640i
$248$		0			0
$249$		−	2.32785e6i		−	2.37934i
$250$		0			0
$251$	785359.	−	785359.i	0.786836	−	0.786836i	−0.194138	−	0.980974i	$-0.562191\pi$
$251$	785359.	−	785359.i	0.786836	−	0.786836i	0.980974	+	0.194138i	$0.0621911\pi$
$252$		0			0
$253$	−268207.	−	268207.i	−0.263432	−	0.263432i
$254$		0			0
$255$	−917732.			−0.883823
$256$		0			0
$257$	96482.9			0.0911208			0.0455604	−	0.998962i	$-0.485493\pi$
$257$	96482.9			0.0911208			0.0455604	+	0.998962i	$0.485493\pi$
$258$		0			0
$259$	−39462.2	−	39462.2i	−0.0365537	−	0.0365537i
$260$		0			0
$261$	−420898.	+	420898.i	−0.382451	+	0.382451i
$262$		0			0
$263$			577421.i			0.514758i	0.966311	+	0.257379i	$0.0828588\pi$
$263$			577421.i			0.514758i	−0.966311	+	0.257379i	$0.917141\pi$
$264$		0			0
$265$		−	36281.8i		−	0.0317376i
$266$		0			0
$267$	−930639.	+	930639.i	−0.798919	+	0.798919i
$268$		0			0
$269$	−946399.	−	946399.i	−0.797432	−	0.797432i	0.185258	−	0.982690i	$-0.440688\pi$
$269$	−946399.	−	946399.i	−0.797432	−	0.797432i	−0.982690	+	0.185258i	$0.940688\pi$
$270$		0			0
$271$	1.69778e6			1.40429			0.702146	−	0.712033i	$-0.252225\pi$
$271$	1.69778e6			1.40429			0.702146	+	0.712033i	$0.252225\pi$
$272$		0			0
$273$	−2.93928e6			−2.38690
$274$		0			0
$275$	65247.2	+	65247.2i	0.0520272	+	0.0520272i
$276$		0			0
$277$	298672.	−	298672.i	0.233881	−	0.233881i	−0.580429	−	0.814311i	$-0.697115\pi$
$277$	298672.	−	298672.i	0.233881	−	0.233881i	0.814311	+	0.580429i	$0.197115\pi$
$278$		0			0
$279$		−	1.17379e6i		−	0.902776i
$280$		0			0
$281$		−	402316.i		−	0.303950i	−0.988384	−	0.151975i	$-0.951437\pi$
$281$		−	402316.i		−	0.303950i	0.988384	−	0.151975i	$-0.0485633\pi$
$282$		0			0
$283$	−664175.	+	664175.i	−0.492965	+	0.492965i	−0.909239	−	0.416274i	$-0.863336\pi$
$283$	−664175.	+	664175.i	−0.492965	+	0.492965i	0.416274	+	0.909239i	$0.363336\pi$
$284$		0			0
$285$	−958299.	−	958299.i	−0.698858	−	0.698858i
$286$		0			0
$287$	−1.76557e6			−1.26526
$288$		0			0
$289$	1.11290e6			0.783812
$290$		0			0
$291$	−750668.	−	750668.i	−0.519655	−	0.519655i
$292$		0			0
$293$	−446120.	+	446120.i	−0.303587	+	0.303587i	−0.842415	−	0.538829i	$-0.818867\pi$
$293$	−446120.	+	446120.i	−0.303587	+	0.303587i	0.538829	+	0.842415i	$0.318867\pi$
$294$		0			0
$295$			601091.i			0.402147i
$296$		0			0
$297$			156843.i			0.103175i
$298$		0			0
$299$	−1.07944e6	+	1.07944e6i	−0.698264	+	0.698264i
$300$		0			0
$301$	2.88676e6	+	2.88676e6i	1.83651	+	1.83651i
$302$		0			0
$303$	−3.28131e6			−2.05325
$304$		0			0
$305$	−697788.			−0.429510
$306$		0			0
$307$	1.87782e6	+	1.87782e6i	1.13712	+	1.13712i	0.988964	+	0.148158i	$0.0473345\pi$
$307$	1.87782e6	+	1.87782e6i	1.13712	+	1.13712i	0.148158	+	0.988964i	$0.452666\pi$
$308$		0			0
$309$	−288787.	+	288787.i	−0.172060	+	0.172060i
$310$		0			0
$311$			1.59793e6i			0.936822i	0.883511	+	0.468411i	$0.155173\pi$
$311$			1.59793e6i			0.936822i	−0.883511	+	0.468411i	$0.844827\pi$
$312$		0			0
$313$			1.22999e6i			0.709645i	0.934934	+	0.354823i	$0.115459\pi$
$313$			1.22999e6i			0.709645i	−0.934934	+	0.354823i	$0.884541\pi$
$314$		0			0
$315$	−1.09583e6	+	1.09583e6i	−0.622254	+	0.622254i
$316$		0			0
$317$	−1.04624e6	−	1.04624e6i	−0.584768	−	0.584768i	0.351442	−	0.936210i	$-0.385691\pi$
$317$	−1.04624e6	−	1.04624e6i	−0.584768	−	0.584768i	−0.936210	+	0.351442i	$0.885691\pi$
$318$		0			0
$319$	−304023.			−0.167274
$320$		0			0
$321$	−439605.			−0.238122
$322$		0			0
$323$	2.64472e6	+	2.64472e6i	1.41050	+	1.41050i
$324$		0			0
$325$	262597.	−	262597.i	0.137906	−	0.137906i
$326$		0			0
$327$		−	4.70256e6i		−	2.43201i
$328$		0			0
$329$		−	2.68507e6i		−	1.36762i
$330$		0			0
$331$	−1.42891e6	+	1.42891e6i	−0.716862	+	0.716862i	−0.967961	−	0.251099i	$-0.919208\pi$
$331$	−1.42891e6	+	1.42891e6i	−0.716862	+	0.716862i	0.251099	+	0.967961i	$0.419208\pi$
$332$		0			0
$333$	53189.7	+	53189.7i	0.0262855	+	0.0262855i
$334$		0			0
$335$	−1.62260e6			−0.789952
$336$		0			0
$337$	−876095.			−0.420220			−0.210110	−	0.977678i	$-0.567382\pi$
$337$	−876095.			−0.420220			−0.210110	+	0.977678i	$0.567382\pi$
$338$		0			0
$339$	−2.44007e6	−	2.44007e6i	−1.15319	−	1.15319i
$340$		0			0
$341$	423926.	−	423926.i	0.197426	−	0.197426i
$342$		0			0
$343$			2.65433e6i			1.21820i
$344$		0			0
$345$			1.48152e6i			0.670129i
$346$		0			0
$347$	646220.	−	646220.i	0.288109	−	0.288109i	−0.548223	−	0.836332i	$-0.684696\pi$
$347$	646220.	−	646220.i	0.288109	−	0.288109i	0.836332	+	0.548223i	$0.184696\pi$
$348$		0			0
$349$	544642.	+	544642.i	0.239358	+	0.239358i	0.816584	−	0.577226i	$-0.195865\pi$
$349$	544642.	+	544642.i	0.239358	+	0.239358i	−0.577226	+	0.816584i	$0.695865\pi$
$350$		0			0
$351$	631240.			0.273481
$352$		0			0
$353$	1.87963e6			0.802854			0.401427	−	0.915891i	$-0.368514\pi$
$353$	1.87963e6			0.802854			0.401427	+	0.915891i	$0.368514\pi$
$354$		0			0
$355$	1.29285e6	+	1.29285e6i	0.544472	+	0.544472i
$356$		0			0
$357$	5.56670e6	−	5.56670e6i	2.31168	−	2.31168i
$358$		0			0
$359$			3.85104e6i			1.57704i	0.615011	+	0.788518i	$0.289151\pi$
$359$			3.85104e6i			1.57704i	−0.615011	+	0.788518i	$0.710849\pi$
$360$		0			0
$361$			3.04715e6i			1.23063i
$362$		0			0
$363$	2.27129e6	−	2.27129e6i	0.904702	−	0.904702i
$364$		0			0
$365$	640325.	+	640325.i	0.251575	+	0.251575i
$366$		0			0
$367$	2.01395e6			0.780521			0.390260	−	0.920705i	$-0.372385\pi$
$367$	2.01395e6			0.780521			0.390260	+	0.920705i	$0.372385\pi$
$368$		0			0
$369$	2.37975e6			0.909840
$370$		0			0
$371$	220075.	+	220075.i	0.0830109	+	0.0830109i
$372$		0			0
$373$	824432.	−	824432.i	0.306819	−	0.306819i	−0.536855	−	0.843674i	$-0.680388\pi$
$373$	824432.	−	824432.i	0.306819	−	0.306819i	0.843674	+	0.536855i	$0.180388\pi$
$374$		0			0
$375$		−	360412.i		−	0.132349i
$376$		0			0
$377$			1.22359e6i			0.443385i
$378$		0			0
$379$	3.04428e6	−	3.04428e6i	1.08864	−	1.08864i	0.0929764	−	0.995668i	$-0.470362\pi$
$379$	3.04428e6	−	3.04428e6i	1.08864	−	1.08864i	0.995668	−	0.0929764i	$-0.0296381\pi$
$380$		0			0
$381$	2.17034e6	+	2.17034e6i	0.765975	+	0.765975i
$382$		0			0
$383$	1.20867e6			0.421029			0.210514	−	0.977591i	$-0.432486\pi$
$383$	1.20867e6			0.421029			0.210514	+	0.977591i	$0.432486\pi$
$384$		0			0
$385$	−791542.			−0.272159
$386$		0			0
$387$	−3.89096e6	−	3.89096e6i	−1.32062	−	1.32062i
$388$		0			0
$389$	−2.51567e6	+	2.51567e6i	−0.842906	+	0.842906i	−0.989236	−	0.146330i	$-0.953254\pi$
$389$	−2.51567e6	+	2.51567e6i	−0.842906	+	0.842906i	0.146330	+	0.989236i	$0.453254\pi$
$390$		0			0
$391$		−	4.08869e6i		−	1.35252i
$392$		0			0
$393$			1.31945e6i			0.430935i
$394$		0			0
$395$	1.26306e6	−	1.26306e6i	0.407316	−	0.407316i
$396$		0			0
$397$	−1.68747e6	−	1.68747e6i	−0.537353	−	0.537353i	0.385398	−	0.922751i	$-0.374064\pi$
$397$	−1.68747e6	−	1.68747e6i	−0.537353	−	0.537353i	−0.922751	+	0.385398i	$0.874064\pi$
$398$		0			0
$399$	1.16255e7			3.65579
$400$		0			0
$401$	5.93518e6			1.84320			0.921600	−	0.388140i	$-0.126882\pi$
$401$	5.93518e6			1.84320			0.921600	+	0.388140i	$0.126882\pi$
$402$		0			0
$403$	−1.70615e6	−	1.70615e6i	−0.523306	−	0.523306i
$404$		0			0
$405$	−808507.	+	808507.i	−0.244932	+	0.244932i
$406$		0			0
$407$			38419.9i			0.0114966i
$408$		0			0
$409$			206918.i			0.0611632i	0.999532	+	0.0305816i	$0.00973595\pi$
$409$			206918.i			0.0611632i	−0.999532	+	0.0305816i	$0.990264\pi$
$410$		0			0
$411$	1.85050e6	−	1.85050e6i	0.540363	−	0.540363i
$412$		0			0
$413$	−3.64604e6	−	3.64604e6i	−1.05183	−	1.05183i
$414$		0			0
$415$	−2.52299e6			−0.719110
$416$		0			0
$417$	5.35278e6			1.50744
$418$		0			0
$419$	−1.26768e6	−	1.26768e6i	−0.352755	−	0.352755i	0.508378	−	0.861134i	$-0.330245\pi$
$419$	−1.26768e6	−	1.26768e6i	−0.352755	−	0.352755i	−0.861134	+	0.508378i	$0.830245\pi$
$420$		0			0
$421$	−4.57007e6	+	4.57007e6i	−1.25666	+	1.25666i	−0.303980	+	0.952678i	$0.598316\pi$
$421$	−4.57007e6	+	4.57007e6i	−1.25666	+	1.25666i	−0.952678	+	0.303980i	$0.901684\pi$
$422$		0			0
$423$			3.61911e6i			0.983446i
$424$		0			0
$425$			994665.i			0.267119i
$426$		0			0
$427$	4.23258e6	−	4.23258e6i	1.12340	−	1.12340i
$428$		0			0
$429$	1.43082e6	+	1.43082e6i	0.375356	+	0.375356i
$430$		0			0
$431$	6.33343e6			1.64227			0.821137	−	0.570731i	$-0.193340\pi$
$431$	6.33343e6			1.64227			0.821137	+	0.570731i	$0.193340\pi$
$432$		0			0
$433$	−1.33762e6			−0.342856			−0.171428	−	0.985197i	$-0.554838\pi$
$433$	−1.33762e6			−0.342856			−0.171428	+	0.985197i	$0.554838\pi$
$434$		0			0
$435$	839678.	+	839678.i	0.212760	+	0.212760i
$436$		0			0
$437$	4.26943e6	−	4.26943e6i	1.06946	−	1.06946i
$438$		0			0
$439$			5.36431e6i			1.32847i	0.747522	+	0.664237i	$0.231243\pi$
$439$			5.36431e6i			1.32847i	−0.747522	+	0.664237i	$0.768757\pi$
$440$		0			0
$441$		−	8.43584e6i		−	2.06553i
$442$		0			0
$443$	−5.59061e6	+	5.59061e6i	−1.35347	+	1.35347i	−0.471730	+	0.881743i	$0.656370\pi$
$443$	−5.59061e6	+	5.59061e6i	−1.35347	+	1.35347i	−0.881743	+	0.471730i	$0.843630\pi$
$444$		0			0
$445$	1.00865e6	+	1.00865e6i	0.241458	+	0.241458i
$446$		0			0
$447$	5.86279e6			1.38783
$448$		0			0
$449$	−643738.			−0.150693			−0.0753465	−	0.997157i	$-0.524006\pi$
$449$	−643738.			−0.150693			−0.0753465	+	0.997157i	$0.524006\pi$
$450$		0			0
$451$	859469.	+	859469.i	0.198971	+	0.198971i
$452$		0			0
$453$	−6.68852e6	+	6.68852e6i	−1.53138	+	1.53138i
$454$		0			0
$455$			3.18568e6i			0.721396i
$456$		0			0
$457$			5.20748e6i			1.16637i	0.812338	+	0.583186i	$0.198194\pi$
$457$			5.20748e6i			1.16637i	−0.812338	+	0.583186i	$0.801806\pi$
$458$		0			0
$459$	−1.19550e6	+	1.19550e6i	−0.264862	+	0.264862i
$460$		0			0
$461$	289027.	+	289027.i	0.0633412	+	0.0633412i	0.738068	−	0.674727i	$-0.235738\pi$
$461$	289027.	+	289027.i	0.0633412	+	0.0633412i	−0.674727	+	0.738068i	$0.735738\pi$
$462$		0			0
$463$	−1.22263e6			−0.265058			−0.132529	−	0.991179i	$-0.542310\pi$
$463$	−1.22263e6			−0.265058			−0.132529	+	0.991179i	$0.542310\pi$
$464$		0			0
$465$	−2.34168e6			−0.502221
$466$		0			0
$467$	3.99501e6	+	3.99501e6i	0.847669	+	0.847669i	0.989842	−	0.142173i	$-0.0454090\pi$
$467$	3.99501e6	+	3.99501e6i	0.847669	+	0.847669i	−0.142173	+	0.989842i	$0.545409\pi$
$468$		0			0
$469$	9.84225e6	−	9.84225e6i	2.06615	−	2.06615i
$470$		0			0
$471$			1.06701e7i			2.21623i
$472$		0			0
$473$		−	2.81051e6i		−	0.577608i
$474$		0			0
$475$	−1.03863e6	+	1.03863e6i	−0.211217	+	0.211217i
$476$		0			0
$477$	−296631.	−	296631.i	−0.0596925	−	0.0596925i
$478$		0			0
$479$	−700748.			−0.139548			−0.0697740	−	0.997563i	$-0.522228\pi$
$479$	−700748.			−0.139548			−0.0697740	+	0.997563i	$0.522228\pi$
$480$		0			0
$481$	154627.			0.0304735
$482$		0			0
$483$	−8.98645e6	−	8.98645e6i	−1.75275	−	1.75275i
$484$		0			0
$485$	−813597.	+	813597.i	−0.157056	+	0.157056i
$486$		0			0
$487$			5.98085e6i			1.14272i	0.820699	+	0.571361i	$0.193584\pi$
$487$			5.98085e6i			1.14272i	−0.820699	+	0.571361i	$0.806416\pi$
$488$		0			0
$489$			1.00860e7i			1.90742i
$490$		0			0
$491$	5.49624e6	−	5.49624e6i	1.02887	−	1.02887i	0.0293036	−	0.999571i	$-0.490671\pi$
$491$	5.49624e6	−	5.49624e6i	1.02887	−	1.02887i	0.999571	−	0.0293036i	$-0.00932895\pi$
$492$		0			0
$493$	−2.31735e6	−	2.31735e6i	−0.429411	−	0.429411i
$494$		0			0
$495$	1.06689e6			0.195707
$496$		0			0
$497$	−1.56840e7			−2.84818
$498$		0			0
$499$	−4.72842e6	−	4.72842e6i	−0.850090	−	0.850090i	0.140054	−	0.990144i	$-0.455272\pi$
$499$	−4.72842e6	−	4.72842e6i	−0.850090	−	0.850090i	−0.990144	+	0.140054i	$0.955272\pi$
$500$		0			0
$501$	5.51077e6	−	5.51077e6i	0.980884	−	0.980884i
$502$		0			0
$503$		−	3.48626e6i		−	0.614384i	−0.951648	−	0.307192i	$-0.900611\pi$
$503$		−	3.48626e6i		−	0.614384i	0.951648	−	0.307192i	$-0.0993894\pi$
$504$		0			0
$505$			3.55638e6i			0.620555i
$506$		0			0
$507$	−297361.	+	297361.i	−0.0513764	+	0.0513764i
$508$		0			0
$509$	−2.36846e6	−	2.36846e6i	−0.405203	−	0.405203i	0.474859	−	0.880062i	$-0.342499\pi$
$509$	−2.36846e6	−	2.36846e6i	−0.405203	−	0.405203i	−0.880062	+	0.474859i	$0.842499\pi$
$510$		0			0
$511$	−7.76805e6			−1.31601
$512$		0			0
$513$	−2.49670e6			−0.418864
$514$		0			0
$515$	312996.	+	312996.i	0.0520020	+	0.0520020i
$516$		0			0
$517$	−1.30708e6	+	1.30708e6i	−0.215067	+	0.215067i
$518$		0			0
$519$		−	5.34126e6i		−	0.870414i
$520$		0			0
$521$			3.07331e6i			0.496034i	0.968756	+	0.248017i	$0.0797789\pi$
$521$			3.07331e6i			0.496034i	−0.968756	+	0.248017i	$0.920221\pi$
$522$		0			0
$523$	−4.87317e6	+	4.87317e6i	−0.779035	+	0.779035i	−0.979667	−	0.200631i	$-0.935701\pi$
$523$	−4.87317e6	+	4.87317e6i	−0.779035	+	0.779035i	0.200631	+	0.979667i	$0.435701\pi$
$524$		0			0
$525$	2.18615e6	+	2.18615e6i	0.346164	+	0.346164i
$526$		0			0
$527$	6.46256e6			1.01363
$528$		0			0
$529$	−164126.			−0.0254998
$530$		0			0
$531$	4.91437e6	+	4.91437e6i	0.756365	+	0.756365i
$532$		0			0
$533$	3.45906e6	−	3.45906e6i	0.527400	−	0.527400i
$534$		0			0
$535$			476457.i			0.0719679i
$536$		0			0
$537$		−	5.55616e6i		−	0.831456i
$538$		0			0
$539$	3.04669e6	−	3.04669e6i	0.451706	−	0.451706i
$540$		0			0
$541$	−2.33199e6	−	2.33199e6i	−0.342557	−	0.342557i	0.514771	−	0.857328i	$-0.327877\pi$
$541$	−2.33199e6	−	2.33199e6i	−0.342557	−	0.342557i	−0.857328	+	0.514771i	$0.827877\pi$
$542$		0			0
$543$	1.41774e6			0.206347
$544$		0			0
$545$	−5.09678e6			−0.735029
$546$		0			0
$547$	1.52399e6	+	1.52399e6i	0.217777	+	0.217777i	0.807561	−	0.589784i	$-0.200787\pi$
$547$	1.52399e6	+	1.52399e6i	0.217777	+	0.217777i	−0.589784	+	0.807561i	$0.700787\pi$
$548$		0			0
$549$	−5.70494e6	+	5.70494e6i	−0.807830	+	0.807830i
$550$		0			0
$551$		−	4.83956e6i		−	0.679090i
$552$		0			0
$553$			1.53227e7i			2.13070i
$554$		0			0
$555$	106112.	−	106112.i	0.0146228	−	0.0146228i
$556$		0			0
$557$	443591.	+	443591.i	0.0605822	+	0.0605822i	0.736749	−	0.676167i	$-0.236360\pi$
$557$	443591.	+	443591.i	0.0605822	+	0.0605822i	−0.676167	+	0.736749i	$0.736360\pi$
$558$		0			0
$559$	−1.13113e7			−1.53103
$560$		0			0
$561$	−5.41967e6			−0.727052
$562$		0			0
$563$	−786756.	−	786756.i	−0.104609	−	0.104609i	0.652865	−	0.757474i	$-0.273567\pi$
$563$	−786756.	−	786756.i	−0.104609	−	0.104609i	−0.757474	+	0.652865i	$0.773567\pi$
$564$		0			0
$565$	−2.64462e6	+	2.64462e6i	−0.348531	+	0.348531i
$566$		0			0
$567$		−	9.80834e6i		−	1.28126i
$568$		0			0
$569$			726341.i			0.0940503i	0.998894	+	0.0470251i	$0.0149741\pi$
$569$			726341.i			0.0940503i	−0.998894	+	0.0470251i	$0.985026\pi$
$570$		0			0
$571$	−1.61331e6	+	1.61331e6i	−0.207074	+	0.207074i	−0.803023	−	0.595948i	$-0.796776\pi$
$571$	−1.61331e6	+	1.61331e6i	−0.207074	+	0.207074i	0.595948	+	0.803023i	$0.296776\pi$
$572$		0			0
$573$	1.07755e7	+	1.07755e7i	1.37105	+	1.37105i
$574$		0			0
$575$	1.60571e6			0.202534
$576$		0			0
$577$	9.84682e6			1.23128			0.615639	−	0.788028i	$-0.288898\pi$
$577$	9.84682e6			1.23128			0.615639	+	0.788028i	$0.288898\pi$
$578$		0			0
$579$	−1.44436e6	−	1.44436e6i	−0.179052	−	0.179052i
$580$		0			0
$581$	1.53037e7	−	1.53037e7i	1.88086	−	1.88086i
$582$		0			0
$583$		−	214262.i		−	0.0261080i
$584$		0			0
$585$		−	4.29386e6i		−	0.518750i
$586$		0			0
$587$	−5.57755e6	+	5.57755e6i	−0.668110	+	0.668110i	−0.957278	−	0.289168i	$-0.906621\pi$
$587$	−5.57755e6	+	5.57755e6i	−0.668110	+	0.668110i	0.289168	+	0.957278i	$0.406621\pi$
$588$		0			0
$589$	6.74824e6	+	6.74824e6i	0.801497	+	0.801497i
$590$		0			0
$591$	−7.69348e6			−0.906054
$592$		0			0
$593$	−4.09361e6			−0.478046			−0.239023	−	0.971014i	$-0.576827\pi$
$593$	−4.09361e6			−0.478046			−0.239023	+	0.971014i	$0.576827\pi$
$594$		0			0
$595$	−6.03335e6	−	6.03335e6i	−0.698661	−	0.698661i
$596$		0			0
$597$	7.15769e6	−	7.15769e6i	0.821935	−	0.821935i
$598$		0			0
$599$		−	1.26630e7i		−	1.44201i	−0.692927	−	0.721007i	$-0.743679\pi$
$599$		−	1.26630e7i		−	1.44201i	0.692927	−	0.721007i	$-0.256321\pi$
$600$		0			0
$601$		−	1.15873e7i		−	1.30857i	−0.756250	−	0.654283i	$-0.772971\pi$
$601$		−	1.15873e7i		−	1.30857i	0.756250	−	0.654283i	$-0.227029\pi$
$602$		0			0
$603$	−1.32660e7	+	1.32660e7i	−1.48575	+	1.48575i
$604$		0			0
$605$	−2.46169e6	−	2.46169e6i	−0.273429	−	0.273429i
$606$		0			0
$607$	−4.69354e6			−0.517046			−0.258523	−	0.966005i	$-0.583236\pi$
$607$	−4.69354e6			−0.517046			−0.258523	+	0.966005i	$0.583236\pi$
$608$		0			0
$609$	−1.01865e7			−1.11296
$610$		0			0
$611$	5.26052e6	+	5.26052e6i	0.570067	+	0.570067i
$612$		0			0
$613$	1.19732e6	−	1.19732e6i	0.128694	−	0.128694i	−0.639826	−	0.768520i	$-0.720993\pi$
$613$	1.19732e6	−	1.19732e6i	0.128694	−	0.128694i	0.768520	+	0.639826i	$0.220993\pi$
$614$		0			0
$615$		−	4.74752e6i		−	0.506150i
$616$		0			0
$617$			1.15235e7i			1.21863i	0.792927	+	0.609317i	$0.208556\pi$
$617$			1.15235e7i			1.21863i	−0.792927	+	0.609317i	$0.791444\pi$
$618$		0			0
$619$	−9.33557e6	+	9.33557e6i	−0.979297	+	0.979297i	−0.999790	−	0.0204933i	$-0.993476\pi$
$619$	−9.33557e6	+	9.33557e6i	−0.979297	+	0.979297i	0.0204933	+	0.999790i	$0.493476\pi$
$620$		0			0
$621$	1.92993e6	+	1.92993e6i	0.200823	+	0.200823i
$622$		0			0
$623$	−1.22364e7			−1.26309
$624$		0			0
$625$	−390625.			−0.0400000
$626$		0			0
$627$	−5.65924e6	−	5.65924e6i	−0.574896	−	0.574896i
$628$		0			0
$629$	−292847.	+	292847.i	−0.0295131	+	0.0295131i
$630$		0			0
$631$			1.88013e6i			0.187982i	0.995573	+	0.0939908i	$0.0299624\pi$
$631$			1.88013e6i			0.187982i	−0.995573	+	0.0939908i	$0.970038\pi$
$632$		0			0
$633$		−	1.73733e7i		−	1.72335i
$634$		0			0
$635$	2.35227e6	−	2.35227e6i	0.231501	−	0.231501i
$636$		0			0
$637$	−1.22619e7	−	1.22619e7i	−1.19731	−	1.19731i
$638$		0			0
$639$	2.11400e7			2.04810
$640$		0			0
$641$	1.23160e7			1.18393			0.591965	−	0.805964i	$-0.298352\pi$
$641$	1.23160e7			1.18393			0.591965	+	0.805964i	$0.298352\pi$
$642$		0			0
$643$	3.01518e6	+	3.01518e6i	0.287598	+	0.287598i	0.836130	−	0.548532i	$-0.184813\pi$
$643$	3.01518e6	+	3.01518e6i	0.287598	+	0.287598i	−0.548532	+	0.836130i	$0.684813\pi$
$644$		0			0
$645$	−7.76234e6	+	7.76234e6i	−0.734672	+	0.734672i
$646$		0			0
$647$			4.22353e6i			0.396657i	0.980136	+	0.198328i	$0.0635513\pi$
$647$			4.22353e6i			0.396657i	−0.980136	+	0.198328i	$0.936449\pi$
$648$		0			0
$649$			3.54975e6i			0.330815i
$650$		0			0
$651$	1.42039e7	−	1.42039e7i	1.31358	−	1.31358i
$652$		0			0
$653$	−2.95193e6	−	2.95193e6i	−0.270909	−	0.270909i	0.558557	−	0.829466i	$-0.311355\pi$
$653$	−2.95193e6	−	2.95193e6i	−0.270909	−	0.270909i	−0.829466	+	0.558557i	$0.811355\pi$
$654$		0			0
$655$	1.43006e6			0.130242
$656$		0			0
$657$	1.04703e7			0.946334
$658$		0			0
$659$	−1.26003e6	−	1.26003e6i	−0.113023	−	0.113023i	0.648334	−	0.761356i	$-0.275466\pi$
$659$	−1.26003e6	−	1.26003e6i	−0.113023	−	0.113023i	−0.761356	+	0.648334i	$0.775466\pi$
$660$		0			0
$661$	2.91137e6	−	2.91137e6i	0.259176	−	0.259176i	−0.565543	−	0.824719i	$-0.691333\pi$
$661$	2.91137e6	−	2.91137e6i	0.259176	−	0.259176i	0.824719	+	0.565543i	$0.191333\pi$
$662$		0			0
$663$			2.18123e7i			1.92716i
$664$		0			0
$665$		−	1.26001e7i		−	1.10489i
$666$		0			0
$667$	−3.74094e6	+	3.74094e6i	−0.325587	+	0.325587i
$668$		0			0
$669$	−1.30644e7	−	1.30644e7i	−1.12855	−	1.12855i
$670$		0			0
$671$	−4.12079e6			−0.353325
$672$		0			0
$673$	−9.00041e6			−0.765993			−0.382997	−	0.923750i	$-0.625108\pi$
$673$	−9.00041e6			−0.765993			−0.382997	+	0.923750i	$0.625108\pi$
$674$		0			0
$675$	−469499.	−	469499.i	−0.0396620	−	0.0396620i
$676$		0			0
$677$	−4.20664e6	+	4.20664e6i	−0.352747	+	0.352747i	−0.861131	−	0.508383i	$-0.830243\pi$
$677$	−4.20664e6	+	4.20664e6i	−0.352747	+	0.352747i	0.508383	+	0.861131i	$0.330243\pi$
$678$		0			0
$679$		−	9.87008e6i		−	0.821573i
$680$		0			0
$681$		−	1.03074e7i		−	0.851689i
$682$		0			0
$683$	−1.40186e7	+	1.40186e7i	−1.14988	+	1.14988i	−0.163303	+	0.986576i	$0.552215\pi$
$683$	−1.40186e7	+	1.40186e7i	−1.14988	+	1.14988i	−0.986576	+	0.163303i	$0.947785\pi$
$684$		0			0
$685$	−2.00563e6	−	2.00563e6i	−0.163314	−	0.163314i
$686$		0			0
$687$	1.65150e7			1.33502
$688$		0			0
$689$	−862330.			−0.0692031
$690$		0			0
$691$	442842.	+	442842.i	0.0352820	+	0.0352820i	0.724528	−	0.689246i	$-0.242058\pi$
$691$	442842.	+	442842.i	0.0352820	+	0.0352820i	−0.689246	+	0.724528i	$0.742058\pi$
$692$		0			0
$693$	−6.47145e6	+	6.47145e6i	−0.511880	+	0.511880i
$694$		0			0
$695$		−	5.80150e6i		−	0.455595i
$696$		0			0
$697$			1.31022e7i			1.02156i
$698$		0			0
$699$	1.73873e7	−	1.73873e7i	1.34598	−	1.34598i
$700$		0			0
$701$	2.64192e6	+	2.64192e6i	0.203060	+	0.203060i	0.801310	−	0.598249i	$-0.204137\pi$
$701$	2.64192e6	+	2.64192e6i	0.203060	+	0.203060i	−0.598249	+	0.801310i	$0.704137\pi$
$702$		0			0
$703$	−611585.			−0.0466733
$704$		0			0
$705$	7.22001e6			0.547098
$706$		0			0
$707$	−2.15720e7	−	2.15720e7i	−1.62309	−	1.62309i
$708$		0			0
$709$	−5.89423e6	+	5.89423e6i	−0.440364	+	0.440364i	−0.892134	−	0.451771i	$-0.850793\pi$
$709$	−5.89423e6	+	5.89423e6i	−0.440364	+	0.440364i	0.451771	+	0.892134i	$0.350793\pi$
$710$		0			0
$711$		−	2.06529e7i		−	1.53217i
$712$		0			0
$713$		−	1.04327e7i		−	0.768549i
$714$		0			0
$715$	1.55077e6	−	1.55077e6i	0.113444	−	0.113444i
$716$		0			0
$717$	4.51926e6	+	4.51926e6i	0.328299	+	0.328299i
$718$		0			0
$719$	−1.25007e7			−0.901807			−0.450903	−	0.892573i	$-0.648898\pi$
$719$	−1.25007e7			−0.901807			−0.450903	+	0.892573i	$0.648898\pi$
$720$		0			0
$721$	−3.79708e6			−0.272027
$722$		0			0
$723$	9.04559e6	+	9.04559e6i	0.643563	+	0.643563i
$724$		0			0
$725$	910068.	−	910068.i	0.0643027	−	0.0643027i
$726$		0			0
$727$			1.84874e7i			1.29730i	0.761086	+	0.648651i	$0.224666\pi$
$727$			1.84874e7i			1.29730i	−0.761086	+	0.648651i	$0.775334\pi$
$728$		0			0
$729$			1.91749e7i			1.33633i
$730$		0			0
$731$	2.14225e7	−	2.14225e7i	1.48278	−	1.48278i
$732$		0			0
$733$	5.07881e6	+	5.07881e6i	0.349142	+	0.349142i	0.859790	−	0.510648i	$-0.170594\pi$
$733$	5.07881e6	+	5.07881e6i	0.349142	+	0.349142i	−0.510648	+	0.859790i	$0.670594\pi$
$734$		0			0
$735$	−1.68292e7			−1.14907
$736$		0			0
$737$	−9.58230e6			−0.649832
$738$		0			0
$739$	1.92860e7	+	1.92860e7i	1.29907	+	1.29907i	0.929008	+	0.370059i	$0.120663\pi$
$739$	1.92860e7	+	1.92860e7i	1.29907	+	1.29907i	0.370059	+	0.929008i	$0.379337\pi$
$740$		0			0
$741$	−2.27765e7	+	2.27765e7i	−1.52385	+	1.52385i
$742$		0			0
$743$			6.35614e6i			0.422398i	0.977443	+	0.211199i	$0.0677368\pi$
$743$			6.35614e6i			0.422398i	−0.977443	+	0.211199i	$0.932263\pi$
$744$		0			0
$745$		−	6.35426e6i		−	0.419445i
$746$		0			0
$747$	−2.06273e7	+	2.06273e7i	−1.35251	+	1.35251i
$748$		0			0
$749$	−2.89005e6	−	2.89005e6i	−0.188235	−	0.188235i
$750$		0			0
$751$	−2.28259e7			−1.47682			−0.738410	−	0.674352i	$-0.764423\pi$
$751$	−2.28259e7			−1.47682			−0.738410	+	0.674352i	$0.764423\pi$
$752$		0			0
$753$	−2.56190e7			−1.64655
$754$		0			0
$755$	7.24922e6	+	7.24922e6i	0.462832	+	0.462832i
$756$		0			0
$757$	−2.02567e7	+	2.02567e7i	−1.28478	+	1.28478i	−0.346866	+	0.937915i	$0.612754\pi$
$757$	−2.02567e7	+	2.02567e7i	−1.28478	+	1.28478i	−0.937915	+	0.346866i	$0.887246\pi$
$758$		0			0
$759$			8.74910e6i			0.551263i
$760$		0			0
$761$		−	2.39601e7i		−	1.49978i	−0.661563	−	0.749890i	$-0.730107\pi$
$761$		−	2.39601e7i		−	1.49978i	0.661563	−	0.749890i	$-0.269893\pi$
$762$		0			0
$763$	3.09156e7	−	3.09156e7i	1.92250	−	1.92250i
$764$		0			0
$765$	8.13213e6	+	8.13213e6i	0.502402	+	0.502402i
$766$		0			0
$767$	1.42865e7			0.876874
$768$		0			0
$769$	−1.71640e7			−1.04665			−0.523327	−	0.852132i	$-0.675309\pi$
$769$	−1.71640e7			−1.04665			−0.523327	+	0.852132i	$0.675309\pi$
$770$		0			0
$771$	−1.57367e6	−	1.57367e6i	−0.0953407	−	0.0953407i
$772$		0			0
$773$	8.61767e6	−	8.61767e6i	0.518730	−	0.518730i	−0.398457	−	0.917187i	$-0.630454\pi$
$773$	8.61767e6	−	8.61767e6i	0.518730	−	0.518730i	0.917187	+	0.398457i	$0.130454\pi$
$774$		0			0
$775$			2.53798e6i			0.151787i
$776$		0			0
$777$			1.28729e6i			0.0764931i
$778$		0			0
$779$	−1.36814e7	+	1.36814e7i	−0.807768	+	0.807768i
$780$		0			0
$781$	7.63490e6	+	7.63490e6i	0.447895	+	0.447895i
$782$		0			0
$783$	2.18765e6			0.127519
$784$		0			0
$785$	1.15646e7			0.669815
$786$		0			0
$787$	473210.	+	473210.i	0.0272343	+	0.0272343i	0.720593	−	0.693358i	$-0.243870\pi$
$787$	473210.	+	473210.i	0.0272343	+	0.0272343i	−0.693358	+	0.720593i	$0.743870\pi$
$788$		0			0
$789$	9.41794e6	−	9.41794e6i	0.538597	−	0.538597i
$790$		0			0
$791$		−	3.20830e7i		−	1.82320i
$792$		0			0
$793$			1.65847e7i			0.936538i
$794$		0			0
$795$	−591769.	+	591769.i	−0.0332074	+	0.0332074i
$796$		0			0
$797$	−5.58940e6	−	5.58940e6i	−0.311688	−	0.311688i	0.533875	−	0.845563i	$-0.320735\pi$
$797$	−5.58940e6	−	5.58940e6i	−0.311688	−	0.311688i	−0.845563	+	0.533875i	$0.820735\pi$
$798$		0			0
$799$	−1.99258e7			−1.10420
$800$		0			0
$801$	1.64930e7			0.908278
$802$		0			0
$803$	3.78144e6	+	3.78144e6i	0.206951	+	0.206951i
$804$		0			0
$805$	−9.73978e6	+	9.73978e6i	−0.529736	+	0.529736i
$806$		0			0
$807$			3.08722e7i			1.66872i
$808$		0			0
$809$			1.58573e7i			0.851841i	0.904761	+	0.425920i	$0.140050\pi$
$809$			1.58573e7i			0.851841i	−0.904761	+	0.425920i	$0.859950\pi$
$810$		0			0
$811$	6.05953e6	−	6.05953e6i	0.323509	−	0.323509i	−0.526602	−	0.850112i	$-0.676534\pi$
$811$	6.05953e6	−	6.05953e6i	0.323509	−	0.323509i	0.850112	+	0.526602i	$0.176534\pi$
$812$		0			0
$813$	−2.76914e7	−	2.76914e7i	−1.46933	−	1.46933i
$814$		0			0
$815$	1.09315e7			0.576480
$816$		0			0
$817$	4.47390e7			2.34494
$818$		0			0
$819$	2.60453e7	+	2.60453e7i	1.35681	+	1.35681i
$820$		0			0
$821$	−1.38644e7	+	1.38644e7i	−0.717867	+	0.717867i	−0.968168	−	0.250301i	$-0.919471\pi$
$821$	−1.38644e7	+	1.38644e7i	−0.717867	+	0.717867i	0.250301	+	0.968168i	$0.419471\pi$
$822$		0			0
$823$			7.18730e6i			0.369884i	0.982749	+	0.184942i	$0.0592098\pi$
$823$			7.18730e6i			0.369884i	−0.982749	+	0.184942i	$0.940790\pi$
$824$		0			0
$825$		−	2.12841e6i		−	0.108873i
$826$		0			0
$827$	−2.18724e6	+	2.18724e6i	−0.111207	+	0.111207i	−0.760521	−	0.649314i	$-0.775056\pi$
$827$	−2.18724e6	+	2.18724e6i	−0.111207	+	0.111207i	0.649314	+	0.760521i	$0.275056\pi$
$828$		0			0
$829$	−1.03893e7	−	1.03893e7i	−0.525048	−	0.525048i	0.394044	−	0.919092i	$-0.371076\pi$
$829$	−1.03893e7	−	1.03893e7i	−0.525048	−	0.525048i	−0.919092	+	0.394044i	$0.871076\pi$
$830$		0			0
$831$	−9.74291e6			−0.489425
$832$		0			0
$833$	4.64454e7			2.31916
$834$		0			0
$835$	−5.97273e6	−	5.97273e6i	−0.296454	−	0.296454i
$836$		0			0
$837$	−3.05044e6	+	3.05044e6i	−0.150504	+	0.150504i
$838$		0			0
$839$		−	1.70694e7i		−	0.837168i	−0.908178	−	0.418584i	$-0.862527\pi$
$839$		−	1.70694e7i		−	0.837168i	0.908178	−	0.418584i	$-0.137473\pi$
$840$		0			0
$841$		−	1.62706e7i		−	0.793258i
$842$		0			0
$843$	−6.56193e6	+	6.56193e6i	−0.318026	+	0.318026i
$844$		0			0
$845$	322288.	+	322288.i	0.0155275	+	0.0155275i
$846$		0			0
$847$	2.98638e7			1.43033
$848$		0			0
$849$	2.16659e7			1.03159
$850$		0			0
$851$	472750.	+	472750.i	0.0223773	+	0.0223773i
$852$		0			0
$853$	−8.55366e6	+	8.55366e6i	−0.402512	+	0.402512i	−0.879118	−	0.476605i	$-0.841867\pi$
$853$	−8.55366e6	+	8.55366e6i	−0.402512	+	0.402512i	0.476605	+	0.879118i	$0.341867\pi$
$854$		0			0
$855$			1.69832e7i			0.794520i
$856$		0			0
$857$		−	1.25686e7i		−	0.584567i	−0.956332	−	0.292284i	$-0.905585\pi$
$857$		−	1.25686e7i		−	0.584567i	0.956332	−	0.292284i	$-0.0944151\pi$
$858$		0			0
$859$	−1.32837e7	+	1.32837e7i	−0.614238	+	0.614238i	−0.944047	−	0.329810i	$-0.893015\pi$
$859$	−1.32837e7	+	1.32837e7i	−0.614238	+	0.614238i	0.329810	+	0.944047i	$0.393015\pi$
$860$		0			0
$861$	2.87971e7	+	2.87971e7i	1.32386	+	1.32386i
$862$		0			0
$863$	−2.91730e7			−1.33338			−0.666690	−	0.745335i	$-0.732289\pi$
$863$	−2.91730e7			−1.33338			−0.666690	+	0.745335i	$0.732289\pi$
$864$		0			0
$865$	−5.78902e6			−0.263066
$866$		0			0
$867$	−1.81518e7	−	1.81518e7i	−0.820111	−	0.820111i
$868$		0			0
$869$	7.45901e6	−	7.45901e6i	0.335067	−	0.335067i
$870$		0			0
$871$			3.85654e7i			1.72247i
$872$		0			0
$873$			1.33035e7i			0.590787i
$874$		0			0
$875$	2.36942e6	−	2.36942e6i	0.104622	−	0.104622i
$876$		0			0
$877$	1.22774e7	+	1.22774e7i	0.539022	+	0.539022i	0.923242	−	0.384219i	$-0.125529\pi$
$877$	1.22774e7	+	1.22774e7i	0.539022	+	0.539022i	−0.384219	+	0.923242i	$0.625529\pi$
$878$		0			0
$879$	1.45528e7			0.635292
$880$		0			0
$881$	−1.28434e7			−0.557495			−0.278747	−	0.960364i	$-0.589919\pi$
$881$	−1.28434e7			−0.557495			−0.278747	+	0.960364i	$0.589919\pi$
$882$		0			0
$883$	9.00217e6	+	9.00217e6i	0.388549	+	0.388549i	0.874169	−	0.485621i	$-0.161406\pi$
$883$	9.00217e6	+	9.00217e6i	0.388549	+	0.388549i	−0.485621	+	0.874169i	$0.661406\pi$
$884$		0			0
$885$	9.80402e6	−	9.80402e6i	0.420771	−	0.420771i
$886$		0			0
$887$		−	3.75839e7i		−	1.60396i	−0.597352	−	0.801979i	$-0.703781\pi$
$887$		−	3.75839e7i		−	1.60396i	0.597352	−	0.801979i	$-0.296219\pi$
$888$		0			0
$889$			2.85364e7i			1.21100i
$890$		0			0
$891$	−4.77464e6	+	4.77464e6i	−0.201487	+	0.201487i
$892$		0			0
$893$	−2.08066e7	−	2.08066e7i	−0.873117	−	0.873117i
$894$		0			0
$895$	−6.02193e6			−0.251292
$896$		0			0
$897$	3.52121e7			1.46120
$898$		0			0
$899$	−5.91292e6	−	5.91292e6i	−0.244007	−	0.244007i
$900$		0			0
$901$	1.63317e6	−	1.63317e6i	0.0670221	−	0.0670221i
$902$		0			0
$903$		−	9.41682e7i		−	3.84313i
$904$		0			0
$905$		−	1.53659e6i		−	0.0623645i
$906$		0			0
$907$	2.29650e7	−	2.29650e7i	0.926934	−	0.926934i	−0.0705730	−	0.997507i	$-0.522483\pi$
$907$	2.29650e7	−	2.29650e7i	0.926934	−	0.926934i	0.997507	+	0.0705730i	$0.0224828\pi$
$908$		0			0
$909$	2.90761e7	+	2.90761e7i	1.16715	+	1.16715i
$910$		0			0
$911$	1.94732e7			0.777395			0.388698	−	0.921365i	$-0.372925\pi$
$911$	1.94732e7			0.777395			0.388698	+	0.921365i	$0.372925\pi$
$912$		0			0
$913$	−1.48995e7			−0.591556
$914$		0			0
$915$	1.13812e7	+	1.13812e7i	0.449401	+	0.449401i
$916$		0			0
$917$	−8.67433e6	+	8.67433e6i	−0.340653	+	0.340653i
$918$		0			0
$919$		−	1.58244e6i		−	0.0618071i	−0.999522	−	0.0309036i	$-0.990162\pi$
$919$		−	1.58244e6i		−	0.0618071i	0.999522	−	0.0309036i	$-0.00983847\pi$
$920$		0			0
$921$		−	6.12557e7i		−	2.37957i
$922$		0			0
$923$	3.07278e7	−	3.07278e7i	1.18721	−	1.18721i
$924$		0			0
$925$	−115007.	−	115007.i	−0.00441947	−	0.00441947i
$926$		0			0
$927$	5.11795e6			0.195612
$928$		0			0
$929$	3.49800e7			1.32978			0.664891	−	0.746940i	$-0.268478\pi$
$929$	3.49800e7			1.32978			0.664891	+	0.746940i	$0.268478\pi$
$930$		0			0
$931$	4.84985e7	+	4.84985e7i	1.83381	+	1.83381i
$932$		0			0
$933$	2.60629e7	−	2.60629e7i	0.980207	−	0.980207i
$934$		0			0
$935$			5.87400e6i			0.219738i
$936$		0			0
$937$		−	5.05957e7i		−	1.88263i	−0.337532	−	0.941314i	$-0.609592\pi$
$937$		−	5.05957e7i		−	1.88263i	0.337532	−	0.941314i	$-0.390408\pi$
$938$		0			0
$939$	2.00616e7	−	2.00616e7i	0.742510	−	0.742510i
$940$		0			0
$941$	760888.	+	760888.i	0.0280122	+	0.0280122i	0.720974	−	0.692962i	$-0.243695\pi$
$941$	760888.	+	760888.i	0.0280122	+	0.0280122i	−0.692962	+	0.720974i	$0.743695\pi$
$942$		0			0
$943$	2.11512e7			0.774562
$944$		0			0
$945$	5.69569e6			0.207475
$946$		0			0
$947$	2.72014e6	+	2.72014e6i	0.0985635	+	0.0985635i	0.754669	−	0.656106i	$-0.227797\pi$
$947$	2.72014e6	+	2.72014e6i	0.0985635	+	0.0985635i	−0.656106	+	0.754669i	$0.727797\pi$
$948$		0			0
$949$	1.52190e7	−	1.52190e7i	0.548555	−	0.548555i
$950$		0			0
$951$			3.41291e7i			1.22370i
$952$		0			0
$953$			2.63977e7i			0.941530i	0.882259	+	0.470765i	$0.156022\pi$
$953$			2.63977e7i			0.941530i	−0.882259	+	0.470765i	$0.843978\pi$
$954$		0			0
$955$	1.16789e7	−	1.16789e7i	0.414374	−	0.414374i
$956$		0			0
$957$	4.95872e6	+	4.95872e6i	0.175021	+	0.175021i
$958$		0			0
$959$	2.43312e7			0.854312
$960$		0			0
$961$	−1.21393e7			−0.424020
$962$		0			0
$963$	3.89539e6	+	3.89539e6i	0.135358	+	0.135358i
$964$		0			0
$965$	−1.56544e6	+	1.56544e6i	−0.0541150	+	0.0541150i
$966$		0			0
$967$			6.87061e6i			0.236281i	0.992997	+	0.118141i	$0.0376933\pi$
$967$			6.87061e6i			0.236281i	−0.992997	+	0.118141i	$0.962307\pi$
$968$		0			0
$969$		−	8.62726e7i		−	2.95164i
$970$		0			0
$971$	−2.28649e7	+	2.28649e7i	−0.778254	+	0.778254i	−0.979534	−	0.201280i	$-0.935490\pi$
$971$	−2.28649e7	+	2.28649e7i	−0.778254	+	0.778254i	0.201280	+	0.979534i	$0.435490\pi$
$972$		0			0
$973$	3.51902e7	+	3.51902e7i	1.19163	+	1.19163i
$974$		0			0
$975$	−8.56612e6			−0.288584
$976$		0			0
$977$	5.76020e6			0.193064			0.0965319	−	0.995330i	$-0.469225\pi$
$977$	5.76020e6			0.193064			0.0965319	+	0.995330i	$0.469225\pi$
$978$		0			0
$979$	5.95661e6	+	5.95661e6i	0.198629	+	0.198629i
$980$		0			0
$981$	−4.16700e7	+	4.16700e7i	−1.38245	+	1.38245i
$982$		0			0
$983$			3.68691e6i			0.121697i	0.998147	+	0.0608483i	$0.0193806\pi$
$983$			3.68691e6i			0.121697i	−0.998147	+	0.0608483i	$0.980619\pi$
$984$		0			0
$985$			8.33842e6i			0.273838i
$986$		0			0
$987$	−4.37945e7	+	4.37945e7i	−1.43096	+	1.43096i
$988$		0			0
$989$	−3.45829e7	−	3.45829e7i	−1.12427	−	1.12427i
$990$		0			0
$991$	−3.97944e7			−1.28718			−0.643588	−	0.765372i	$-0.722555\pi$
$991$	−3.97944e7			−1.28718			−0.643588	+	0.765372i	$0.722555\pi$
$992$		0			0
$993$	4.66122e7			1.50012
$994$		0			0
$995$	−7.75772e6	−	7.75772e6i	−0.248414	−	0.248414i
$996$		0			0
$997$	−611454.	+	611454.i	−0.0194817	+	0.0194817i	−0.716781	−	0.697299i	$-0.754385\pi$
$997$	−611454.	+	611454.i	−0.0194817	+	0.0194817i	0.697299	+	0.716781i	$0.254385\pi$
$998$		0			0
$999$		−	276458.i		−	0.00876426i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.6.l.a.81.5		80
4.3	odd	2		80.6.l.a.61.27	yes	80
16.5	even	4	inner	320.6.l.a.241.5		80
16.11	odd	4		80.6.l.a.21.27	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.27	✓	80	16.11	odd	4
80.6.l.a.61.27	yes	80	4.3	odd	2
320.6.l.a.81.5		80	1.1	even	1	trivial
320.6.l.a.241.5		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)

\(f(q)\)	\(=\)	\(q+(-16.3104 - 16.3104i) q^{3} +(-17.6777 + 17.6777i) q^{5} -214.455i q^{7} +289.056i q^{9} +O(q^{10})\)	\(q+(-16.3104 - 16.3104i) q^{3} +(-17.6777 + 17.6777i) q^{5} -214.455i q^{7} +289.056i q^{9} +(-104.396 + 104.396i) q^{11} +(420.156 + 420.156i) q^{13} +576.659 q^{15} -1591.46 q^{17} +(-1661.81 - 1661.81i) q^{19} +(-3497.85 + 3497.85i) q^{21} +2569.14i q^{23} -625.000i q^{25} +(751.198 - 751.198i) q^{27} +(1456.11 + 1456.11i) q^{29} -4060.77 q^{31} +3405.46 q^{33} +(3791.07 + 3791.07i) q^{35} +(184.011 - 184.011i) q^{37} -13705.8i q^{39} -8232.81i q^{41} +(-13460.9 + 13460.9i) q^{43} +(-5109.84 - 5109.84i) q^{45} +12520.4 q^{47} -29184.1 q^{49} +(25957.4 + 25957.4i) q^{51} +(-1026.20 + 1026.20i) q^{53} -3690.94i q^{55} +54209.6i q^{57} +(17001.4 - 17001.4i) q^{59} +(19736.4 + 19736.4i) q^{61} +61989.7 q^{63} -14854.7 q^{65} +(45894.2 + 45894.2i) q^{67} +(41903.6 - 41903.6i) q^{69} -73134.4i q^{71} -36222.2i q^{73} +(-10194.0 + 10194.0i) q^{75} +(22388.2 + 22388.2i) q^{77} -71449.5 q^{79} +45736.1 q^{81} +(71360.9 + 71360.9i) q^{83} +(28133.4 - 28133.4i) q^{85} -47499.4i q^{87} -57058.1i q^{89} +(90104.6 - 90104.6i) q^{91} +(66232.6 + 66232.6i) q^{93} +58754.0 q^{95} +46024.0 q^{97} +(-30176.2 - 30176.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q+O(q^{10}) \) 80 * q	\( 80 q - 1208 q^{11} + 1800 q^{15} - 2360 q^{19} + 7464 q^{27} - 8144 q^{29} + 21296 q^{37} - 32072 q^{43} + 88360 q^{47} - 192080 q^{49} + 5920 q^{51} - 49456 q^{53} - 44984 q^{59} + 48080 q^{61} - 158760 q^{63} - 61160 q^{67} - 22320 q^{69} - 14896 q^{77} - 177680 q^{79} - 524880 q^{81} + 329240 q^{83} + 132400 q^{85} - 364832 q^{91} - 362352 q^{93} - 288800 q^{95} - 659000 q^{99}+O(q^{100}) \) 80 * q - 1208 * q^11 + 1800 * q^15 - 2360 * q^19 + 7464 * q^27 - 8144 * q^29 + 21296 * q^37 - 32072 * q^43 + 88360 * q^47 - 192080 * q^49 + 5920 * q^51 - 49456 * q^53 - 44984 * q^59 + 48080 * q^61 - 158760 * q^63 - 61160 * q^67 - 22320 * q^69 - 14896 * q^77 - 177680 * q^79 - 524880 * q^81 + 329240 * q^83 + 132400 * q^85 - 364832 * q^91 - 362352 * q^93 - 288800 * q^95 - 659000 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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