LMFDB - Embedded newform 320.6.l.a.81.7

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			81.7
Character	$\chi$	$=$	320.81
Dual form			320.6.l.a.241.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-15.7717 - 15.7717i) q^{3} +(-17.6777 + 17.6777i) q^{5} -14.9661i q^{7} +254.492i q^{9} +O(q^{10})$	\(q+(-15.7717 - 15.7717i) q^{3} +(-17.6777 + 17.6777i) q^{5} -14.9661i q^{7} +254.492i q^{9} +(280.821 - 280.821i) q^{11} +(-223.510 - 223.510i) q^{13} +557.613 q^{15} +55.2985 q^{17} +(-1689.10 - 1689.10i) q^{19} +(-236.040 + 236.040i) q^{21} -1590.38i q^{23} -625.000i q^{25} +(181.249 - 181.249i) q^{27} +(-3477.05 - 3477.05i) q^{29} -729.785 q^{31} -8858.05 q^{33} +(264.565 + 264.565i) q^{35} +(-3723.22 + 3723.22i) q^{37} +7050.25i q^{39} +3498.56i q^{41} +(15040.3 - 15040.3i) q^{43} +(-4498.83 - 4498.83i) q^{45} -25930.2 q^{47} +16583.0 q^{49} +(-872.151 - 872.151i) q^{51} +(-7577.88 + 7577.88i) q^{53} +9928.53i q^{55} +53279.8i q^{57} +(18115.4 - 18115.4i) q^{59} +(29176.1 + 29176.1i) q^{61} +3808.75 q^{63} +7902.26 q^{65} +(-25445.4 - 25445.4i) q^{67} +(-25082.9 + 25082.9i) q^{69} +53030.7i q^{71} +32532.0i q^{73} +(-9857.30 + 9857.30i) q^{75} +(-4202.79 - 4202.79i) q^{77} +5708.74 q^{79} +56124.4 q^{81} +(33001.2 + 33001.2i) q^{83} +(-977.549 + 977.549i) q^{85} +109678. i q^{87} +97013.9i q^{89} +(-3345.06 + 3345.06i) q^{91} +(11509.9 + 11509.9i) q^{93} +59718.6 q^{95} +66285.8 q^{97} +(71466.7 + 71466.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−15.7717	−	15.7717i	−1.01175	−	1.01175i	−0.999930	−	0.0118239i	$-0.996236\pi$
$3$	−15.7717	−	15.7717i	−1.01175	−	1.01175i	−0.0118239	−	0.999930i	$-0.503764\pi$
$4$		0			0
$5$	−17.6777	+	17.6777i	−0.316228	+	0.316228i
$5$	−17.6777	+	17.6777i	−0.316228	+	0.316228i
$6$		0			0
$7$		−	14.9661i		−	0.115442i	−0.998333	−	0.0577209i	$-0.981617\pi$
$7$		−	14.9661i		−	0.115442i	0.998333	−	0.0577209i	$-0.0183833\pi$
$8$		0			0
$9$			254.492i			1.04729i
$10$		0			0
$11$	280.821	−	280.821i	0.699758	−	0.699758i	−0.264600	−	0.964358i	$-0.585240\pi$
$11$	280.821	−	280.821i	0.699758	−	0.699758i	0.964358	+	0.264600i	$0.0852399\pi$
$12$		0			0
$13$	−223.510	−	223.510i	−0.366807	−	0.366807i	0.499504	−	0.866311i	$-0.333516\pi$
$13$	−223.510	−	223.510i	−0.366807	−	0.366807i	−0.866311	+	0.499504i	$0.833516\pi$
$14$		0			0
$15$	557.613			0.639889
$16$		0			0
$17$	55.2985			0.0464078			0.0232039	−	0.999731i	$-0.492613\pi$
$17$	55.2985			0.0464078			0.0232039	+	0.999731i	$0.492613\pi$
$18$		0			0
$19$	−1689.10	−	1689.10i	−1.07342	−	1.07342i	−0.997082	−	0.0763413i	$-0.975676\pi$
$19$	−1689.10	−	1689.10i	−1.07342	−	1.07342i	−0.0763413	−	0.997082i	$-0.524324\pi$
$20$		0			0
$21$	−236.040	+	236.040i	−0.116799	+	0.116799i
$22$		0			0
$23$		−	1590.38i		−	0.626875i	−0.949609	−	0.313437i	$-0.898519\pi$
$23$		−	1590.38i		−	0.626875i	0.949609	−	0.313437i	$-0.101481\pi$
$24$		0			0
$25$		−	625.000i		−	0.200000i
$26$		0			0
$27$	181.249	−	181.249i	0.0478482	−	0.0478482i
$28$		0			0
$29$	−3477.05	−	3477.05i	−0.767743	−	0.767743i	0.209966	−	0.977709i	$-0.432665\pi$
$29$	−3477.05	−	3477.05i	−0.767743	−	0.767743i	−0.977709	+	0.209966i	$0.932665\pi$
$30$		0			0
$31$	−729.785			−0.136393			−0.0681963	−	0.997672i	$-0.521724\pi$
$31$	−729.785			−0.136393			−0.0681963	+	0.997672i	$0.521724\pi$
$32$		0			0
$33$	−8858.05			−1.41597
$34$		0			0
$35$	264.565	+	264.565i	0.0365059	+	0.0365059i
$36$		0			0
$37$	−3723.22	+	3723.22i	−0.447110	+	0.447110i	−0.894393	−	0.447283i	$-0.852392\pi$
$37$	−3723.22	+	3723.22i	−0.447110	+	0.447110i	0.447283	+	0.894393i	$0.352392\pi$
$38$		0			0
$39$			7050.25i			0.742237i
$40$		0			0
$41$			3498.56i			0.325034i	0.986706	+	0.162517i	$0.0519613\pi$
$41$			3498.56i			0.325034i	−0.986706	+	0.162517i	$0.948039\pi$
$42$		0			0
$43$	15040.3	−	15040.3i	1.24047	−	1.24047i	0.280660	−	0.959807i	$-0.409447\pi$
$43$	15040.3	−	15040.3i	1.24047	−	1.24047i	0.959807	−	0.280660i	$-0.0905533\pi$
$44$		0			0
$45$	−4498.83	−	4498.83i	−0.331183	−	0.331183i
$46$		0			0
$47$	−25930.2			−1.71223			−0.856114	−	0.516786i	$-0.827128\pi$
$47$	−25930.2			−1.71223			−0.856114	+	0.516786i	$0.827128\pi$
$48$		0			0
$49$	16583.0			0.986673
$50$		0			0
$51$	−872.151	−	872.151i	−0.0469533	−	0.0469533i
$52$		0			0
$53$	−7577.88	+	7577.88i	−0.370559	+	0.370559i	−0.867681	−	0.497121i	$-0.834390\pi$
$53$	−7577.88	+	7577.88i	−0.370559	+	0.370559i	0.497121	+	0.867681i	$0.334390\pi$
$54$		0			0
$55$			9928.53i			0.442566i
$56$		0			0
$57$			53279.8i			2.17208i
$58$		0			0
$59$	18115.4	−	18115.4i	0.677515	−	0.677515i	−0.281922	−	0.959437i	$-0.590972\pi$
$59$	18115.4	−	18115.4i	0.677515	−	0.677515i	0.959437	+	0.281922i	$0.0909721\pi$
$60$		0			0
$61$	29176.1	+	29176.1i	1.00393	+	1.00393i	0.999992	+	0.00393562i	$0.00125275\pi$
$61$	29176.1	+	29176.1i	1.00393	+	1.00393i	0.00393562	+	0.999992i	$0.498747\pi$
$62$		0			0
$63$	3808.75			0.120901
$64$		0			0
$65$	7902.26			0.231989
$66$		0			0
$67$	−25445.4	−	25445.4i	−0.692503	−	0.692503i	0.270279	−	0.962782i	$-0.412884\pi$
$67$	−25445.4	−	25445.4i	−0.692503	−	0.692503i	−0.962782	+	0.270279i	$0.912884\pi$
$68$		0			0
$69$	−25082.9	+	25082.9i	−0.634243	+	0.634243i
$70$		0			0
$71$			53030.7i			1.24848i	0.781232	+	0.624240i	$0.214591\pi$
$71$			53030.7i			1.24848i	−0.781232	+	0.624240i	$0.785409\pi$
$72$		0			0
$73$			32532.0i			0.714502i	0.934008	+	0.357251i	$0.116286\pi$
$73$			32532.0i			0.714502i	−0.934008	+	0.357251i	$0.883714\pi$
$74$		0			0
$75$	−9857.30	+	9857.30i	−0.202351	+	0.202351i
$76$		0			0
$77$	−4202.79	−	4202.79i	−0.0807813	−	0.0807813i
$78$		0			0
$79$	5708.74			0.102914			0.0514568	−	0.998675i	$-0.483614\pi$
$79$	5708.74			0.102914			0.0514568	+	0.998675i	$0.483614\pi$
$80$		0			0
$81$	56124.4			0.950471
$82$		0			0
$83$	33001.2	+	33001.2i	0.525818	+	0.525818i	0.919322	−	0.393505i	$-0.128738\pi$
$83$	33001.2	+	33001.2i	0.525818	+	0.525818i	−0.393505	+	0.919322i	$0.628738\pi$
$84$		0			0
$85$	−977.549	+	977.549i	−0.0146754	+	0.0146754i
$86$		0			0
$87$			109678.i			1.55353i
$88$		0			0
$89$			97013.9i			1.29825i	0.760681	+	0.649126i	$0.224865\pi$
$89$			97013.9i			1.29825i	−0.760681	+	0.649126i	$0.775135\pi$
$90$		0			0
$91$	−3345.06	+	3345.06i	−0.0423449	+	0.0423449i
$92$		0			0
$93$	11509.9	+	11509.9i	0.137996	+	0.137996i
$94$		0			0
$95$	59718.6			0.678892
$96$		0			0
$97$	66285.8			0.715305			0.357652	−	0.933855i	$-0.383577\pi$
$97$	66285.8			0.715305			0.357652	+	0.933855i	$0.383577\pi$
$98$		0			0
$99$	71466.7	+	71466.7i	0.732852	+	0.732852i
$100$		0			0
$101$	40924.2	−	40924.2i	0.399188	−	0.399188i	−0.478759	−	0.877947i	$-0.658913\pi$
$101$	40924.2	−	40924.2i	0.399188	−	0.399188i	0.877947	+	0.478759i	$0.158913\pi$
$102$		0			0
$103$			185824.i			1.72587i	0.505312	+	0.862937i	$0.331377\pi$
$103$			185824.i			1.72587i	−0.505312	+	0.862937i	$0.668623\pi$
$104$		0			0
$105$		−	8345.28i		−	0.0738699i
$106$		0			0
$107$	−62634.0	+	62634.0i	−0.528872	+	0.528872i	−0.920236	−	0.391364i	$-0.872003\pi$
$107$	−62634.0	+	62634.0i	−0.528872	+	0.528872i	0.391364	+	0.920236i	$0.372003\pi$
$108$		0			0
$109$	−71469.6	−	71469.6i	−0.576176	−	0.576176i	0.357671	−	0.933848i	$-0.383571\pi$
$109$	−71469.6	−	71469.6i	−0.576176	−	0.576176i	−0.933848	+	0.357671i	$0.883571\pi$
$110$		0			0
$111$	117443.			0.904731
$112$		0			0
$113$	−225233.			−1.65934			−0.829672	−	0.558252i	$-0.811472\pi$
$113$	−225233.			−1.65934			−0.829672	+	0.558252i	$0.811472\pi$
$114$		0			0
$115$	28114.2	+	28114.2i	0.198235	+	0.198235i
$116$		0			0
$117$	56881.4	−	56881.4i	0.384154	−	0.384154i
$118$		0			0
$119$		−	827.602i		−	0.00535740i
$120$		0			0
$121$			3329.96i			0.0206764i
$122$		0			0
$123$	55178.1	−	55178.1i	0.328855	−	0.328855i
$124$		0			0
$125$	11048.5	+	11048.5i	0.0632456	+	0.0632456i
$126$		0			0
$127$	−265506.			−1.46071			−0.730356	−	0.683066i	$-0.760646\pi$
$127$	−265506.			−1.46071			−0.730356	+	0.683066i	$0.760646\pi$
$128$		0			0
$129$	−474422.			−2.51010
$130$		0			0
$131$	−27805.2	−	27805.2i	−0.141562	−	0.141562i	0.632774	−	0.774336i	$-0.281916\pi$
$131$	−27805.2	−	27805.2i	−0.141562	−	0.141562i	−0.774336	+	0.632774i	$0.781916\pi$
$132$		0			0
$133$	−25279.2	+	25279.2i	−0.123918	+	0.123918i
$134$		0			0
$135$			6408.11i			0.0302618i
$136$		0			0
$137$		−	199915.i		−	0.910008i	−0.890489	−	0.455004i	$-0.849638\pi$
$137$		−	199915.i		−	0.910008i	0.890489	−	0.455004i	$-0.150362\pi$
$138$		0			0
$139$	−297801.	+	297801.i	−1.30734	+	1.30734i	−0.384016	+	0.923326i	$0.625459\pi$
$139$	−297801.	+	297801.i	−1.30734	+	1.30734i	−0.923326	+	0.384016i	$0.874541\pi$
$140$		0			0
$141$	408963.	+	408963.i	1.73235	+	1.73235i
$142$		0			0
$143$	−125532.			−0.513353
$144$		0			0
$145$	122932.			0.485563
$146$		0			0
$147$	−261542.	−	261542.i	−0.998271	−	0.998271i
$148$		0			0
$149$	145128.	−	145128.i	0.535531	−	0.535531i	−0.386682	−	0.922213i	$-0.626379\pi$
$149$	145128.	−	145128.i	0.535531	−	0.535531i	0.922213	+	0.386682i	$0.126379\pi$
$150$		0			0
$151$			77693.1i			0.277294i	0.990342	+	0.138647i	$0.0442753\pi$
$151$			77693.1i			0.277294i	−0.990342	+	0.138647i	$0.955725\pi$
$152$		0			0
$153$			14073.0i			0.0486026i
$154$		0			0
$155$	12900.9	−	12900.9i	0.0431311	−	0.0431311i
$156$		0			0
$157$	−5766.89	−	5766.89i	−0.0186721	−	0.0186721i	0.697709	−	0.716381i	$-0.254203\pi$
$157$	−5766.89	−	5766.89i	−0.0186721	−	0.0186721i	−0.716381	+	0.697709i	$0.754203\pi$
$158$		0			0
$159$	239032.			0.749830
$160$		0			0
$161$	−23801.7			−0.0723675
$162$		0			0
$163$	−415423.	−	415423.i	−1.22468	−	1.22468i	−0.965951	−	0.258724i	$-0.916698\pi$
$163$	−415423.	−	415423.i	−1.22468	−	1.22468i	−0.258724	−	0.965951i	$-0.583302\pi$
$164$		0			0
$165$	156590.	−	156590.i	0.447768	−	0.447768i
$166$		0			0
$167$			445294.i			1.23554i	0.786361	+	0.617768i	$0.211963\pi$
$167$			445294.i			1.23554i	−0.786361	+	0.617768i	$0.788037\pi$
$168$		0			0
$169$		−	271380.i		−	0.730905i
$170$		0			0
$171$	429862.	−	429862.i	1.12419	−	1.12419i
$172$		0			0
$173$	483890.	+	483890.i	1.22923	+	1.22923i	0.964257	+	0.264969i	$0.0853618\pi$
$173$	483890.	+	483890.i	1.22923	+	1.22923i	0.264969	+	0.964257i	$0.414638\pi$
$174$		0			0
$175$	−9353.80			−0.0230883
$176$		0			0
$177$	−571422.			−1.37096
$178$		0			0
$179$	152984.	+	152984.i	0.356873	+	0.356873i	0.862659	−	0.505786i	$-0.168797\pi$
$179$	152984.	+	152984.i	0.356873	+	0.356873i	−0.505786	+	0.862659i	$0.668797\pi$
$180$		0			0
$181$	331130.	−	331130.i	0.751281	−	0.751281i	−0.223437	−	0.974718i	$-0.571728\pi$
$181$	331130.	−	331130.i	0.751281	−	0.751281i	0.974718	+	0.223437i	$0.0717278\pi$
$182$		0			0
$183$		−	920312.i		−	2.03146i
$184$		0			0
$185$		−	131636.i		−	0.282777i
$186$		0			0
$187$	15529.0	−	15529.0i	0.0324743	−	0.0324743i
$188$		0			0
$189$	−2712.58	−	2712.58i	−0.00552367	−	0.00552367i
$190$		0			0
$191$	894847.			1.77486			0.887432	−	0.460938i	$-0.152487\pi$
$191$	894847.			1.77486			0.887432	+	0.460938i	$0.152487\pi$
$192$		0			0
$193$	−267587.			−0.517096			−0.258548	−	0.965998i	$-0.583244\pi$
$193$	−267587.			−0.517096			−0.258548	+	0.965998i	$0.583244\pi$
$194$		0			0
$195$	−124632.	−	124632.i	−0.234716	−	0.234716i
$196$		0			0
$197$	−492211.	+	492211.i	−0.903620	+	0.903620i	−0.995747	−	0.0921275i	$-0.970633\pi$
$197$	−492211.	+	492211.i	−0.903620	+	0.903620i	0.0921275	+	0.995747i	$0.470633\pi$
$198$		0			0
$199$			337905.i			0.604870i	0.953170	+	0.302435i	$0.0977996\pi$
$199$			337905.i			0.604870i	−0.953170	+	0.302435i	$0.902200\pi$
$200$		0			0
$201$			802632.i			1.40128i
$202$		0			0
$203$	−52037.8	+	52037.8i	−0.0886296	+	0.0886296i
$204$		0			0
$205$	−61846.3	−	61846.3i	−0.102785	−	0.102785i
$206$		0			0
$207$	404739.			0.656521
$208$		0			0
$209$	−948669.			−1.50227
$210$		0			0
$211$	460800.	+	460800.i	0.712535	+	0.712535i	0.967065	−	0.254530i	$-0.0819206\pi$
$211$	460800.	+	460800.i	0.712535	+	0.712535i	−0.254530	+	0.967065i	$0.581921\pi$
$212$		0			0
$213$	836384.	−	836384.i	1.26316	−	1.26316i
$214$		0			0
$215$			531755.i			0.784540i
$216$		0			0
$217$			10922.0i			0.0157454i
$218$		0			0
$219$	513085.	−	513085.i	0.722901	−	0.722901i
$220$		0			0
$221$	−12359.8	−	12359.8i	−0.0170227	−	0.0170227i
$222$		0			0
$223$	−599421.			−0.807178			−0.403589	−	0.914940i	$-0.632237\pi$
$223$	−599421.			−0.807178			−0.403589	+	0.914940i	$0.632237\pi$
$224$		0			0
$225$	159058.			0.209458
$226$		0			0
$227$	−757102.	−	757102.i	−0.975191	−	0.975191i	0.0245088	−	0.999700i	$-0.492198\pi$
$227$	−757102.	−	757102.i	−0.975191	−	0.975191i	−0.999700	+	0.0245088i	$0.992198\pi$
$228$		0			0
$229$	427533.	−	427533.i	0.538742	−	0.538742i	−0.384417	−	0.923159i	$-0.625598\pi$
$229$	427533.	−	427533.i	0.538742	−	0.538742i	0.923159	+	0.384417i	$0.125598\pi$
$230$		0			0
$231$			132570.i			0.163462i
$232$		0			0
$233$			673501.i			0.812734i	0.913710	+	0.406367i	$0.133205\pi$
$233$			673501.i			0.812734i	−0.913710	+	0.406367i	$0.866795\pi$
$234$		0			0
$235$	458386.	−	458386.i	0.541454	−	0.541454i
$236$		0			0
$237$	−90036.5	−	90036.5i	−0.104123	−	0.104123i
$238$		0			0
$239$	25168.6			0.0285012			0.0142506	−	0.999898i	$-0.495464\pi$
$239$	25168.6			0.0285012			0.0142506	+	0.999898i	$0.495464\pi$
$240$		0			0
$241$	−39931.0			−0.0442861			−0.0221431	−	0.999755i	$-0.507049\pi$
$241$	−39931.0			−0.0442861			−0.0221431	+	0.999755i	$0.507049\pi$
$242$		0			0
$243$	−929219.	−	929219.i	−1.00949	−	1.00949i
$244$		0			0
$245$	−293149.	+	293149.i	−0.312013	+	0.312013i
$246$		0			0
$247$			755059.i			0.787479i
$248$		0			0
$249$		−	1.04097e6i		−	1.06400i
$250$		0			0
$251$	403242.	−	403242.i	0.404000	−	0.404000i	−0.475640	−	0.879640i	$-0.657784\pi$
$251$	403242.	−	403242.i	0.404000	−	0.404000i	0.879640	+	0.475640i	$0.157784\pi$
$252$		0			0
$253$	−446612.	−	446612.i	−0.438661	−	0.438661i
$254$		0			0
$255$	30835.2			0.0296959
$256$		0			0
$257$	1.57421e6			1.48673			0.743363	−	0.668889i	$-0.233230\pi$
$257$	1.57421e6			1.48673			0.743363	+	0.668889i	$0.233230\pi$
$258$		0			0
$259$	55722.0	+	55722.0i	0.0516151	+	0.0516151i
$260$		0			0
$261$	884881.	−	884881.i	0.804051	−	0.804051i
$262$		0			0
$263$		−	1.02566e6i		−	0.914356i	−0.889375	−	0.457178i	$-0.848860\pi$
$263$		−	1.02566e6i		−	0.914356i	0.889375	−	0.457178i	$-0.151140\pi$
$264$		0			0
$265$		−	267918.i		−	0.234362i
$266$		0			0
$267$	1.53007e6	−	1.53007e6i	1.31351	−	1.31351i
$268$		0			0
$269$	227228.	+	227228.i	0.191461	+	0.191461i	0.796327	−	0.604866i	$-0.206773\pi$
$269$	227228.	+	227228.i	0.191461	+	0.191461i	−0.604866	+	0.796327i	$0.706773\pi$
$270$		0			0
$271$	−816336.			−0.675221			−0.337610	−	0.941286i	$-0.609619\pi$
$271$	−816336.			−0.675221			−0.337610	+	0.941286i	$0.609619\pi$
$272$		0			0
$273$	105515.			0.0856852
$274$		0			0
$275$	−175513.	−	175513.i	−0.139952	−	0.139952i
$276$		0			0
$277$	−1.23607e6	+	1.23607e6i	−0.967930	+	0.967930i	−0.999502	−	0.0315711i	$-0.989949\pi$
$277$	−1.23607e6	+	1.23607e6i	−0.967930	+	0.967930i	0.0315711	+	0.999502i	$0.489949\pi$
$278$		0			0
$279$		−	185725.i		−	0.142843i
$280$		0			0
$281$		−	240041.i		−	0.181351i	−0.995881	−	0.0906753i	$-0.971097\pi$
$281$		−	240041.i		−	0.181351i	0.995881	−	0.0906753i	$-0.0289025\pi$
$282$		0			0
$283$	−95340.4	+	95340.4i	−0.0707637	+	0.0707637i	−0.741603	−	0.670839i	$-0.765934\pi$
$283$	−95340.4	+	95340.4i	−0.0707637	+	0.0707637i	0.670839	+	0.741603i	$0.265934\pi$
$284$		0			0
$285$	−941864.	−	941864.i	−0.686872	−	0.686872i
$286$		0			0
$287$	52359.7			0.0375225
$288$		0			0
$289$	−1.41680e6			−0.997846
$290$		0			0
$291$	−1.04544e6	−	1.04544e6i	−0.723712	−	0.723712i
$292$		0			0
$293$	−226039.	+	226039.i	−0.153821	+	0.153821i	−0.779822	−	0.626001i	$-0.784690\pi$
$293$	−226039.	+	226039.i	−0.153821	+	0.153821i	0.626001	+	0.779822i	$0.284690\pi$
$294$		0			0
$295$			640477.i			0.428498i
$296$		0			0
$297$		−	101797.i		−	0.0669643i
$298$		0			0
$299$	−355465.	+	355465.i	−0.229942	+	0.229942i
$300$		0			0
$301$	−225094.	−	225094.i	−0.143202	−	0.143202i
$302$		0			0
$303$	−1.29089e6			−0.807760
$304$		0			0
$305$	−1.03153e6			−0.634940
$306$		0			0
$307$	−993334.	−	993334.i	−0.601519	−	0.601519i	0.339196	−	0.940716i	$-0.389845\pi$
$307$	−993334.	−	993334.i	−0.601519	−	0.601519i	−0.940716	+	0.339196i	$0.889845\pi$
$308$		0			0
$309$	2.93076e6	−	2.93076e6i	1.74616	−	1.74616i
$310$		0			0
$311$			1.06506e6i			0.624412i	0.950014	+	0.312206i	$0.101068\pi$
$311$			1.06506e6i			0.624412i	−0.950014	+	0.312206i	$0.898932\pi$
$312$		0			0
$313$		−	1.63061e6i		−	0.940781i	−0.882458	−	0.470391i	$-0.844113\pi$
$313$		−	1.63061e6i		−	0.940781i	0.882458	−	0.470391i	$-0.155887\pi$
$314$		0			0
$315$	−67329.8	+	67329.8i	−0.0382323	+	0.0382323i
$316$		0			0
$317$	−1.93665e6	−	1.93665e6i	−1.08244	−	1.08244i	−0.996282	−	0.0861546i	$-0.972542\pi$
$317$	−1.93665e6	−	1.93665e6i	−1.08244	−	1.08244i	−0.0861546	−	0.996282i	$-0.527458\pi$
$318$		0			0
$319$	−1.95286e6			−1.07447
$320$		0			0
$321$	1.97569e6			1.07018
$322$		0			0
$323$	−93404.6	−	93404.6i	−0.0498152	−	0.0498152i
$324$		0			0
$325$	−139694.	+	139694.i	−0.0733614	+	0.0733614i
$326$		0			0
$327$			2.25439e6i			1.16590i
$328$		0			0
$329$			388074.i			0.197663i
$330$		0			0
$331$	−1.61017e6	+	1.61017e6i	−0.807798	+	0.807798i	−0.984300	−	0.176502i	$-0.943522\pi$
$331$	−1.61017e6	+	1.61017e6i	−0.807798	+	0.807798i	0.176502	+	0.984300i	$0.443522\pi$
$332$		0			0
$333$	−947530.	−	947530.i	−0.468255	−	0.468255i
$334$		0			0
$335$	899629.			0.437977
$336$		0			0
$337$	2.75810e6			1.32292			0.661462	−	0.749979i	$-0.269936\pi$
$337$	2.75810e6			1.32292			0.661462	+	0.749979i	$0.269936\pi$
$338$		0			0
$339$	3.55231e6	+	3.55231e6i	1.67885	+	1.67885i
$340$		0			0
$341$	−204939.	+	204939.i	−0.0954419	+	0.0954419i
$342$		0			0
$343$		−	499718.i		−	0.229345i
$344$		0			0
$345$		−	886816.i		−	0.401131i
$346$		0			0
$347$	1.32572e6	−	1.32572e6i	0.591054	−	0.591054i	−0.346862	−	0.937916i	$-0.612753\pi$
$347$	1.32572e6	−	1.32572e6i	0.591054	−	0.591054i	0.937916	+	0.346862i	$0.112753\pi$
$348$		0			0
$349$	1.16961e6	+	1.16961e6i	0.514019	+	0.514019i	0.915755	−	0.401736i	$-0.131593\pi$
$349$	1.16961e6	+	1.16961e6i	0.514019	+	0.514019i	−0.401736	+	0.915755i	$0.631593\pi$
$350$		0			0
$351$	−81021.6			−0.0351021
$352$		0			0
$353$	−2.09168e6			−0.893424			−0.446712	−	0.894678i	$-0.647405\pi$
$353$	−2.09168e6			−0.893424			−0.446712	+	0.894678i	$0.647405\pi$
$354$		0			0
$355$	−937460.	−	937460.i	−0.394804	−	0.394804i
$356$		0			0
$357$	−13052.7	+	13052.7i	−0.00542037	+	0.00542037i
$358$		0			0
$359$		−	414112.i		−	0.169583i	−0.996399	−	0.0847914i	$-0.972978\pi$
$359$		−	414112.i		−	0.169583i	0.996399	−	0.0847914i	$-0.0270224\pi$
$360$		0			0
$361$			3.23001e6i			1.30447i
$362$		0			0
$363$	52519.0	−	52519.0i	0.0209194	−	0.0209194i
$364$		0			0
$365$	−575090.	−	575090.i	−0.225946	−	0.225946i
$366$		0			0
$367$	4.20372e6			1.62918			0.814588	−	0.580039i	$-0.196963\pi$
$367$	4.20372e6			1.62918			0.814588	+	0.580039i	$0.196963\pi$
$368$		0			0
$369$	−890355.			−0.340406
$370$		0			0
$371$	113411.	+	113411.i	0.0427780	+	0.0427780i
$372$		0			0
$373$	−1.08814e6	+	1.08814e6i	−0.404961	+	0.404961i	−0.879977	−	0.475016i	$-0.842442\pi$
$373$	−1.08814e6	+	1.08814e6i	−0.404961	+	0.404961i	0.475016	+	0.879977i	$0.342442\pi$
$374$		0			0
$375$		−	348508.i		−	0.127978i
$376$		0			0
$377$			1.55431e6i			0.563227i
$378$		0			0
$379$	−3.49796e6	+	3.49796e6i	−1.25088	+	1.25088i	−0.295558	+	0.955325i	$0.595506\pi$
$379$	−3.49796e6	+	3.49796e6i	−1.25088	+	1.25088i	−0.955325	+	0.295558i	$0.904494\pi$
$380$		0			0
$381$	4.18747e6	+	4.18747e6i	1.47788	+	1.47788i
$382$		0			0
$383$	30998.9			0.0107981			0.00539907	−	0.999985i	$-0.498281\pi$
$383$	30998.9			0.0107981			0.00539907	+	0.999985i	$0.498281\pi$
$384$		0			0
$385$	148591.			0.0510906
$386$		0			0
$387$	3.82764e6	+	3.82764e6i	1.29913	+	1.29913i
$388$		0			0
$389$	−2.17680e6	+	2.17680e6i	−0.729365	+	0.729365i	−0.970493	−	0.241128i	$-0.922483\pi$
$389$	−2.17680e6	+	2.17680e6i	−0.729365	+	0.729365i	0.241128	+	0.970493i	$0.422483\pi$
$390$		0			0
$391$		−	87945.5i		−	0.0290919i
$392$		0			0
$393$			877069.i			0.286452i
$394$		0			0
$395$	−100917.	+	100917.i	−0.0325441	+	0.0325441i
$396$		0			0
$397$	4.25959e6	+	4.25959e6i	1.35641	+	1.35641i	0.878297	+	0.478116i	$0.158680\pi$
$397$	4.25959e6	+	4.25959e6i	1.35641	+	1.35641i	0.478116	+	0.878297i	$0.341320\pi$
$398$		0			0
$399$	797390.			0.250749
$400$		0			0
$401$	−5.08012e6			−1.57766			−0.788829	−	0.614613i	$-0.789312\pi$
$401$	−5.08012e6			−1.57766			−0.788829	+	0.614613i	$0.789312\pi$
$402$		0			0
$403$	163114.	+	163114.i	0.0500298	+	0.0500298i
$404$		0			0
$405$	−992148.	+	992148.i	−0.300565	+	0.300565i
$406$		0			0
$407$			2.09112e6i			0.625738i
$408$		0			0
$409$		−	1.92582e6i		−	0.569255i	−0.958638	−	0.284627i	$-0.908130\pi$
$409$		−	1.92582e6i		−	0.569255i	0.958638	−	0.284627i	$-0.0918699\pi$
$410$		0			0
$411$	−3.15300e6	+	3.15300e6i	−0.920704	+	0.920704i
$412$		0			0
$413$	−271117.	−	271117.i	−0.0782135	−	0.0782135i
$414$		0			0
$415$	−1.16677e6			−0.332556
$416$		0			0
$417$	9.39365e6			2.64542
$418$		0			0
$419$	3.64174e6	+	3.64174e6i	1.01338	+	1.01338i	0.999909	+	0.0134751i	$0.00428939\pi$
$419$	3.64174e6	+	3.64174e6i	1.01338	+	1.01338i	0.0134751	+	0.999909i	$0.495711\pi$
$420$		0			0
$421$	−4.83514e6	+	4.83514e6i	−1.32955	+	1.32955i	−0.423784	+	0.905763i	$0.639298\pi$
$421$	−4.83514e6	+	4.83514e6i	−1.32955	+	1.32955i	−0.905763	+	0.423784i	$0.860702\pi$
$422$		0			0
$423$		−	6.59904e6i		−	1.79320i
$424$		0			0
$425$		−	34561.6i		−	0.00928156i
$426$		0			0
$427$	436652.	−	436652.i	0.115895	−	0.115895i
$428$		0			0
$429$	1.97986e6	+	1.97986e6i	0.519387	+	0.519387i
$430$		0			0
$431$	3.40224e6			0.882208			0.441104	−	0.897456i	$-0.354587\pi$
$431$	3.40224e6			0.882208			0.441104	+	0.897456i	$0.354587\pi$
$432$		0			0
$433$	−4.42175e6			−1.13338			−0.566688	−	0.823932i	$-0.691776\pi$
$433$	−4.42175e6			−1.13338			−0.566688	+	0.823932i	$0.691776\pi$
$434$		0			0
$435$	−1.93885e6	−	1.93885e6i	−0.491271	−	0.491271i
$436$		0			0
$437$	−2.68630e6	+	2.68630e6i	−0.672902	+	0.672902i
$438$		0			0
$439$		−	4.73562e6i		−	1.17278i	−0.810030	−	0.586389i	$-0.800549\pi$
$439$		−	4.73562e6i		−	1.17278i	0.810030	−	0.586389i	$-0.199451\pi$
$440$		0			0
$441$			4.22025e6i			1.03334i
$442$		0			0
$443$	−1.39278e6	+	1.39278e6i	−0.337188	+	0.337188i	−0.855308	−	0.518120i	$-0.826632\pi$
$443$	−1.39278e6	+	1.39278e6i	−0.337188	+	0.337188i	0.518120	+	0.855308i	$0.326632\pi$
$444$		0			0
$445$	−1.71498e6	−	1.71498e6i	−0.410543	−	0.410543i
$446$		0			0
$447$	−4.57781e6			−1.08365
$448$		0			0
$449$	4.77397e6			1.11754			0.558771	−	0.829322i	$-0.311273\pi$
$449$	4.77397e6			1.11754			0.558771	+	0.829322i	$0.311273\pi$
$450$		0			0
$451$	982469.	+	982469.i	0.227446	+	0.227446i
$452$		0			0
$453$	1.22535e6	−	1.22535e6i	0.280553	−	0.280553i
$454$		0			0
$455$		−	118266.i		−	0.0267812i
$456$		0			0
$457$		−	2.55272e6i		−	0.571759i	−0.958266	−	0.285879i	$-0.907714\pi$
$457$		−	2.55272e6i		−	0.571759i	0.958266	−	0.285879i	$-0.0922857\pi$
$458$		0			0
$459$	10022.8	−	10022.8i	0.00222053	−	0.00222053i
$460$		0			0
$461$	−98156.9	−	98156.9i	−0.0215114	−	0.0215114i	0.696269	−	0.717781i	$-0.254842\pi$
$461$	−98156.9	−	98156.9i	−0.0215114	−	0.0215114i	−0.717781	+	0.696269i	$0.754842\pi$
$462$		0			0
$463$	−2.09188e6			−0.453506			−0.226753	−	0.973952i	$-0.572811\pi$
$463$	−2.09188e6			−0.453506			−0.226753	+	0.973952i	$0.572811\pi$
$464$		0			0
$465$	−406938.			−0.0872762
$466$		0			0
$467$	4.26438e6	+	4.26438e6i	0.904823	+	0.904823i	0.995849	−	0.0910255i	$-0.0290145\pi$
$467$	4.26438e6	+	4.26438e6i	0.904823	+	0.904823i	−0.0910255	+	0.995849i	$0.529014\pi$
$468$		0			0
$469$	−380817.	+	380817.i	−0.0799437	+	0.0799437i
$470$		0			0
$471$			181907.i			0.0377831i
$472$		0			0
$473$		−	8.44727e6i		−	1.73605i
$474$		0			0
$475$	−1.05569e6	+	1.05569e6i	−0.214685	+	0.214685i
$476$		0			0
$477$	−1.92851e6	−	1.92851e6i	−0.388084	−	0.388084i
$478$		0			0
$479$	6.92154e6			1.37836			0.689182	−	0.724588i	$-0.257970\pi$
$479$	6.92154e6			1.37836			0.689182	+	0.724588i	$0.257970\pi$
$480$		0			0
$481$	1.66435e6			0.328006
$482$		0			0
$483$	375393.	+	375393.i	0.0732181	+	0.0732181i
$484$		0			0
$485$	−1.17178e6	+	1.17178e6i	−0.226199	+	0.226199i
$486$		0			0
$487$		−	1.54589e6i		−	0.295364i	−0.989035	−	0.147682i	$-0.952819\pi$
$487$		−	1.54589e6i		−	0.295364i	0.989035	−	0.147682i	$-0.0471812\pi$
$488$		0			0
$489$			1.31038e7i			2.47814i
$490$		0			0
$491$	−2.04164e6	+	2.04164e6i	−0.382187	+	0.382187i	−0.871890	−	0.489702i	$-0.837105\pi$
$491$	−2.04164e6	+	2.04164e6i	−0.382187	+	0.382187i	0.489702	+	0.871890i	$0.337105\pi$
$492$		0			0
$493$	−192276.	−	192276.i	−0.0356293	−	0.0356293i
$494$		0			0
$495$	−2.52673e6			−0.463496
$496$		0			0
$497$	793662.			0.144127
$498$		0			0
$499$	−3.23274e6	−	3.23274e6i	−0.581192	−	0.581192i	0.354039	−	0.935231i	$-0.384808\pi$
$499$	−3.23274e6	−	3.23274e6i	−0.581192	−	0.581192i	−0.935231	+	0.354039i	$0.884808\pi$
$500$		0			0
$501$	7.02303e6	−	7.02303e6i	1.25006	−	1.25006i
$502$		0			0
$503$		−	3.14289e6i		−	0.553873i	−0.960888	−	0.276936i	$-0.910681\pi$
$503$		−	3.14289e6i		−	0.553873i	0.960888	−	0.276936i	$-0.0893191\pi$
$504$		0			0
$505$			1.44689e6i			0.252469i
$506$		0			0
$507$	−4.28012e6	+	4.28012e6i	−0.739496	+	0.739496i
$508$		0			0
$509$	−3.69156e6	−	3.69156e6i	−0.631561	−	0.631561i	0.316899	−	0.948459i	$-0.397359\pi$
$509$	−3.69156e6	−	3.69156e6i	−0.631561	−	0.631561i	−0.948459	+	0.316899i	$0.897359\pi$
$510$		0			0
$511$	486876.			0.0824834
$512$		0			0
$513$	−612293.			−0.102723
$514$		0			0
$515$	−3.28494e6	−	3.28494e6i	−0.545769	−	0.545769i
$516$		0			0
$517$	−7.28176e6	+	7.28176e6i	−1.19815	+	1.19815i
$518$		0			0
$519$		−	1.52635e7i		−	2.48735i
$520$		0			0
$521$		−	1.00920e6i		−	0.162886i	−0.996678	−	0.0814429i	$-0.974047\pi$
$521$		−	1.00920e6i		−	0.162886i	0.996678	−	0.0814429i	$-0.0259528\pi$
$522$		0			0
$523$	−2.47098e6	+	2.47098e6i	−0.395016	+	0.395016i	−0.876471	−	0.481455i	$-0.840109\pi$
$523$	−2.47098e6	+	2.47098e6i	−0.395016	+	0.395016i	0.481455	+	0.876471i	$0.340109\pi$
$524$		0			0
$525$	147525.	+	147525.i	0.0233597	+	0.0233597i
$526$		0			0
$527$	−40356.0			−0.00632968
$528$		0			0
$529$	3.90704e6			0.607028
$530$		0			0
$531$	4.61023e6	+	4.61023e6i	0.709556	+	0.709556i
$532$		0			0
$533$	781961.	−	781961.i	0.119225	−	0.119225i
$534$		0			0
$535$		−	2.21445e6i		−	0.334488i
$536$		0			0
$537$		−	4.82563e6i		−	0.722135i
$538$		0			0
$539$	4.65686e6	−	4.65686e6i	0.690433	−	0.690433i
$540$		0			0
$541$	−7.81291e6	−	7.81291e6i	−1.14768	−	1.14768i	−0.987009	−	0.160668i	$-0.948635\pi$
$541$	−7.81291e6	−	7.81291e6i	−1.14768	−	1.14768i	−0.160668	−	0.987009i	$-0.551365\pi$
$542$		0			0
$543$	−1.04450e7			−1.52022
$544$		0			0
$545$	2.52683e6			0.364406
$546$		0			0
$547$	−4.76831e6	−	4.76831e6i	−0.681391	−	0.681391i	0.278923	−	0.960313i	$-0.410023\pi$
$547$	−4.76831e6	−	4.76831e6i	−0.681391	−	0.681391i	−0.960313	+	0.278923i	$0.910023\pi$
$548$		0			0
$549$	−7.42508e6	+	7.42508e6i	−1.05141	+	1.05141i
$550$		0			0
$551$			1.17462e7i			1.64823i
$552$		0			0
$553$		−	85437.5i		−	0.0118805i
$554$		0			0
$555$	−2.07612e6	+	2.07612e6i	−0.286101	+	0.286101i
$556$		0			0
$557$	3.71659e6	+	3.71659e6i	0.507583	+	0.507583i	0.913784	−	0.406201i	$-0.133147\pi$
$557$	3.71659e6	+	3.71659e6i	0.507583	+	0.507583i	−0.406201	+	0.913784i	$0.633147\pi$
$558$		0			0
$559$	−6.72330e6			−0.910025
$560$		0			0
$561$	−489837.			−0.0657119
$562$		0			0
$563$	−1.60705e6	−	1.60705e6i	−0.213678	−	0.213678i	0.592150	−	0.805828i	$-0.298279\pi$
$563$	−1.60705e6	−	1.60705e6i	−0.213678	−	0.213678i	−0.805828	+	0.592150i	$0.798279\pi$
$564$		0			0
$565$	3.98160e6	−	3.98160e6i	0.524730	−	0.524730i
$566$		0			0
$567$		−	839962.i		−	0.109724i
$568$		0			0
$569$		−	9.51364e6i		−	1.23187i	−0.787796	−	0.615936i	$-0.788778\pi$
$569$		−	9.51364e6i		−	1.23187i	0.787796	−	0.615936i	$-0.211222\pi$
$570$		0			0
$571$	8.50185e6	−	8.50185e6i	1.09125	−	1.09125i	0.0958518	−	0.995396i	$-0.469443\pi$
$571$	8.50185e6	−	8.50185e6i	1.09125	−	1.09125i	0.995396	−	0.0958518i	$-0.0305575\pi$
$572$		0			0
$573$	−1.41132e7	−	1.41132e7i	−1.79573	−	1.79573i
$574$		0			0
$575$	−993986.			−0.125375
$576$		0			0
$577$	7.23412e6			0.904578			0.452289	−	0.891871i	$-0.350608\pi$
$577$	7.23412e6			0.904578			0.452289	+	0.891871i	$0.350608\pi$
$578$		0			0
$579$	4.22029e6	+	4.22029e6i	0.523174	+	0.523174i
$580$		0			0
$581$	493899.	−	493899.i	0.0607013	−	0.0607013i
$582$		0			0
$583$			4.25606e6i			0.518604i
$584$		0			0
$585$			2.01106e6i			0.242961i
$586$		0			0
$587$	3.94829e6	−	3.94829e6i	0.472948	−	0.472948i	−0.429919	−	0.902867i	$-0.641458\pi$
$587$	3.94829e6	−	3.94829e6i	0.472948	−	0.472948i	0.902867	+	0.429919i	$0.141458\pi$
$588$		0			0
$589$	1.23268e6	+	1.23268e6i	0.146407	+	0.146407i
$590$		0			0
$591$	1.55260e7			1.82848
$592$		0			0
$593$	5.92280e6			0.691656			0.345828	−	0.938298i	$-0.387598\pi$
$593$	5.92280e6			0.691656			0.345828	+	0.938298i	$0.387598\pi$
$594$		0			0
$595$	14630.1	+	14630.1i	0.00169416	+	0.00169416i
$596$		0			0
$597$	5.32933e6	−	5.32933e6i	0.611980	−	0.611980i
$598$		0			0
$599$			1.19621e7i			1.36219i	0.732193	+	0.681097i	$0.238497\pi$
$599$			1.19621e7i			1.36219i	−0.732193	+	0.681097i	$0.761503\pi$
$600$		0			0
$601$			3.98238e6i			0.449734i	0.974389	+	0.224867i	$0.0721948\pi$
$601$			3.98238e6i			0.449734i	−0.974389	+	0.224867i	$0.927805\pi$
$602$		0			0
$603$	6.47564e6	−	6.47564e6i	0.725253	−	0.725253i
$604$		0			0
$605$	−58865.9	−	58865.9i	−0.00653845	−	0.00653845i
$606$		0			0
$607$	−4.78592e6			−0.527222			−0.263611	−	0.964629i	$-0.584913\pi$
$607$	−4.78592e6			−0.527222			−0.263611	+	0.964629i	$0.584913\pi$
$608$		0			0
$609$	1.64145e6			0.179343
$610$		0			0
$611$	5.79566e6	+	5.79566e6i	0.628058	+	0.628058i
$612$		0			0
$613$	−5.79007e6	+	5.79007e6i	−0.622347	+	0.622347i	−0.946131	−	0.323784i	$-0.895045\pi$
$613$	−5.79007e6	+	5.79007e6i	−0.622347	+	0.622347i	0.323784	+	0.946131i	$0.395045\pi$
$614$		0			0
$615$			1.95084e6i			0.207986i
$616$		0			0
$617$		−	6.08179e6i		−	0.643159i	−0.946883	−	0.321579i	$-0.895786\pi$
$617$		−	6.08179e6i		−	0.643159i	0.946883	−	0.321579i	$-0.104214\pi$
$618$		0			0
$619$	−2.75870e6	+	2.75870e6i	−0.289386	+	0.289386i	−0.836838	−	0.547451i	$-0.815598\pi$
$619$	−2.75870e6	+	2.75870e6i	−0.289386	+	0.289386i	0.547451	+	0.836838i	$0.315598\pi$
$620$		0			0
$621$	−288254.	−	288254.i	−0.0299948	−	0.0299948i
$622$		0			0
$623$	1.45192e6			0.149872
$624$		0			0
$625$	−390625.			−0.0400000
$626$		0			0
$627$	1.49621e7	+	1.49621e7i	1.51993	+	1.51993i
$628$		0			0
$629$	−205889.	+	205889.i	−0.0207494	+	0.0207494i
$630$		0			0
$631$			9.05714e6i			0.905561i	0.891622	+	0.452781i	$0.149568\pi$
$631$			9.05714e6i			0.905561i	−0.891622	+	0.452781i	$0.850432\pi$
$632$		0			0
$633$		−	1.45352e7i		−	1.44182i
$634$		0			0
$635$	4.69352e6	−	4.69352e6i	0.461918	−	0.461918i
$636$		0			0
$637$	−3.70646e6	−	3.70646e6i	−0.361919	−	0.361919i
$638$		0			0
$639$	−1.34959e7			−1.30752
$640$		0			0
$641$	1.48586e7			1.42834			0.714171	−	0.699971i	$-0.246804\pi$
$641$	1.48586e7			1.42834			0.714171	+	0.699971i	$0.246804\pi$
$642$		0			0
$643$	−7.21073e6	−	7.21073e6i	−0.687784	−	0.687784i	0.273958	−	0.961742i	$-0.411667\pi$
$643$	−7.21073e6	−	7.21073e6i	−0.687784	−	0.687784i	−0.961742	+	0.273958i	$0.911667\pi$
$644$		0			0
$645$	8.38667e6	−	8.38667e6i	0.793762	−	0.793762i
$646$		0			0
$647$		−	8.76755e6i		−	0.823413i	−0.911317	−	0.411706i	$-0.864933\pi$
$647$		−	8.76755e6i		−	0.823413i	0.911317	−	0.411706i	$-0.135067\pi$
$648$		0			0
$649$		−	1.01744e7i		−	0.948193i
$650$		0			0
$651$	172259.	−	172259.i	0.0159305	−	0.0159305i
$652$		0			0
$653$	−2.93112e6	−	2.93112e6i	−0.268999	−	0.268999i	0.559698	−	0.828697i	$-0.310917\pi$
$653$	−2.93112e6	−	2.93112e6i	−0.268999	−	0.268999i	−0.828697	+	0.559698i	$0.810917\pi$
$654$		0			0
$655$	983062.			0.0895319
$656$		0			0
$657$	−8.27914e6			−0.748293
$658$		0			0
$659$	−1.03644e7	−	1.03644e7i	−0.929674	−	0.929674i	0.0680108	−	0.997685i	$-0.478335\pi$
$659$	−1.03644e7	−	1.03644e7i	−0.929674	−	0.929674i	−0.997685	+	0.0680108i	$0.978335\pi$
$660$		0			0
$661$	1.21724e7	−	1.21724e7i	1.08361	−	1.08361i	0.0874373	−	0.996170i	$-0.472132\pi$
$661$	1.21724e7	−	1.21724e7i	1.08361	−	1.08361i	0.996170	−	0.0874373i	$-0.0278677\pi$
$662$		0			0
$663$			389868.i			0.0344456i
$664$		0			0
$665$		−	893754.i		−	0.0783725i
$666$		0			0
$667$	−5.52982e6	+	5.52982e6i	−0.481279	+	0.481279i
$668$		0			0
$669$	9.45387e6	+	9.45387e6i	0.816666	+	0.816666i
$670$		0			0
$671$	1.63865e7			1.40501
$672$		0			0
$673$	−7.18049e6			−0.611106			−0.305553	−	0.952175i	$-0.598841\pi$
$673$	−7.18049e6			−0.611106			−0.305553	+	0.952175i	$0.598841\pi$
$674$		0			0
$675$	−113280.	−	113280.i	−0.00956963	−	0.00956963i
$676$		0			0
$677$	−999865.	+	999865.i	−0.0838436	+	0.0838436i	−0.747785	−	0.663941i	$-0.768883\pi$
$677$	−999865.	+	999865.i	−0.0838436	+	0.0838436i	0.663941	+	0.747785i	$0.268883\pi$
$678$		0			0
$679$		−	992038.i		−	0.0825760i
$680$		0			0
$681$			2.38815e7i			1.97331i
$682$		0			0
$683$	−1.30857e6	+	1.30857e6i	−0.107336	+	0.107336i	−0.758735	−	0.651399i	$-0.774182\pi$
$683$	−1.30857e6	+	1.30857e6i	−0.107336	+	0.107336i	0.651399	+	0.758735i	$0.274182\pi$
$684$		0			0
$685$	3.53404e6	+	3.53404e6i	0.287770	+	0.287770i
$686$		0			0
$687$	−1.34858e7			−1.09015
$688$		0			0
$689$	3.38746e6			0.271848
$690$		0			0
$691$	−1.15909e7	−	1.15909e7i	−0.923467	−	0.923467i	0.0738056	−	0.997273i	$-0.476486\pi$
$691$	−1.15909e7	−	1.15909e7i	−0.923467	−	0.923467i	−0.997273	+	0.0738056i	$0.976486\pi$
$692$		0			0
$693$	1.06958e6	−	1.06958e6i	0.0846017	−	0.0846017i
$694$		0			0
$695$		−	1.05289e7i		−	0.826836i
$696$		0			0
$697$			193465.i			0.0150841i
$698$		0			0
$699$	1.06222e7	−	1.06222e7i	0.822287	−	0.822287i
$700$		0			0
$701$	1.31868e7	+	1.31868e7i	1.01355	+	1.01355i	0.999907	+	0.0136427i	$0.00434274\pi$
$701$	1.31868e7	+	1.31868e7i	1.01355	+	1.01355i	0.0136427	+	0.999907i	$0.495657\pi$
$702$		0			0
$703$	1.25778e7			0.959876
$704$		0			0
$705$	−1.44590e7			−1.09564
$706$		0			0
$707$	−612475.	−	612475.i	−0.0460829	−	0.0460829i
$708$		0			0
$709$	−2.30012e6	+	2.30012e6i	−0.171844	+	0.171844i	−0.787789	−	0.615945i	$-0.788774\pi$
$709$	−2.30012e6	+	2.30012e6i	−0.171844	+	0.171844i	0.615945	+	0.787789i	$0.288774\pi$
$710$		0			0
$711$			1.45283e6i			0.107781i
$712$		0			0
$713$			1.16063e6i			0.0855011i
$714$		0			0
$715$	2.21912e6	−	2.21912e6i	0.162336	−	0.162336i
$716$		0			0
$717$	−396951.	−	396951.i	−0.0288362	−	0.0288362i
$718$		0			0
$719$	−7.75750e6			−0.559628			−0.279814	−	0.960054i	$-0.590273\pi$
$719$	−7.75750e6			−0.559628			−0.279814	+	0.960054i	$0.590273\pi$
$720$		0			0
$721$	2.78106e6			0.199238
$722$		0			0
$723$	629779.	+	629779.i	0.0448067	+	0.0448067i
$724$		0			0
$725$	−2.17316e6	+	2.17316e6i	−0.153549	+	0.153549i
$726$		0			0
$727$		−	2.50491e7i		−	1.75775i	−0.477055	−	0.878873i	$-0.658296\pi$
$727$		−	2.50491e7i		−	1.75775i	0.477055	−	0.878873i	$-0.341704\pi$
$728$		0			0
$729$			1.56725e7i			1.09224i
$730$		0			0
$731$	831706.	−	831706.i	0.0575674	−	0.0575674i
$732$		0			0
$733$	−1.89295e7	−	1.89295e7i	−1.30131	−	1.30131i	−0.927511	−	0.373796i	$-0.878056\pi$
$733$	−1.89295e7	−	1.89295e7i	−1.30131	−	1.30131i	−0.373796	−	0.927511i	$-0.621944\pi$
$734$		0			0
$735$	9.24691e6			0.631362
$736$		0			0
$737$	−1.42912e7			−0.969169
$738$		0			0
$739$	−1.37903e7	−	1.37903e7i	−0.928889	−	0.928889i	0.0687448	−	0.997634i	$-0.478101\pi$
$739$	−1.37903e7	−	1.37903e7i	−0.928889	−	0.928889i	−0.997634	+	0.0687448i	$0.978101\pi$
$740$		0			0
$741$	1.19086e7	−	1.19086e7i	0.796735	−	0.796735i
$742$		0			0
$743$		−	1.36586e7i		−	0.907684i	−0.891082	−	0.453842i	$-0.850053\pi$
$743$		−	1.36586e7i		−	0.907684i	0.891082	−	0.453842i	$-0.149947\pi$
$744$		0			0
$745$			5.13104e6i			0.338699i
$746$		0			0
$747$	−8.39855e6	+	8.39855e6i	−0.550685	+	0.550685i
$748$		0			0
$749$	937385.	+	937385.i	0.0610539	+	0.0610539i
$750$		0			0
$751$	3.55866e6			0.230243			0.115121	−	0.993351i	$-0.463274\pi$
$751$	3.55866e6			0.230243			0.115121	+	0.993351i	$0.463274\pi$
$752$		0			0
$753$	−1.27196e7			−0.817497
$754$		0			0
$755$	−1.37343e6	−	1.37343e6i	−0.0876880	−	0.0876880i
$756$		0			0
$757$	−5.87699e6	+	5.87699e6i	−0.372748	+	0.372748i	−0.868477	−	0.495729i	$-0.834901\pi$
$757$	−5.87699e6	+	5.87699e6i	−0.372748	+	0.372748i	0.495729	+	0.868477i	$0.334901\pi$
$758$		0			0
$759$			1.40876e7i			0.887634i
$760$		0			0
$761$		−	2.39309e6i		−	0.149795i	−0.997191	−	0.0748976i	$-0.976137\pi$
$761$		−	2.39309e6i		−	0.149795i	0.997191	−	0.0748976i	$-0.0238630\pi$
$762$		0			0
$763$	−1.06962e6	+	1.06962e6i	−0.0665148	+	0.0665148i
$764$		0			0
$765$	−248778.	−	248778.i	−0.0153695	−	0.0153695i
$766$		0			0
$767$	−8.09795e6			−0.497035
$768$		0			0
$769$	8.78362e6			0.535621			0.267810	−	0.963472i	$-0.413700\pi$
$769$	8.78362e6			0.535621			0.267810	+	0.963472i	$0.413700\pi$
$770$		0			0
$771$	−2.48280e7	−	2.48280e7i	−1.50420	−	1.50420i
$772$		0			0
$773$	1.97602e6	−	1.97602e6i	0.118944	−	0.118944i	−0.645129	−	0.764073i	$-0.723197\pi$
$773$	1.97602e6	−	1.97602e6i	0.118944	−	0.118944i	0.764073	+	0.645129i	$0.223197\pi$
$774$		0			0
$775$			456116.i			0.0272785i
$776$		0			0
$777$		−	1.75766e6i		−	0.104444i
$778$		0			0
$779$	5.90941e6	−	5.90941e6i	0.348899	−	0.348899i
$780$		0			0
$781$	1.48922e7	+	1.48922e7i	0.873635	+	0.873635i
$782$		0			0
$783$	−1.26042e6			−0.0734702
$784$		0			0
$785$	203891.			0.0118093
$786$		0			0
$787$	1.36269e7	+	1.36269e7i	0.784263	+	0.784263i	0.980547	−	0.196284i	$-0.0628875\pi$
$787$	1.36269e7	+	1.36269e7i	0.784263	+	0.784263i	−0.196284	+	0.980547i	$0.562887\pi$
$788$		0			0
$789$	−1.61764e7	+	1.61764e7i	−0.925103	+	0.925103i
$790$		0			0
$791$			3.37086e6i			0.191557i
$792$		0			0
$793$		−	1.30423e7i		−	0.736496i
$794$		0			0
$795$	−4.22552e6	+	4.22552e6i	−0.237117	+	0.237117i
$796$		0			0
$797$	1.93683e7	+	1.93683e7i	1.08005	+	1.08005i	0.996504	+	0.0835500i	$0.0266258\pi$
$797$	1.93683e7	+	1.93683e7i	1.08005	+	1.08005i	0.0835500	+	0.996504i	$0.473374\pi$
$798$		0			0
$799$	−1.43390e6			−0.0794608
$800$		0			0
$801$	−2.46893e7			−1.35965
$802$		0			0
$803$	9.13568e6	+	9.13568e6i	0.499979	+	0.499979i
$804$		0			0
$805$	420759.	−	420759.i	0.0228846	−	0.0228846i
$806$		0			0
$807$		−	7.16753e6i		−	0.387424i
$808$		0			0
$809$		−	2.76506e7i		−	1.48537i	−0.669643	−	0.742683i	$-0.733553\pi$
$809$		−	2.76506e7i		−	1.48537i	0.669643	−	0.742683i	$-0.266447\pi$
$810$		0			0
$811$	−1.92195e7	+	1.92195e7i	−1.02610	+	1.02610i	−0.0264493	+	0.999650i	$0.508420\pi$
$811$	−1.92195e7	+	1.92195e7i	−1.02610	+	1.02610i	−0.999650	+	0.0264493i	$0.991580\pi$
$812$		0			0
$813$	1.28750e7	+	1.28750e7i	0.683157	+	0.683157i
$814$		0			0
$815$	1.46874e7			0.774553
$816$		0			0
$817$	−5.08091e7			−2.66309
$818$		0			0
$819$	−851292.	−	851292.i	−0.0443474	−	0.0443474i
$820$		0			0
$821$	1.69500e7	−	1.69500e7i	0.877630	−	0.877630i	−0.115659	−	0.993289i	$-0.536898\pi$
$821$	1.69500e7	−	1.69500e7i	0.877630	−	0.877630i	0.993289	+	0.115659i	$0.0368980\pi$
$822$		0			0
$823$			3.27117e7i			1.68346i	0.539897	+	0.841731i	$0.318463\pi$
$823$			3.27117e7i			1.68346i	−0.539897	+	0.841731i	$0.681537\pi$
$824$		0			0
$825$			5.53628e6i			0.283193i
$826$		0			0
$827$	5.51442e6	−	5.51442e6i	0.280373	−	0.280373i	−0.552885	−	0.833258i	$-0.686473\pi$
$827$	5.51442e6	−	5.51442e6i	0.280373	−	0.280373i	0.833258	+	0.552885i	$0.186473\pi$
$828$		0			0
$829$	−1.22663e7	−	1.22663e7i	−0.619906	−	0.619906i	0.325601	−	0.945507i	$-0.394433\pi$
$829$	−1.22663e7	−	1.22663e7i	−0.619906	−	0.619906i	−0.945507	+	0.325601i	$0.894433\pi$
$830$		0			0
$831$	3.89899e7			1.95861
$832$		0			0
$833$	917016.			0.0457894
$834$		0			0
$835$	−7.87175e6	−	7.87175e6i	−0.390711	−	0.390711i
$836$		0			0
$837$	−132273.	+	132273.i	−0.00652613	+	0.00652613i
$838$		0			0
$839$			1.37757e7i			0.675629i	0.941213	+	0.337814i	$0.109688\pi$
$839$			1.37757e7i			0.675629i	−0.941213	+	0.337814i	$0.890312\pi$
$840$		0			0
$841$			3.66860e6i			0.178859i
$842$		0			0
$843$	−3.78584e6	+	3.78584e6i	−0.183482	+	0.183482i
$844$		0			0
$845$	4.79736e6	+	4.79736e6i	0.231132	+	0.231132i
$846$		0			0
$847$	49836.4			0.00238692
$848$		0			0
$849$	3.00736e6			0.143191
$850$		0			0
$851$	5.92133e6	+	5.92133e6i	0.280282	+	0.280282i
$852$		0			0
$853$	−6.91197e6	+	6.91197e6i	−0.325259	+	0.325259i	−0.850780	−	0.525521i	$-0.823870\pi$
$853$	−6.91197e6	+	6.91197e6i	−0.325259	+	0.325259i	0.525521	+	0.850780i	$0.323870\pi$
$854$		0			0
$855$			1.51979e7i			0.710999i
$856$		0			0
$857$		−	3.97104e6i		−	0.184694i	−0.995727	−	0.0923468i	$-0.970563\pi$
$857$		−	3.97104e6i		−	0.184694i	0.995727	−	0.0923468i	$-0.0294368\pi$
$858$		0			0
$859$	4.60913e6	−	4.60913e6i	0.213126	−	0.213126i	−0.592468	−	0.805594i	$-0.701846\pi$
$859$	4.60913e6	−	4.60913e6i	0.213126	−	0.213126i	0.805594	+	0.592468i	$0.201846\pi$
$860$		0			0
$861$	−825800.	−	825800.i	−0.0379636	−	0.0379636i
$862$		0			0
$863$	−1.32363e7			−0.604980			−0.302490	−	0.953153i	$-0.597818\pi$
$863$	−1.32363e7			−0.604980			−0.302490	+	0.953153i	$0.597818\pi$
$864$		0			0
$865$	−1.71081e7			−0.777431
$866$		0			0
$867$	2.23453e7	+	2.23453e7i	1.00957	+	1.00957i
$868$		0			0
$869$	1.60314e6	−	1.60314e6i	0.0720146	−	0.0720146i
$870$		0			0
$871$			1.13746e7i			0.508030i
$872$		0			0
$873$			1.68692e7i			0.749133i
$874$		0			0
$875$	165353.	−	165353.i	0.00730118	−	0.00730118i
$876$		0			0
$877$	−3.65142e6	−	3.65142e6i	−0.160311	−	0.160311i	0.622394	−	0.782704i	$-0.286160\pi$
$877$	−3.65142e6	−	3.65142e6i	−0.160311	−	0.160311i	−0.782704	+	0.622394i	$0.786160\pi$
$878$		0			0
$879$	7.13003e6			0.311257
$880$		0			0
$881$	−1.93219e7			−0.838705			−0.419353	−	0.907823i	$-0.637743\pi$
$881$	−1.93219e7			−0.838705			−0.419353	+	0.907823i	$0.637743\pi$
$882$		0			0
$883$	−1.26435e7	−	1.26435e7i	−0.545713	−	0.545713i	0.379485	−	0.925198i	$-0.376101\pi$
$883$	−1.26435e7	−	1.26435e7i	−0.545713	−	0.545713i	−0.925198	+	0.379485i	$0.876101\pi$
$884$		0			0
$885$	1.01014e7	−	1.01014e7i	0.433535	−	0.433535i
$886$		0			0
$887$		−	1.59291e6i		−	0.0679802i	−0.999422	−	0.0339901i	$-0.989179\pi$
$887$		−	1.59291e6i		−	0.0679802i	0.999422	−	0.0339901i	$-0.0108215\pi$
$888$		0			0
$889$			3.97358e6i			0.168627i
$890$		0			0
$891$	1.57609e7	−	1.57609e7i	0.665100	−	0.665100i
$892$		0			0
$893$	4.37987e7	+	4.37987e7i	1.83795	+	1.83795i
$894$		0			0
$895$	−5.40880e6			−0.225706
$896$		0			0
$897$	1.12126e7			0.465290
$898$		0			0
$899$	2.53750e6	+	2.53750e6i	0.104714	+	0.104714i
$900$		0			0
$901$	−419045.	+	419045.i	−0.0171969	+	0.0171969i
$902$		0			0
$903$			7.10023e6i			0.289770i
$904$		0			0
$905$			1.17072e7i			0.475152i
$906$		0			0
$907$	3.90129e6	−	3.90129e6i	0.157467	−	0.157467i	−0.623976	−	0.781443i	$-0.714484\pi$
$907$	3.90129e6	−	3.90129e6i	0.157467	−	0.157467i	0.781443	+	0.623976i	$0.214484\pi$
$908$		0			0
$909$	1.04149e7	+	1.04149e7i	0.418066	+	0.418066i
$910$		0			0
$911$	662961.			0.0264662			0.0132331	−	0.999912i	$-0.495788\pi$
$911$	662961.			0.0264662			0.0132331	+	0.999912i	$0.495788\pi$
$912$		0			0
$913$	1.85349e7			0.735890
$914$		0			0
$915$	1.62690e7	+	1.62690e7i	0.642403	+	0.642403i
$916$		0			0
$917$	−416135.	+	416135.i	−0.0163422	+	0.0163422i
$918$		0			0
$919$			3.48024e7i			1.35932i	0.733529	+	0.679658i	$0.237872\pi$
$919$			3.48024e7i			1.35932i	−0.733529	+	0.679658i	$0.762128\pi$
$920$		0			0
$921$			3.13331e7i			1.21718i
$922$		0			0
$923$	1.18529e7	−	1.18529e7i	0.457952	−	0.457952i
$924$		0			0
$925$	2.32701e6	+	2.32701e6i	0.0894220	+	0.0894220i
$926$		0			0
$927$	−4.72908e7			−1.80749
$928$		0			0
$929$	3.88261e7			1.47599			0.737996	−	0.674805i	$-0.235772\pi$
$929$	3.88261e7			1.47599			0.737996	+	0.674805i	$0.235772\pi$
$930$		0			0
$931$	−2.80103e7	−	2.80103e7i	−1.05912	−	1.05912i
$932$		0			0
$933$	1.67977e7	−	1.67977e7i	0.631752	−	0.631752i
$934$		0			0
$935$			549033.i			0.0205385i
$936$		0			0
$937$			1.80287e7i			0.670834i	0.942070	+	0.335417i	$0.108877\pi$
$937$			1.80287e7i			0.670834i	−0.942070	+	0.335417i	$0.891123\pi$
$938$		0			0
$939$	−2.57174e7	+	2.57174e7i	−0.951839	+	0.951839i
$940$		0			0
$941$	−2.62045e7	−	2.62045e7i	−0.964720	−	0.964720i	0.0346783	−	0.999399i	$-0.488959\pi$
$941$	−2.62045e7	−	2.62045e7i	−0.964720	−	0.964720i	−0.999399	+	0.0346783i	$0.988959\pi$
$942$		0			0
$943$	5.56403e6			0.203756
$944$		0			0
$945$	95904.2			0.00349348
$946$		0			0
$947$	2.38599e7	+	2.38599e7i	0.864556	+	0.864556i	0.991863	−	0.127307i	$-0.0406335\pi$
$947$	2.38599e7	+	2.38599e7i	0.864556	+	0.864556i	−0.127307	+	0.991863i	$0.540633\pi$
$948$		0			0
$949$	7.27122e6	−	7.27122e6i	0.262085	−	0.262085i
$950$		0			0
$951$			6.10884e7i			2.19032i
$952$		0			0
$953$			4.45663e7i			1.58955i	0.606904	+	0.794775i	$0.292411\pi$
$953$			4.45663e7i			1.58955i	−0.606904	+	0.794775i	$0.707589\pi$
$954$		0			0
$955$	−1.58188e7	+	1.58188e7i	−0.561262	+	0.561262i
$956$		0			0
$957$	3.07999e7	+	3.07999e7i	1.08710	+	1.08710i
$958$		0			0
$959$	−2.99195e6			−0.105053
$960$		0			0
$961$	−2.80966e7			−0.981397
$962$		0			0
$963$	−1.59399e7	−	1.59399e7i	−0.553884	−	0.553884i
$964$		0			0
$965$	4.73031e6	−	4.73031e6i	0.163520	−	0.163520i
$966$		0			0
$967$		−	4.76772e6i		−	0.163963i	−0.996634	−	0.0819813i	$-0.973875\pi$
$967$		−	4.76772e6i		−	0.163963i	0.996634	−	0.0819813i	$-0.0261248\pi$
$968$		0			0
$969$			2.94630e6i			0.100802i
$970$		0			0
$971$	5.21615e6	−	5.21615e6i	0.177542	−	0.177542i	−0.612741	−	0.790284i	$-0.709933\pi$
$971$	5.21615e6	−	5.21615e6i	0.177542	−	0.177542i	0.790284	+	0.612741i	$0.209933\pi$
$972$		0			0
$973$	4.45692e6	+	4.45692e6i	0.150922	+	0.150922i
$974$		0			0
$975$	4.40640e6			0.148447
$976$		0			0
$977$	3.83903e7			1.28672			0.643362	−	0.765562i	$-0.277539\pi$
$977$	3.83903e7			1.28672			0.643362	+	0.765562i	$0.277539\pi$
$978$		0			0
$979$	2.72435e7	+	2.72435e7i	0.908462	+	0.908462i
$980$		0			0
$981$	1.81885e7	−	1.81885e7i	0.603425	−	0.603425i
$982$		0			0
$983$			3.62456e7i			1.19639i	0.801352	+	0.598194i	$0.204115\pi$
$983$			3.62456e7i			1.19639i	−0.801352	+	0.598194i	$0.795885\pi$
$984$		0			0
$985$		−	1.74023e7i		−	0.571499i
$986$		0			0
$987$	6.12058e6	−	6.12058e6i	0.199986	−	0.199986i
$988$		0			0
$989$	−2.39198e7	−	2.39198e7i	−0.777618	−	0.777618i
$990$		0			0
$991$	−2.71452e7			−0.878029			−0.439015	−	0.898480i	$-0.644672\pi$
$991$	−2.71452e7			−0.878029			−0.439015	+	0.898480i	$0.644672\pi$
$992$		0			0
$993$	5.07903e7			1.63459
$994$		0			0
$995$	−5.97338e6	−	5.97338e6i	−0.191277	−	0.191277i
$996$		0			0
$997$	−1.01235e7	+	1.01235e7i	−0.322546	+	0.322546i	−0.849743	−	0.527197i	$-0.823243\pi$
$997$	−1.01235e7	+	1.01235e7i	−0.322546	+	0.322546i	0.527197	+	0.849743i	$0.323243\pi$
$998$		0			0
$999$			1.34966e6i			0.0427868i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.6.l.a.81.7		80
4.3	odd	2		80.6.l.a.61.23	yes	80
16.5	even	4	inner	320.6.l.a.241.7		80
16.11	odd	4		80.6.l.a.21.23	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.23	✓	80	16.11	odd	4
80.6.l.a.61.23	yes	80	4.3	odd	2
320.6.l.a.81.7		80	1.1	even	1	trivial
320.6.l.a.241.7		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)

\(f(q)\)	\(=\)	\(q+(-15.7717 - 15.7717i) q^{3} +(-17.6777 + 17.6777i) q^{5} -14.9661i q^{7} +254.492i q^{9} +O(q^{10})\)	\(q+(-15.7717 - 15.7717i) q^{3} +(-17.6777 + 17.6777i) q^{5} -14.9661i q^{7} +254.492i q^{9} +(280.821 - 280.821i) q^{11} +(-223.510 - 223.510i) q^{13} +557.613 q^{15} +55.2985 q^{17} +(-1689.10 - 1689.10i) q^{19} +(-236.040 + 236.040i) q^{21} -1590.38i q^{23} -625.000i q^{25} +(181.249 - 181.249i) q^{27} +(-3477.05 - 3477.05i) q^{29} -729.785 q^{31} -8858.05 q^{33} +(264.565 + 264.565i) q^{35} +(-3723.22 + 3723.22i) q^{37} +7050.25i q^{39} +3498.56i q^{41} +(15040.3 - 15040.3i) q^{43} +(-4498.83 - 4498.83i) q^{45} -25930.2 q^{47} +16583.0 q^{49} +(-872.151 - 872.151i) q^{51} +(-7577.88 + 7577.88i) q^{53} +9928.53i q^{55} +53279.8i q^{57} +(18115.4 - 18115.4i) q^{59} +(29176.1 + 29176.1i) q^{61} +3808.75 q^{63} +7902.26 q^{65} +(-25445.4 - 25445.4i) q^{67} +(-25082.9 + 25082.9i) q^{69} +53030.7i q^{71} +32532.0i q^{73} +(-9857.30 + 9857.30i) q^{75} +(-4202.79 - 4202.79i) q^{77} +5708.74 q^{79} +56124.4 q^{81} +(33001.2 + 33001.2i) q^{83} +(-977.549 + 977.549i) q^{85} +109678. i q^{87} +97013.9i q^{89} +(-3345.06 + 3345.06i) q^{91} +(11509.9 + 11509.9i) q^{93} +59718.6 q^{95} +66285.8 q^{97} +(71466.7 + 71466.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q+O(q^{10}) \) 80 * q	\( 80 q - 1208 q^{11} + 1800 q^{15} - 2360 q^{19} + 7464 q^{27} - 8144 q^{29} + 21296 q^{37} - 32072 q^{43} + 88360 q^{47} - 192080 q^{49} + 5920 q^{51} - 49456 q^{53} - 44984 q^{59} + 48080 q^{61} - 158760 q^{63} - 61160 q^{67} - 22320 q^{69} - 14896 q^{77} - 177680 q^{79} - 524880 q^{81} + 329240 q^{83} + 132400 q^{85} - 364832 q^{91} - 362352 q^{93} - 288800 q^{95} - 659000 q^{99}+O(q^{100}) \) 80 * q - 1208 * q^11 + 1800 * q^15 - 2360 * q^19 + 7464 * q^27 - 8144 * q^29 + 21296 * q^37 - 32072 * q^43 + 88360 * q^47 - 192080 * q^49 + 5920 * q^51 - 49456 * q^53 - 44984 * q^59 + 48080 * q^61 - 158760 * q^63 - 61160 * q^67 - 22320 * q^69 - 14896 * q^77 - 177680 * q^79 - 524880 * q^81 + 329240 * q^83 + 132400 * q^85 - 364832 * q^91 - 362352 * q^93 - 288800 * q^95 - 659000 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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