LMFDB - Embedded newform 160.6.n.c.63.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,6,Mod(63,160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(160, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("160.63");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	160.n (of order $4$, degree $2$, 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:	$25.6614111701$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 1375 x^{14} + 743087 x^{12} + 198706725 x^{10} + 26872635188 x^{8} + 1612811892960 x^{6} + \cdots + 177426662425600 $ x^16 + 1375x^14 + 743087x^12 + 198706725x^10 + 26872635188x^8 + 1612811892960x^6 + 24971013117824x^4 + 124211190826240*x^2 + 177426662425600
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{41}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			63.4
Root			$-2.29308i$ of defining polynomial
Character	$\chi$	$=$	160.63
Dual form			160.6.n.c.127.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.29308 + 3.29308i) q^{3} +(35.3847 - 43.2773i) q^{5} +(5.96093 + 5.96093i) q^{7} +221.311i q^{9} +O(q^{10})$	\(q+(-3.29308 + 3.29308i) q^{3} +(35.3847 - 43.2773i) q^{5} +(5.96093 + 5.96093i) q^{7} +221.311i q^{9} -634.109i q^{11} +(226.441 + 226.441i) q^{13} +(25.9911 + 259.040i) q^{15} +(429.196 - 429.196i) q^{17} -540.685 q^{19} -39.2596 q^{21} +(-1345.21 + 1345.21i) q^{23} +(-620.850 - 3062.71i) q^{25} +(-1529.01 - 1529.01i) q^{27} +1942.50i q^{29} -8018.95i q^{31} +(2088.17 + 2088.17i) q^{33} +(468.898 - 47.0474i) q^{35} +(11033.1 - 11033.1i) q^{37} -1491.37 q^{39} +13026.2 q^{41} +(10539.1 - 10539.1i) q^{43} +(9577.76 + 7831.03i) q^{45} +(-14464.6 - 14464.6i) q^{47} -16735.9i q^{49} +2826.75i q^{51} +(-6059.07 - 6059.07i) q^{53} +(-27442.5 - 22437.7i) q^{55} +(1780.52 - 1780.52i) q^{57} +405.643 q^{59} +10881.1 q^{61} +(-1319.22 + 1319.22i) q^{63} +(17812.3 - 1787.22i) q^{65} +(8886.87 + 8886.87i) q^{67} -8859.76i q^{69} -12438.9i q^{71} +(17069.9 + 17069.9i) q^{73} +(12130.2 + 8041.22i) q^{75} +(3779.87 - 3779.87i) q^{77} -69057.3 q^{79} -43708.3 q^{81} +(40609.1 - 40609.1i) q^{83} +(-3387.49 - 33761.4i) q^{85} +(-6396.80 - 6396.80i) q^{87} +64770.8i q^{89} +2699.59i q^{91} +(26407.0 + 26407.0i) q^{93} +(-19132.0 + 23399.4i) q^{95} +(35342.6 - 35342.6i) q^{97} +140335. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 10 q^{3} - 42 q^{5} + 86 q^{7}+O(q^{10}) $ 16 * q - 10 * q^3 - 42 * q^5 + 86 * q^7	$ 16 q - 10 q^{3} - 42 q^{5} + 86 q^{7} + 536 q^{13} + 698 q^{15} - 1828 q^{17} - 2512 q^{19} - 4284 q^{21} + 7642 q^{23} + 9140 q^{25} + 12272 q^{27} + 11876 q^{33} - 10518 q^{35} - 7620 q^{37} - 11244 q^{39} - 21284 q^{41} - 20002 q^{43} + 686 q^{45} - 25298 q^{47} + 12852 q^{53} + 10584 q^{55} + 55848 q^{57} + 142704 q^{59} - 20564 q^{61} + 115282 q^{63} - 38256 q^{65} + 10506 q^{67} + 15432 q^{73} - 256226 q^{75} + 133852 q^{77} + 159344 q^{79} - 236116 q^{81} + 61222 q^{83} + 7056 q^{85} - 162176 q^{87} + 122180 q^{93} - 267512 q^{95} - 17344 q^{97} - 107332 q^{99}+O(q^{100}) $ 16 * q - 10 * q^3 - 42 * q^5 + 86 * q^7 + 536 * q^13 + 698 * q^15 - 1828 * q^17 - 2512 * q^19 - 4284 * q^21 + 7642 * q^23 + 9140 * q^25 + 12272 * q^27 + 11876 * q^33 - 10518 * q^35 - 7620 * q^37 - 11244 * q^39 - 21284 * q^41 - 20002 * q^43 + 686 * q^45 - 25298 * q^47 + 12852 * q^53 + 10584 * q^55 + 55848 * q^57 + 142704 * q^59 - 20564 * q^61 + 115282 * q^63 - 38256 * q^65 + 10506 * q^67 + 15432 * q^73 - 256226 * q^75 + 133852 * q^77 + 159344 * q^79 - 236116 * q^81 + 61222 * q^83 + 7056 * q^85 - 162176 * q^87 + 122180 * q^93 - 267512 * q^95 - 17344 * q^97 - 107332 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−3.29308	+	3.29308i	−0.211251	+	0.211251i	−0.804799	−	0.593548i	$-0.797727\pi$
$3$	−3.29308	+	3.29308i	−0.211251	+	0.211251i	0.593548	+	0.804799i	$0.297727\pi$
$4$		0			0
$5$	35.3847	−	43.2773i	0.632980	−	0.774168i
$5$	35.3847	−	43.2773i	0.632980	−	0.774168i
$6$		0			0
$7$	5.96093	+	5.96093i	0.0459800	+	0.0459800i	0.729723	−	0.683743i	$-0.239649\pi$
$7$	5.96093	+	5.96093i	0.0459800	+	0.0459800i	−0.683743	+	0.729723i	$0.739649\pi$
$8$		0			0
$9$			221.311i			0.910746i
$10$		0			0
$11$		−	634.109i		−	1.58009i	−0.613048	−	0.790045i	$-0.710057\pi$
$11$		−	634.109i		−	1.58009i	0.613048	−	0.790045i	$-0.289943\pi$
$12$		0			0
$13$	226.441	+	226.441i	0.371618	+	0.371618i	0.868066	−	0.496448i	$-0.165363\pi$
$13$	226.441	+	226.441i	0.371618	+	0.371618i	−0.496448	+	0.868066i	$0.665363\pi$
$14$		0			0
$15$	25.9911	+	259.040i	0.0298260	+	0.297261i
$16$		0			0
$17$	429.196	−	429.196i	0.360192	−	0.360192i	−0.503692	−	0.863883i	$-0.668025\pi$
$17$	429.196	−	429.196i	0.360192	−	0.360192i	0.863883	+	0.503692i	$0.168025\pi$
$18$		0			0
$19$	−540.685			−0.343606			−0.171803	−	0.985131i	$-0.554959\pi$
$19$	−540.685			−0.343606			−0.171803	+	0.985131i	$0.554959\pi$
$20$		0			0
$21$	−39.2596			−0.0194266
$22$		0			0
$23$	−1345.21	+	1345.21i	−0.530237	+	0.530237i	−0.920643	−	0.390406i	$-0.872335\pi$
$23$	−1345.21	+	1345.21i	−0.530237	+	0.530237i	0.390406	+	0.920643i	$0.372335\pi$
$24$		0			0
$25$	−620.850	−	3062.71i	−0.198672	−	0.980066i
$26$		0			0
$27$	−1529.01	−	1529.01i	−0.403647	−	0.403647i
$28$		0			0
$29$			1942.50i			0.428910i	0.976734	+	0.214455i	$0.0687975\pi$
$29$			1942.50i			0.428910i	−0.976734	+	0.214455i	$0.931202\pi$
$30$		0			0
$31$		−	8018.95i		−	1.49869i	−0.662177	−	0.749347i	$-0.730367\pi$
$31$		−	8018.95i		−	1.49869i	0.662177	−	0.749347i	$-0.269633\pi$
$32$		0			0
$33$	2088.17	+	2088.17i	0.333796	+	0.333796i
$34$		0			0
$35$	468.898	−	47.0474i	0.0647006	−	0.00649181i
$36$		0			0
$37$	11033.1	−	11033.1i	1.32493	−	1.32493i	0.415205	−	0.909728i	$-0.363710\pi$
$37$	11033.1	−	11033.1i	1.32493	−	1.32493i	0.909728	−	0.415205i	$-0.136290\pi$
$38$		0			0
$39$	−1491.37			−0.157009
$40$		0			0
$41$	13026.2			1.21021			0.605103	−	0.796147i	$-0.293132\pi$
$41$	13026.2			1.21021			0.605103	+	0.796147i	$0.293132\pi$
$42$		0			0
$43$	10539.1	−	10539.1i	0.869226	−	0.869226i	−0.123161	−	0.992387i	$-0.539303\pi$
$43$	10539.1	−	10539.1i	0.869226	−	0.869226i	0.992387	+	0.123161i	$0.0393031\pi$
$44$		0			0
$45$	9577.76	+	7831.03i	0.705070	+	0.576484i
$46$		0			0
$47$	−14464.6	−	14464.6i	−0.955126	−	0.955126i	0.0439100	−	0.999035i	$-0.486019\pi$
$47$	−14464.6	−	14464.6i	−0.955126	−	0.955126i	−0.999035	+	0.0439100i	$0.986019\pi$
$48$		0			0
$49$		−	16735.9i		−	0.995772i
$50$		0			0
$51$			2826.75i			0.152182i
$52$		0			0
$53$	−6059.07	−	6059.07i	−0.296290	−	0.296290i	0.543269	−	0.839559i	$-0.317186\pi$
$53$	−6059.07	−	6059.07i	−0.296290	−	0.296290i	−0.839559	+	0.543269i	$0.817186\pi$
$54$		0			0
$55$	−27442.5	−	22437.7i	−1.22326	−	1.00017i
$56$		0			0
$57$	1780.52	−	1780.52i	0.0725870	−	0.0725870i
$58$		0			0
$59$	405.643			0.0151710			0.00758550	−	0.999971i	$-0.497585\pi$
$59$	405.643			0.0151710			0.00758550	+	0.999971i	$0.497585\pi$
$60$		0			0
$61$	10881.1			0.374412			0.187206	−	0.982321i	$-0.440057\pi$
$61$	10881.1			0.374412			0.187206	+	0.982321i	$0.440057\pi$
$62$		0			0
$63$	−1319.22	+	1319.22i	−0.0418761	+	0.0418761i
$64$		0			0
$65$	17812.3	−	1787.22i	0.522921	−	0.0524679i
$66$		0			0
$67$	8886.87	+	8886.87i	0.241859	+	0.241859i	0.817619	−	0.575760i	$-0.195294\pi$
$67$	8886.87	+	8886.87i	0.241859	+	0.241859i	−0.575760	+	0.817619i	$0.695294\pi$
$68$		0			0
$69$		−	8859.76i		−	0.224026i
$70$		0			0
$71$		−	12438.9i		−	0.292844i	−0.989222	−	0.146422i	$-0.953224\pi$
$71$		−	12438.9i		−	0.292844i	0.989222	−	0.146422i	$-0.0467758\pi$
$72$		0			0
$73$	17069.9	+	17069.9i	0.374907	+	0.374907i	0.869261	−	0.494354i	$-0.164595\pi$
$73$	17069.9	+	17069.9i	0.374907	+	0.374907i	−0.494354	+	0.869261i	$0.664595\pi$
$74$		0			0
$75$	12130.2	+	8041.22i	0.249010	+	0.165070i
$76$		0			0
$77$	3779.87	−	3779.87i	0.0726525	−	0.0726525i
$78$		0			0
$79$	−69057.3			−1.24492			−0.622460	−	0.782651i	$-0.713867\pi$
$79$	−69057.3			−1.24492			−0.622460	+	0.782651i	$0.713867\pi$
$80$		0			0
$81$	−43708.3			−0.740204
$82$		0			0
$83$	40609.1	−	40609.1i	0.647035	−	0.647035i	−0.305240	−	0.952275i	$-0.598737\pi$
$83$	40609.1	−	40609.1i	0.647035	−	0.647035i	0.952275	+	0.305240i	$0.0987368\pi$
$84$		0			0
$85$	−3387.49	−	33761.4i	−0.0508546	−	0.506843i
$86$		0			0
$87$	−6396.80	−	6396.80i	−0.0906076	−	0.0906076i
$88$		0			0
$89$			64770.8i			0.866771i	0.901209	+	0.433386i	$0.142681\pi$
$89$			64770.8i			0.866771i	−0.901209	+	0.433386i	$0.857319\pi$
$90$		0			0
$91$			2699.59i			0.0341739i
$92$		0			0
$93$	26407.0	+	26407.0i	0.316601	+	0.316601i
$94$		0			0
$95$	−19132.0	+	23399.4i	−0.217496	+	0.266008i
$96$		0			0
$97$	35342.6	−	35342.6i	0.381390	−	0.381390i	−0.490213	−	0.871603i	$-0.663081\pi$
$97$	35342.6	−	35342.6i	0.381390	−	0.381390i	0.871603	+	0.490213i	$0.163081\pi$
$98$		0			0
$99$	140335.			1.43906
$100$		0			0
$101$	−104115.			−1.01557			−0.507784	−	0.861484i	$-0.669535\pi$
$101$	−104115.			−1.01557			−0.507784	+	0.861484i	$0.669535\pi$
$102$		0			0
$103$	−43067.5	+	43067.5i	−0.399997	+	0.399997i	−0.878232	−	0.478235i	$-0.841277\pi$
$103$	−43067.5	+	43067.5i	−0.399997	+	0.399997i	0.478235	+	0.878232i	$0.341277\pi$
$104$		0			0
$105$	−1389.19	+	1699.05i	−0.0122967	+	0.0150395i
$106$		0			0
$107$	139966.	+	139966.i	1.18185	+	1.18185i	0.979265	+	0.202585i	$0.0649341\pi$
$107$	139966.	+	139966.i	1.18185	+	1.18185i	0.202585	+	0.979265i	$0.435066\pi$
$108$		0			0
$109$			96865.6i			0.780914i	0.920621	+	0.390457i	$0.127683\pi$
$109$			96865.6i			0.780914i	−0.920621	+	0.390457i	$0.872317\pi$
$110$		0			0
$111$			72665.8i			0.559787i
$112$		0			0
$113$	−58802.8	−	58802.8i	−0.433213	−	0.433213i	0.456507	−	0.889720i	$-0.349100\pi$
$113$	−58802.8	−	58802.8i	−0.433213	−	0.433213i	−0.889720	+	0.456507i	$0.849100\pi$
$114$		0			0
$115$	10617.3	+	105817.i	0.0748630	+	0.746123i
$116$		0			0
$117$	−50113.9	+	50113.9i	−0.338449	+	0.338449i
$118$		0			0
$119$	5116.81			0.0331232
$120$		0			0
$121$	−241043.			−1.49669
$122$		0			0
$123$	−42896.4	+	42896.4i	−0.255657	+	0.255657i
$124$		0			0
$125$	−154514.	−	81504.1i	−0.884491	−	0.466557i
$126$		0			0
$127$	−156941.	−	156941.i	−0.863428	−	0.863428i	0.128306	−	0.991735i	$-0.459046\pi$
$127$	−156941.	−	156941.i	−0.863428	−	0.863428i	−0.991735	+	0.128306i	$0.959046\pi$
$128$		0			0
$129$			69412.2i			0.367250i
$130$		0			0
$131$			328683.i			1.67340i	0.547663	+	0.836699i	$0.315518\pi$
$131$			328683.i			1.67340i	−0.547663	+	0.836699i	$0.684482\pi$
$132$		0			0
$133$	−3222.98	−	3222.98i	−0.0157990	−	0.0157990i
$134$		0			0
$135$	−120275.	+	12067.9i	−0.567991	+	0.0569900i
$136$		0			0
$137$	−68941.8	+	68941.8i	−0.313820	+	0.313820i	−0.846388	−	0.532567i	$-0.821227\pi$
$137$	−68941.8	+	68941.8i	−0.313820	+	0.313820i	0.532567	+	0.846388i	$0.321227\pi$
$138$		0			0
$139$	357947.			1.57138			0.785692	−	0.618618i	$-0.212307\pi$
$139$	357947.			1.57138			0.785692	+	0.618618i	$0.212307\pi$
$140$		0			0
$141$	95265.8			0.403542
$142$		0			0
$143$	143588.	−	143588.i	0.587190	−	0.587190i
$144$		0			0
$145$	84066.2	+	68734.7i	0.332048	+	0.271492i
$146$		0			0
$147$	55112.7	+	55112.7i	0.210358	+	0.210358i
$148$		0			0
$149$			181781.i			0.670784i	0.942079	+	0.335392i	$0.108869\pi$
$149$			181781.i			0.670784i	−0.942079	+	0.335392i	$0.891131\pi$
$150$		0			0
$151$			281792.i			1.00574i	0.864361	+	0.502871i	$0.167723\pi$
$151$			281792.i			1.00574i	−0.864361	+	0.502871i	$0.832277\pi$
$152$		0			0
$153$	94986.0	+	94986.0i	0.328043	+	0.328043i
$154$		0			0
$155$	−347039.	−	283748.i	−1.16024	−	0.948644i
$156$		0			0
$157$	18154.8	−	18154.8i	0.0587817	−	0.0587817i	−0.677105	−	0.735887i	$-0.736766\pi$
$157$	18154.8	−	18154.8i	0.0587817	−	0.0587817i	0.735887	+	0.677105i	$0.236766\pi$
$158$		0			0
$159$	39906.0			0.125183
$160$		0			0
$161$	−16037.4			−0.0487606
$162$		0			0
$163$	288172.	−	288172.i	0.849537	−	0.849537i	−0.140538	−	0.990075i	$-0.544883\pi$
$163$	288172.	−	288172.i	0.849537	−	0.849537i	0.990075	+	0.140538i	$0.0448832\pi$
$164$		0			0
$165$	164259.	−	16481.2i	0.469700	−	0.0471279i
$166$		0			0
$167$	−31141.0	−	31141.0i	−0.0864055	−	0.0864055i	0.662583	−	0.748989i	$-0.269460\pi$
$167$	−31141.0	−	31141.0i	−0.0864055	−	0.0864055i	−0.748989	+	0.662583i	$0.769460\pi$
$168$		0			0
$169$		−	268742.i		−	0.723800i
$170$		0			0
$171$		−	119660.i		−	0.312937i
$172$		0			0
$173$	159322.	+	159322.i	0.404726	+	0.404726i	0.879895	−	0.475169i	$-0.157613\pi$
$173$	159322.	+	159322.i	0.404726	+	0.404726i	−0.475169	+	0.879895i	$0.657613\pi$
$174$		0			0
$175$	14555.7	−	21957.4i	0.0359285	−	0.0541983i
$176$		0			0
$177$	−1335.81	+	1335.81i	−0.00320489	+	0.00320489i
$178$		0			0
$179$	−657790.			−1.53446			−0.767229	−	0.641373i	$-0.778365\pi$
$179$	−657790.			−1.53446			−0.767229	+	0.641373i	$0.778365\pi$
$180$		0			0
$181$	−662330.			−1.50272			−0.751360	−	0.659892i	$-0.770602\pi$
$181$	−662330.			−1.50272			−0.751360	+	0.659892i	$0.770602\pi$
$182$		0			0
$183$	−35832.4	+	35832.4i	−0.0790949	+	0.0790949i
$184$		0			0
$185$	−87080.4	−	867887.i	−0.187064	−	1.86438i
$186$		0			0
$187$	−272157.	−	272157.i	−0.569135	−	0.569135i
$188$		0			0
$189$		−	18228.7i		−	0.0371193i
$190$		0			0
$191$			414623.i			0.822375i	0.911551	+	0.411187i	$0.134886\pi$
$191$			414623.i			0.822375i	−0.911551	+	0.411187i	$0.865114\pi$
$192$		0			0
$193$	688506.	+	688506.i	1.33050	+	1.33050i	0.904923	+	0.425575i	$0.139928\pi$
$193$	688506.	+	688506.i	1.33050	+	1.33050i	0.425575	+	0.904923i	$0.360072\pi$
$194$		0			0
$195$	−52771.8	+	64542.7i	−0.0993837	+	0.121552i
$196$		0			0
$197$	683608.	−	683608.i	1.25499	−	1.25499i	0.301540	−	0.953453i	$-0.402499\pi$
$197$	683608.	−	683608.i	1.25499	−	1.25499i	0.953453	−	0.301540i	$-0.0975007\pi$
$198$		0			0
$199$	808934.			1.44804			0.724020	−	0.689779i	$-0.242292\pi$
$199$	808934.			1.44804			0.724020	+	0.689779i	$0.242292\pi$
$200$		0			0
$201$	−58530.3			−0.102186
$202$		0			0
$203$	−11579.1	+	11579.1i	−0.0197213	+	0.0197213i
$204$		0			0
$205$	460929.	−	563740.i	0.766036	−	0.936903i
$206$		0			0
$207$	−297710.	−	297710.i	−0.482912	−	0.482912i
$208$		0			0
$209$			342853.i			0.542928i
$210$		0			0
$211$		−	308765.i		−	0.477444i	−0.971088	−	0.238722i	$-0.923272\pi$
$211$		−	308765.i		−	0.477444i	0.971088	−	0.238722i	$-0.0767284\pi$
$212$		0			0
$213$	40962.3	+	40962.3i	0.0618636	+	0.0618636i
$214$		0			0
$215$	−83181.3	−	829027.i	−0.122724	−	1.22313i
$216$		0			0
$217$	47800.4	−	47800.4i	0.0689099	−	0.0689099i
$218$		0			0
$219$	−112425.			−0.158399
$220$		0			0
$221$	194375.			0.267707
$222$		0			0
$223$	410489.	−	410489.i	0.552763	−	0.552763i	−0.374474	−	0.927237i	$-0.622177\pi$
$223$	410489.	−	410489.i	0.552763	−	0.552763i	0.927237	+	0.374474i	$0.122177\pi$
$224$		0			0
$225$	677812.	−	137401.i	0.892591	−	0.180940i
$226$		0			0
$227$	−811943.	−	811943.i	−1.04583	−	1.04583i	−0.998898	−	0.0469317i	$-0.985056\pi$
$227$	−811943.	−	811943.i	−1.04583	−	1.04583i	−0.0469317	−	0.998898i	$-0.514944\pi$
$228$		0			0
$229$			681576.i			0.858866i	0.903099	+	0.429433i	$0.141287\pi$
$229$			681576.i			0.858866i	−0.903099	+	0.429433i	$0.858713\pi$
$230$		0			0
$231$			24894.8i			0.0306958i
$232$		0			0
$233$	−130959.	−	130959.i	−0.158032	−	0.158032i	0.623662	−	0.781694i	$-0.285644\pi$
$233$	−130959.	−	130959.i	−0.158032	−	0.158032i	−0.781694	+	0.623662i	$0.785644\pi$
$234$		0			0
$235$	−1.13781e6	+	114163.i	−1.34400	+	0.134852i
$236$		0			0
$237$	227411.	−	227411.i	0.262991	−	0.262991i
$238$		0			0
$239$	697425.			0.789773			0.394887	−	0.918730i	$-0.370784\pi$
$239$	697425.			0.789773			0.394887	+	0.918730i	$0.370784\pi$
$240$		0			0
$241$	−82389.9			−0.0913758			−0.0456879	−	0.998956i	$-0.514548\pi$
$241$	−82389.9			−0.0913758			−0.0456879	+	0.998956i	$0.514548\pi$
$242$		0			0
$243$	515485.	−	515485.i	0.560016	−	0.560016i
$244$		0			0
$245$	−724286.	−	592196.i	−0.770895	−	0.630304i
$246$		0			0
$247$	−122433.	−	122433.i	−0.127690	−	0.127690i
$248$		0			0
$249$			267458.i			0.273374i
$250$		0			0
$251$			863770.i			0.865394i	0.901540	+	0.432697i	$0.142438\pi$
$251$			863770.i			0.865394i	−0.901540	+	0.432697i	$0.857562\pi$
$252$		0			0
$253$	853009.	+	853009.i	0.837823	+	0.837823i
$254$		0			0
$255$	122334.	+	100024.i	0.117814	+	0.0963280i
$256$		0			0
$257$	993849.	−	993849.i	0.938615	−	0.938615i	−0.0596069	−	0.998222i	$-0.518985\pi$
$257$	993849.	−	993849.i	0.938615	−	0.938615i	0.998222	+	0.0596069i	$0.0189847\pi$
$258$		0			0
$259$	131535.			0.121841
$260$		0			0
$261$	−429897.			−0.390628
$262$		0			0
$263$	−180655.	+	180655.i	−0.161050	+	0.161050i	−0.783032	−	0.621982i	$-0.786328\pi$
$263$	−180655.	+	180655.i	−0.161050	+	0.161050i	0.621982	+	0.783032i	$0.286328\pi$
$264$		0			0
$265$	−476619.	+	47822.1i	−0.416924	+	0.0418325i
$266$		0			0
$267$	−213295.	−	213295.i	−0.183106	−	0.183106i
$268$		0			0
$269$			72265.9i			0.0608909i	0.999536	+	0.0304455i	$0.00969259\pi$
$269$			72265.9i			0.0608909i	−0.999536	+	0.0304455i	$0.990307\pi$
$270$		0			0
$271$			2.05138e6i			1.69677i	0.529379	+	0.848385i	$0.322425\pi$
$271$			2.05138e6i			1.69677i	−0.529379	+	0.848385i	$0.677575\pi$
$272$		0			0
$273$	−8889.97	−	8889.97i	−0.00721928	−	0.00721928i
$274$		0			0
$275$	−1.94209e6	+	393687.i	−1.54859	+	0.313920i
$276$		0			0
$277$	−958531.	+	958531.i	−0.750597	+	0.750597i	−0.974591	−	0.223994i	$-0.928090\pi$
$277$	−958531.	+	958531.i	−0.750597	+	0.750597i	0.223994	+	0.974591i	$0.428090\pi$
$278$		0			0
$279$	1.77468e6			1.36493
$280$		0			0
$281$	−2.20230e6			−1.66384			−0.831920	−	0.554896i	$-0.812758\pi$
$281$	−2.20230e6			−1.66384			−0.831920	+	0.554896i	$0.812758\pi$
$282$		0			0
$283$	872678.	−	872678.i	0.647721	−	0.647721i	−0.304721	−	0.952442i	$-0.598563\pi$
$283$	872678.	−	872678.i	0.647721	−	0.647721i	0.952442	+	0.304721i	$0.0985632\pi$
$284$		0			0
$285$	−14053.0	−	140059.i	−0.0102484	−	0.102141i
$286$		0			0
$287$	77648.4	+	77648.4i	0.0556452	+	0.0556452i
$288$		0			0
$289$			1.05144e6i			0.740524i
$290$		0			0
$291$			232772.i			0.161138i
$292$		0			0
$293$	−811890.	−	811890.i	−0.552495	−	0.552495i	0.374665	−	0.927160i	$-0.377758\pi$
$293$	−811890.	−	811890.i	−0.552495	−	0.552495i	−0.927160	+	0.374665i	$0.877758\pi$
$294$		0			0
$295$	14353.6	−	17555.2i	0.00960295	−	0.0117449i
$296$		0			0
$297$	−969560.	+	969560.i	−0.637799	+	0.637799i
$298$		0			0
$299$	−609221.			−0.394091
$300$		0			0
$301$	125646.			0.0799339
$302$		0			0
$303$	342858.	−	342858.i	0.214540	−	0.214540i
$304$		0			0
$305$	385025.	−	470906.i	0.236995	−	0.289858i
$306$		0			0
$307$	1.50108e6	+	1.50108e6i	0.908989	+	0.908989i	0.996191	−	0.0872016i	$-0.0277924\pi$
$307$	1.50108e6	+	1.50108e6i	0.908989	+	0.908989i	−0.0872016	+	0.996191i	$0.527792\pi$
$308$		0			0
$309$		−	283649.i		−	0.168999i
$310$		0			0
$311$			2.99788e6i			1.75757i	0.477213	+	0.878787i	$0.341647\pi$
$311$			2.99788e6i			1.75757i	−0.477213	+	0.878787i	$0.658353\pi$
$312$		0			0
$313$	186130.	+	186130.i	0.107388	+	0.107388i	0.758759	−	0.651371i	$-0.225806\pi$
$313$	186130.	+	186130.i	0.107388	+	0.107388i	−0.651371	+	0.758759i	$0.725806\pi$
$314$		0			0
$315$	10412.1	+	103772.i	0.00591239	+	0.0589258i
$316$		0			0
$317$	−269555.	+	269555.i	−0.150661	+	0.150661i	−0.778413	−	0.627752i	$-0.783975\pi$
$317$	−269555.	+	269555.i	−0.150661	+	0.150661i	0.627752	+	0.778413i	$0.283975\pi$
$318$		0			0
$319$	1.23176e6			0.677717
$320$		0			0
$321$	−921835.			−0.499334
$322$		0			0
$323$	−232060.	+	232060.i	−0.123764	+	0.123764i
$324$		0			0
$325$	552936.	−	834108.i	0.290380	−	0.438040i
$326$		0			0
$327$	−318986.	−	318986.i	−0.164969	−	0.164969i
$328$		0			0
$329$		−	172444.i		−	0.0878333i
$330$		0			0
$331$		−	656419.i		−	0.329315i	−0.986351	−	0.164657i	$-0.947348\pi$
$331$		−	656419.i		−	0.329315i	0.986351	−	0.164657i	$-0.0526518\pi$
$332$		0			0
$333$	2.44175e6	+	2.44175e6i	1.20668	+	1.20668i
$334$		0			0
$335$	699059.	−	70140.8i	0.340331	−	0.0341475i
$336$		0			0
$337$	1.29668e6	−	1.29668e6i	0.621954	−	0.621954i	−0.324077	−	0.946031i	$-0.605054\pi$
$337$	1.29668e6	−	1.29668e6i	0.621954	−	0.621954i	0.946031	+	0.324077i	$0.105054\pi$
$338$		0			0
$339$	387284.			0.183033
$340$		0			0
$341$	−5.08489e6			−2.36807
$342$		0			0
$343$	199947.	−	199947.i	0.0917655	−	0.0917655i
$344$		0			0
$345$	−383426.	−	313500.i	−0.173434	−	0.141804i
$346$		0			0
$347$	2.79696e6	+	2.79696e6i	1.24699	+	1.24699i	0.957042	+	0.289948i	$0.0936382\pi$
$347$	2.79696e6	+	2.79696e6i	1.24699	+	1.24699i	0.289948	+	0.957042i	$0.406362\pi$
$348$		0			0
$349$			2.63211e6i			1.15675i	0.815770	+	0.578376i	$0.196313\pi$
$349$			2.63211e6i			1.15675i	−0.815770	+	0.578376i	$0.803687\pi$
$350$		0			0
$351$		−	692462.i		−	0.300005i
$352$		0			0
$353$	324347.	+	324347.i	0.138539	+	0.138539i	0.772975	−	0.634436i	$-0.218768\pi$
$353$	324347.	+	324347.i	0.138539	+	0.138539i	−0.634436	+	0.772975i	$0.718768\pi$
$354$		0			0
$355$	−538323.	−	440147.i	−0.226711	−	0.185365i
$356$		0			0
$357$	−16850.1	+	16850.1i	−0.00699731	+	0.00699731i
$358$		0			0
$359$	−2.87581e6			−1.17767			−0.588835	−	0.808253i	$-0.700413\pi$
$359$	−2.87581e6			−1.17767			−0.588835	+	0.808253i	$0.700413\pi$
$360$		0			0
$361$	−2.18376e6			−0.881935
$362$		0			0
$363$	793772.	−	793772.i	0.316176	−	0.316176i
$364$		0			0
$365$	1.34275e6	−	134727.i	0.527550	−	0.0529323i
$366$		0			0
$367$	−1.93322e6	−	1.93322e6i	−0.749232	−	0.749232i	0.225103	−	0.974335i	$-0.427728\pi$
$367$	−1.93322e6	−	1.93322e6i	−0.749232	−	0.749232i	−0.974335	+	0.225103i	$0.927728\pi$
$368$		0			0
$369$			2.88285e6i			1.10219i
$370$		0			0
$371$		−	72235.4i		−	0.0272468i
$372$		0			0
$373$	−2.22939e6	−	2.22939e6i	−0.829685	−	0.829685i	0.157788	−	0.987473i	$-0.449564\pi$
$373$	−2.22939e6	−	2.22939e6i	−0.829685	−	0.829685i	−0.987473	+	0.157788i	$0.949564\pi$
$374$		0			0
$375$	777227.	−	240428.i	0.285410	−	0.0882890i
$376$		0			0
$377$	−439862.	+	439862.i	−0.159391	+	0.159391i
$378$		0			0
$379$	1.42092e6			0.508127			0.254064	−	0.967187i	$-0.418233\pi$
$379$	1.42092e6			0.508127			0.254064	+	0.967187i	$0.418233\pi$
$380$		0			0
$381$	1.03364e6			0.364800
$382$		0			0
$383$	−3.39383e6	+	3.39383e6i	−1.18220	+	1.18220i	−0.203032	+	0.979172i	$0.565080\pi$
$383$	−3.39383e6	+	3.39383e6i	−1.18220	+	1.18220i	−0.979172	+	0.203032i	$0.934920\pi$
$384$		0			0
$385$	−29833.2	−	297332.i	−0.0102576	−	0.102233i
$386$		0			0
$387$	2.33242e6	+	2.33242e6i	0.791644	+	0.791644i
$388$		0			0
$389$		−	3.31303e6i		−	1.11007i	−0.831826	−	0.555036i	$-0.812704\pi$
$389$		−	3.31303e6i		−	1.11007i	0.831826	−	0.555036i	$-0.187296\pi$
$390$		0			0
$391$			1.15472e6i			0.381974i
$392$		0			0
$393$	−1.08238e6	−	1.08238e6i	−0.353507	−	0.353507i
$394$		0			0
$395$	−2.44357e6	+	2.98861e6i	−0.788010	+	0.963778i
$396$		0			0
$397$	2.40606e6	−	2.40606e6i	0.766179	−	0.766179i	−0.211253	−	0.977431i	$-0.567754\pi$
$397$	2.40606e6	−	2.40606e6i	0.766179	−	0.766179i	0.977431	+	0.211253i	$0.0677544\pi$
$398$		0			0
$399$	21227.1			0.00667510
$400$		0			0
$401$	5.13661e6			1.59520			0.797601	−	0.603185i	$-0.206102\pi$
$401$	5.13661e6			1.59520			0.797601	+	0.603185i	$0.206102\pi$
$402$		0			0
$403$	1.81582e6	−	1.81582e6i	0.556942	−	0.556942i
$404$		0			0
$405$	−1.54660e6	+	1.89158e6i	−0.468535	+	0.573043i
$406$		0			0
$407$	−6.99619e6	−	6.99619e6i	−2.09351	−	2.09351i
$408$		0			0
$409$		−	1.51107e6i		−	0.446658i	−0.974743	−	0.223329i	$-0.928308\pi$
$409$		−	1.51107e6i		−	0.446658i	0.974743	−	0.223329i	$-0.0716924\pi$
$410$		0			0
$411$		−	454061.i		−	0.132590i
$412$		0			0
$413$	2418.01	+	2418.01i	0.000697562	+	0.000697562i
$414$		0			0
$415$	−320513.	−	3.19439e6i	−0.0913534	−	0.910474i
$416$		0			0
$417$	−1.17875e6	+	1.17875e6i	−0.331956	+	0.331956i
$418$		0			0
$419$	1.07646e6			0.299544			0.149772	−	0.988721i	$-0.452146\pi$
$419$	1.07646e6			0.299544			0.149772	+	0.988721i	$0.452146\pi$
$420$		0			0
$421$	3.18241e6			0.875086			0.437543	−	0.899197i	$-0.355849\pi$
$421$	3.18241e6			0.875086			0.437543	+	0.899197i	$0.355849\pi$
$422$		0			0
$423$	3.20117e6	−	3.20117e6i	0.869877	−	0.869877i
$424$		0			0
$425$	−1.58097e6	−	1.04804e6i	−0.424572	−	0.281452i
$426$		0			0
$427$	64861.6	+	64861.6i	0.0172154	+	0.0172154i
$428$		0			0
$429$			945694.i			0.248089i
$430$		0			0
$431$		−	1.46800e6i		−	0.380657i	−0.981720	−	0.190329i	$-0.939045\pi$
$431$		−	1.46800e6i		−	0.380657i	0.981720	−	0.190329i	$-0.0609553\pi$
$432$		0			0
$433$	4.49367e6	+	4.49367e6i	1.15181	+	1.15181i	0.986189	+	0.165623i	$0.0529634\pi$
$433$	4.49367e6	+	4.49367e6i	1.15181	+	1.15181i	0.165623	+	0.986189i	$0.447037\pi$
$434$		0			0
$435$	−503185.	+	50487.6i	−0.127498	+	0.0127927i
$436$		0			0
$437$	727335.	−	727335.i	0.182193	−	0.182193i
$438$		0			0
$439$	25222.7			0.00624641			0.00312320	−	0.999995i	$-0.499006\pi$
$439$	25222.7			0.00624641			0.00312320	+	0.999995i	$0.499006\pi$
$440$		0			0
$441$	3.70385e6			0.906895
$442$		0			0
$443$	3.20085e6	−	3.20085e6i	0.774919	−	0.774919i	−0.204043	−	0.978962i	$-0.565408\pi$
$443$	3.20085e6	−	3.20085e6i	0.774919	−	0.774919i	0.978962	+	0.204043i	$0.0654083\pi$
$444$		0			0
$445$	2.80311e6	+	2.29189e6i	0.671027	+	0.548649i
$446$		0			0
$447$	−598618.	−	598618.i	−0.141704	−	0.141704i
$448$		0			0
$449$		−	4.85115e6i		−	1.13561i	−0.823164	−	0.567804i	$-0.807793\pi$
$449$		−	4.85115e6i		−	1.13561i	0.823164	−	0.567804i	$-0.192207\pi$
$450$		0			0
$451$		−	8.26005e6i		−	1.91224i
$452$		0			0
$453$	−927963.	−	927963.i	−0.212464	−	0.212464i
$454$		0			0
$455$	116831.	+	95524.3i	0.0264564	+	0.0216314i
$456$		0			0
$457$	1.87370e6	−	1.87370e6i	0.419671	−	0.419671i	−0.465419	−	0.885090i	$-0.654097\pi$
$457$	1.87370e6	−	1.87370e6i	0.419671	−	0.419671i	0.885090	+	0.465419i	$0.154097\pi$
$458$		0			0
$459$	−1.31249e6			−0.290780
$460$		0			0
$461$	2.47636e6			0.542702			0.271351	−	0.962480i	$-0.412530\pi$
$461$	2.47636e6			0.542702			0.271351	+	0.962480i	$0.412530\pi$
$462$		0			0
$463$	−5.78796e6	+	5.78796e6i	−1.25480	+	1.25480i	−0.301252	+	0.953544i	$0.597405\pi$
$463$	−5.78796e6	+	5.78796e6i	−1.25480	+	1.25480i	−0.953544	+	0.301252i	$0.902595\pi$
$464$		0			0
$465$	2.07723e6	−	208421.i	0.445504	−	0.0447001i
$466$		0			0
$467$	1.55806e6	+	1.55806e6i	0.330591	+	0.330591i	0.852811	−	0.522220i	$-0.174896\pi$
$467$	1.55806e6	+	1.55806e6i	0.330591	+	0.330591i	−0.522220	+	0.852811i	$0.674896\pi$
$468$		0			0
$469$			105948.i			0.0222413i
$470$		0			0
$471$			119570.i			0.0248354i
$472$		0			0
$473$	−6.68294e6	−	6.68294e6i	−1.37346	−	1.37346i
$474$		0			0
$475$	335684.	+	1.65596e6i	0.0682649	+	0.336756i
$476$		0			0
$477$	1.34094e6	−	1.34094e6i	0.269845	−	0.269845i
$478$		0			0
$479$	−1.81391e6			−0.361224			−0.180612	−	0.983554i	$-0.557808\pi$
$479$	−1.81391e6			−0.361224			−0.180612	+	0.983554i	$0.557808\pi$
$480$		0			0
$481$	4.99670e6			0.984737
$482$		0			0
$483$	52812.3	−	52812.3i	0.0103007	−	0.0103007i
$484$		0			0
$485$	−278946.	−	2.78012e6i	−0.0538476	−	0.536673i
$486$		0			0
$487$	898602.	+	898602.i	0.171690	+	0.171690i	0.787722	−	0.616031i	$-0.211261\pi$
$487$	898602.	+	898602.i	0.171690	+	0.171690i	−0.616031	+	0.787722i	$0.711261\pi$
$488$		0			0
$489$			1.89794e6i			0.358931i
$490$		0			0
$491$		−	1.86137e6i		−	0.348441i	−0.984707	−	0.174220i	$-0.944260\pi$
$491$		−	1.86137e6i		−	0.348441i	0.984707	−	0.174220i	$-0.0557405\pi$
$492$		0			0
$493$	833714.	+	833714.i	0.154490	+	0.154490i
$494$		0			0
$495$	4.96572e6	−	6.07334e6i	0.910897	−	1.11408i
$496$		0			0
$497$	74147.5	−	74147.5i	0.0134650	−	0.0134650i
$498$		0			0
$499$	−3.04071e6			−0.546668			−0.273334	−	0.961919i	$-0.588126\pi$
$499$	−3.04071e6			−0.546668			−0.273334	+	0.961919i	$0.588126\pi$
$500$		0			0
$501$	205099.			0.0365065
$502$		0			0
$503$	−7.23935e6	+	7.23935e6i	−1.27579	+	1.27579i	−0.332791	+	0.943001i	$0.607990\pi$
$503$	−7.23935e6	+	7.23935e6i	−1.27579	+	1.27579i	−0.943001	+	0.332791i	$0.892010\pi$
$504$		0			0
$505$	−3.68407e6	+	4.50581e6i	−0.642835	+	0.786221i
$506$		0			0
$507$	884988.	+	884988.i	0.152904	+	0.152904i
$508$		0			0
$509$		−	8.84454e6i		−	1.51315i	−0.653910	−	0.756573i	$-0.726872\pi$
$509$		−	8.84454e6i		−	1.51315i	0.653910	−	0.756573i	$-0.273128\pi$
$510$		0			0
$511$			203505.i			0.0344764i
$512$		0			0
$513$	826714.	+	826714.i	0.138695	+	0.138695i
$514$		0			0
$515$	339916.	+	3.38777e6i	0.0564747	+	0.562855i
$516$		0			0
$517$	−9.17210e6	+	9.17210e6i	−1.50918	+	1.50918i
$518$		0			0
$519$	−1.04932e6			−0.170998
$520$		0			0
$521$	−9.43074e6			−1.52213			−0.761065	−	0.648676i	$-0.775323\pi$
$521$	−9.43074e6			−1.52213			−0.761065	+	0.648676i	$0.775323\pi$
$522$		0			0
$523$	3.70150e6	−	3.70150e6i	0.591729	−	0.591729i	−0.346369	−	0.938098i	$-0.612585\pi$
$523$	3.70150e6	−	3.70150e6i	0.591729	−	0.591729i	0.938098	+	0.346369i	$0.112585\pi$
$524$		0			0
$525$	24374.3	+	120241.i	0.00385953	+	0.0190394i
$526$		0			0
$527$	−3.44170e6	−	3.44170e6i	−0.539817	−	0.539817i
$528$		0			0
$529$			2.81716e6i			0.437696i
$530$		0			0
$531$			89773.5i			0.0138169i
$532$		0			0
$533$	2.94967e6	+	2.94967e6i	0.449734	+	0.449734i
$534$		0			0
$535$	1.10100e7	−	1.10470e6i	1.66304	−	0.166863i
$536$		0			0
$537$	2.16615e6	−	2.16615e6i	0.324156	−	0.324156i
$538$		0			0
$539$	−1.06124e7			−1.57341
$540$		0			0
$541$	4.64526e6			0.682365			0.341183	−	0.939997i	$-0.389173\pi$
$541$	4.64526e6			0.682365			0.341183	+	0.939997i	$0.389173\pi$
$542$		0			0
$543$	2.18110e6	−	2.18110e6i	0.317451	−	0.317451i
$544$		0			0
$545$	4.19208e6	+	3.42756e6i	0.604559	+	0.494303i
$546$		0			0
$547$	8.51024e6	+	8.51024e6i	1.21611	+	1.21611i	0.968983	+	0.247128i	$0.0794870\pi$
$547$	8.51024e6	+	8.51024e6i	1.21611	+	1.21611i	0.247128	+	0.968983i	$0.420513\pi$
$548$		0			0
$549$			2.40812e6i			0.340994i
$550$		0			0
$551$		−	1.05028e6i		−	0.147376i
$552$		0			0
$553$	−411645.	−	411645.i	−0.0572414	−	0.0572414i
$554$		0			0
$555$	3.14478e6	+	2.57125e6i	0.433369	+	0.354334i
$556$		0			0
$557$	−1.60437e6	+	1.60437e6i	−0.219113	+	0.219113i	−0.808124	−	0.589012i	$-0.799517\pi$
$557$	−1.60437e6	+	1.60437e6i	−0.219113	+	0.219113i	0.589012	+	0.808124i	$0.299517\pi$
$558$		0			0
$559$	4.77297e6			0.646040
$560$		0			0
$561$	1.79247e6			0.240461
$562$		0			0
$563$	−9.82070e6	+	9.82070e6i	−1.30578	+	1.30578i	−0.381355	+	0.924429i	$0.624542\pi$
$563$	−9.82070e6	+	9.82070e6i	−1.30578	+	1.30578i	−0.924429	+	0.381355i	$0.875458\pi$
$564$		0			0
$565$	−4.62554e6	+	464109.i	−0.609595	+	0.0611644i
$566$		0			0
$567$	−260542.	−	260542.i	−0.0340346	−	0.0340346i
$568$		0			0
$569$		−	7.73484e6i		−	1.00155i	−0.865579	−	0.500773i	$-0.833049\pi$
$569$		−	7.73484e6i		−	1.00155i	0.865579	−	0.500773i	$-0.166951\pi$
$570$		0			0
$571$		−	8.13215e6i		−	1.04380i	−0.853008	−	0.521898i	$-0.825224\pi$
$571$		−	8.13215e6i		−	1.04380i	0.853008	−	0.521898i	$-0.174776\pi$
$572$		0			0
$573$	−1.36538e6	−	1.36538e6i	−0.173727	−	0.173727i
$574$		0			0
$575$	4.95516e6	+	3.28481e6i	0.625011	+	0.414324i
$576$		0			0
$577$	−5.27077e6	+	5.27077e6i	−0.659074	+	0.659074i	−0.955161	−	0.296087i	$-0.904318\pi$
$577$	−5.27077e6	+	5.27077e6i	−0.659074	+	0.659074i	0.296087	+	0.955161i	$0.404318\pi$
$578$		0			0
$579$	−4.53460e6			−0.562138
$580$		0			0
$581$	484135.			0.0595013
$582$		0			0
$583$	−3.84211e6	+	3.84211e6i	−0.468165	+	0.468165i
$584$		0			0
$585$	395531.	+	3.94206e6i	0.0477849	+	0.476249i
$586$		0			0
$587$	4.02268e6	+	4.02268e6i	0.481859	+	0.481859i	0.905725	−	0.423866i	$-0.139327\pi$
$587$	4.02268e6	+	4.02268e6i	0.481859	+	0.481859i	−0.423866	+	0.905725i	$0.639327\pi$
$588$		0			0
$589$			4.33573e6i			0.514960i
$590$		0			0
$591$			4.50235e6i			0.530237i
$592$		0			0
$593$	−5.59217e6	−	5.59217e6i	−0.653046	−	0.653046i	0.300679	−	0.953725i	$-0.402787\pi$
$593$	−5.59217e6	−	5.59217e6i	−0.653046	−	0.653046i	−0.953725	+	0.300679i	$0.902787\pi$
$594$		0			0
$595$	181057.	−	221442.i	0.0209663	−	0.0256429i
$596$		0			0
$597$	−2.66388e6	+	2.66388e6i	−0.305900	+	0.305900i
$598$		0			0
$599$	1.15230e7			1.31220			0.656099	−	0.754675i	$-0.272205\pi$
$599$	1.15230e7			1.31220			0.656099	+	0.754675i	$0.272205\pi$
$600$		0			0
$601$	2.44067e6			0.275628			0.137814	−	0.990458i	$-0.455992\pi$
$601$	2.44067e6			0.275628			0.137814	+	0.990458i	$0.455992\pi$
$602$		0			0
$603$	−1.96676e6	+	1.96676e6i	−0.220272	+	0.220272i
$604$		0			0
$605$	−8.52922e6	+	1.04317e7i	−0.947373	+	1.15869i
$606$		0			0
$607$	3.35790e6	+	3.35790e6i	0.369910	+	0.369910i	0.867444	−	0.497535i	$-0.165761\pi$
$607$	3.35790e6	+	3.35790e6i	0.369910	+	0.369910i	−0.497535	+	0.867444i	$0.665761\pi$
$608$		0			0
$609$		−	76261.7i		−	0.00833227i
$610$		0			0
$611$		−	6.55073e6i		−	0.709883i
$612$		0			0
$613$	−1.00846e7	−	1.00846e7i	−1.08395	−	1.08395i	−0.996137	−	0.0878091i	$-0.972013\pi$
$613$	−1.00846e7	−	1.00846e7i	−1.08395	−	1.08395i	−0.0878091	−	0.996137i	$-0.527987\pi$
$614$		0			0
$615$	338566.	+	3.37431e6i	0.0360957	+	0.359748i
$616$		0			0
$617$	−8.65775e6	+	8.65775e6i	−0.915571	+	0.915571i	−0.996703	−	0.0811322i	$-0.974146\pi$
$617$	−8.65775e6	+	8.65775e6i	−0.915571	+	0.915571i	0.0811322	+	0.996703i	$0.474146\pi$
$618$		0			0
$619$	691475.			0.0725354			0.0362677	−	0.999342i	$-0.488453\pi$
$619$	691475.			0.0725354			0.0362677	+	0.999342i	$0.488453\pi$
$620$		0			0
$621$	4.11369e6			0.428057
$622$		0			0
$623$	−386094.	+	386094.i	−0.0398541	+	0.0398541i
$624$		0			0
$625$	−8.99471e6	+	3.80296e6i	−0.921059	+	0.389424i
$626$		0			0
$627$	−1.12904e6	−	1.12904e6i	−0.114694	−	0.114694i
$628$		0			0
$629$		−	9.47074e6i		−	0.954459i
$630$		0			0
$631$			1.44466e7i			1.44441i	0.691677	+	0.722207i	$0.256872\pi$
$631$			1.44466e7i			1.44441i	−0.691677	+	0.722207i	$0.743128\pi$
$632$		0			0
$633$	1.01679e6	+	1.01679e6i	0.100860	+	0.100860i
$634$		0			0
$635$	−1.23453e7	+	1.23868e6i	−1.21497	+	0.121906i
$636$		0			0
$637$	3.78970e6	−	3.78970e6i	0.370047	−	0.370047i
$638$		0			0
$639$	2.75287e6			0.266707
$640$		0			0
$641$	1.13910e7			1.09501			0.547504	−	0.836803i	$-0.315578\pi$
$641$	1.13910e7			1.09501			0.547504	+	0.836803i	$0.315578\pi$
$642$		0			0
$643$	7.53859e6	−	7.53859e6i	0.719056	−	0.719056i	−0.249356	−	0.968412i	$-0.580219\pi$
$643$	7.53859e6	−	7.53859e6i	0.719056	−	0.719056i	0.968412	+	0.249356i	$0.0802188\pi$
$644$		0			0
$645$	3.00397e6	+	2.45613e6i	0.284313	+	0.232462i
$646$		0			0
$647$	8.23733e6	+	8.23733e6i	0.773616	+	0.773616i	0.978737	−	0.205120i	$-0.0657586\pi$
$647$	8.23733e6	+	8.23733e6i	0.773616	+	0.773616i	−0.205120	+	0.978737i	$0.565759\pi$
$648$		0			0
$649$		−	257222.i		−	0.0239716i
$650$		0			0
$651$			314820.i			0.0291146i
$652$		0			0
$653$	−7.48193e6	−	7.48193e6i	−0.686642	−	0.686642i	0.274846	−	0.961488i	$-0.411373\pi$
$653$	−7.48193e6	−	7.48193e6i	−0.686642	−	0.686642i	−0.961488	+	0.274846i	$0.911373\pi$
$654$		0			0
$655$	1.42245e7	+	1.16303e7i	1.29549	+	1.05923i
$656$		0			0
$657$	−3.77776e6	+	3.77776e6i	−0.341445	+	0.341445i
$658$		0			0
$659$	−1.09855e7			−0.985390			−0.492695	−	0.870202i	$-0.663988\pi$
$659$	−1.09855e7			−0.985390			−0.492695	+	0.870202i	$0.663988\pi$
$660$		0			0
$661$	6.62528e6			0.589795			0.294897	−	0.955529i	$-0.404715\pi$
$661$	6.62528e6			0.589795			0.294897	+	0.955529i	$0.404715\pi$
$662$		0			0
$663$	−640092.	+	640092.i	−0.0565534	+	0.0565534i
$664$		0			0
$665$	−253526.	+	25437.8i	−0.0222315	+	0.00223062i
$666$		0			0
$667$	−2.61307e6	−	2.61307e6i	−0.227424	−	0.227424i
$668$		0			0
$669$			2.70354e6i			0.233544i
$670$		0			0
$671$		−	6.89982e6i		−	0.591605i
$672$		0			0
$673$	−5.68585e6	−	5.68585e6i	−0.483902	−	0.483902i	0.422473	−	0.906375i	$-0.361162\pi$
$673$	−5.68585e6	−	5.68585e6i	−0.483902	−	0.483902i	−0.906375	+	0.422473i	$0.861162\pi$
$674$		0			0
$675$	−3.73363e6	+	5.63220e6i	−0.315407	+	0.475794i
$676$		0			0
$677$	2.53436e6	−	2.53436e6i	0.212519	−	0.212519i	−0.592818	−	0.805337i	$-0.701985\pi$
$677$	2.53436e6	−	2.53436e6i	0.212519	−	0.212519i	0.805337	+	0.592818i	$0.201985\pi$
$678$		0			0
$679$	421350.			0.0350726
$680$		0			0
$681$	5.34758e6			0.441865
$682$		0			0
$683$	−1.05560e7	+	1.05560e7i	−0.865864	+	0.865864i	−0.992011	−	0.126148i	$-0.959739\pi$
$683$	−1.05560e7	+	1.05560e7i	−0.865864	+	0.865864i	0.126148	+	0.992011i	$0.459739\pi$
$684$		0			0
$685$	544132.	+	5.42310e6i	0.0443076	+	0.441592i
$686$		0			0
$687$	−2.24448e6	−	2.24448e6i	−0.181436	−	0.181436i
$688$		0			0
$689$		−	2.74404e6i		−	0.220213i
$690$		0			0
$691$		−	2.17073e7i		−	1.72946i	−0.502239	−	0.864729i	$-0.667490\pi$
$691$		−	2.17073e7i		−	1.72946i	0.502239	−	0.864729i	$-0.332510\pi$
$692$		0			0
$693$	836529.	+	836529.i	0.0661680	+	0.0661680i
$694$		0			0
$695$	1.26658e7	−	1.54910e7i	0.994654	−	1.21651i
$696$		0			0
$697$	5.59081e6	−	5.59081e6i	0.435906	−	0.435906i
$698$		0			0
$699$	862514.			0.0667687
$700$		0			0
$701$	−2.03600e6			−0.156488			−0.0782441	−	0.996934i	$-0.524931\pi$
$701$	−2.03600e6			−0.156488			−0.0782441	+	0.996934i	$0.524931\pi$
$702$		0			0
$703$	−5.96544e6	+	5.96544e6i	−0.455254	+	0.455254i
$704$		0			0
$705$	3.37095e6	−	4.12285e6i	0.255434	−	0.312410i
$706$		0			0
$707$	−620621.	−	620621.i	−0.0466958	−	0.0466958i
$708$		0			0
$709$			5.59025e6i			0.417653i	0.977953	+	0.208827i	$0.0669644\pi$
$709$			5.59025e6i			0.417653i	−0.977953	+	0.208827i	$0.933036\pi$
$710$		0			0
$711$		−	1.52832e7i		−	1.13381i
$712$		0			0
$713$	1.07872e7	+	1.07872e7i	0.794664	+	0.794664i
$714$		0			0
$715$	−1.13329e6	−	1.12949e7i	−0.0829040	−	0.826263i
$716$		0			0
$717$	−2.29667e6	+	2.29667e6i	−0.166840	+	0.166840i
$718$		0			0
$719$	−1.30592e7			−0.942093			−0.471046	−	0.882108i	$-0.656124\pi$
$719$	−1.30592e7			−0.942093			−0.471046	+	0.882108i	$0.656124\pi$
$720$		0			0
$721$	−513444.			−0.0367837
$722$		0			0
$723$	271316.	−	271316.i	0.0193032	−	0.0193032i
$724$		0			0
$725$	5.94931e6	−	1.20600e6i	0.420360	−	0.0852125i
$726$		0			0
$727$	−1.15104e7	−	1.15104e7i	−0.807707	−	0.807707i	0.176579	−	0.984286i	$-0.443497\pi$
$727$	−1.15104e7	−	1.15104e7i	−0.807707	−	0.807707i	−0.984286	+	0.176579i	$0.943497\pi$
$728$		0			0
$729$		−	7.22606e6i		−	0.503597i
$730$		0			0
$731$		−	9.04669e6i		−	0.626176i
$732$		0			0
$733$	1.05032e7	+	1.05032e7i	0.722038	+	0.722038i	0.969020	−	0.246982i	$-0.0794388\pi$
$733$	1.05032e7	+	1.05032e7i	0.722038	+	0.722038i	−0.246982	+	0.969020i	$0.579439\pi$
$734$		0			0
$735$	4.33527e6	−	434985.i	0.296004	−	0.0296999i
$736$		0			0
$737$	5.63524e6	−	5.63524e6i	0.382159	−	0.382159i
$738$		0			0
$739$	−9.39982e6			−0.633153			−0.316576	−	0.948567i	$-0.602533\pi$
$739$	−9.39982e6			−0.633153			−0.316576	+	0.948567i	$0.602533\pi$
$740$		0			0
$741$	806364.			0.0539493
$742$		0			0
$743$	1.05839e7	−	1.05839e7i	0.703354	−	0.703354i	−0.261775	−	0.965129i	$-0.584308\pi$
$743$	1.05839e7	−	1.05839e7i	0.703354	−	0.703354i	0.965129	+	0.261775i	$0.0843078\pi$
$744$		0			0
$745$	7.86699e6	+	6.43226e6i	0.519299	+	0.424593i
$746$		0			0
$747$	8.98724e6	+	8.98724e6i	0.589285	+	0.589285i
$748$		0			0
$749$			1.66865e6i			0.108683i
$750$		0			0
$751$		−	2.49520e6i		−	0.161438i	−0.996737	−	0.0807189i	$-0.974278\pi$
$751$		−	2.49520e6i		−	0.161438i	0.996737	−	0.0807189i	$-0.0257216\pi$
$752$		0			0
$753$	−2.84446e6	−	2.84446e6i	−0.182815	−	0.182815i
$754$		0			0
$755$	1.21952e7	+	9.97113e6i	0.778613	+	0.636615i
$756$		0			0
$757$	1.90732e7	−	1.90732e7i	1.20972	−	1.20972i	0.238597	−	0.971119i	$-0.423312\pi$
$757$	1.90732e7	−	1.90732e7i	1.20972	−	1.20972i	0.971119	−	0.238597i	$-0.0766876\pi$
$758$		0			0
$759$	−5.61805e6			−0.353982
$760$		0			0
$761$	2.61451e6			0.163655			0.0818274	−	0.996647i	$-0.473924\pi$
$761$	2.61451e6			0.163655			0.0818274	+	0.996647i	$0.473924\pi$
$762$		0			0
$763$	−577409.	+	577409.i	−0.0359064	+	0.0359064i
$764$		0			0
$765$	7.47178e6	−	749690.i	0.461605	−	0.0463157i
$766$		0			0
$767$	91854.3	+	91854.3i	0.00563782	+	0.00563782i
$768$		0			0
$769$		−	1.65153e7i		−	1.00709i	−0.863968	−	0.503547i	$-0.832028\pi$
$769$		−	1.65153e7i		−	1.00709i	0.863968	−	0.503547i	$-0.167972\pi$
$770$		0			0
$771$			6.54564e6i			0.396567i
$772$		0			0
$773$	−5.55165e6	−	5.55165e6i	−0.334174	−	0.334174i	0.519995	−	0.854169i	$-0.325934\pi$
$773$	−5.55165e6	−	5.55165e6i	−0.334174	−	0.334174i	−0.854169	+	0.519995i	$0.825934\pi$
$774$		0			0
$775$	−2.45597e7	+	4.97857e6i	−1.46882	+	0.297749i
$776$		0			0
$777$	−433155.	+	433155.i	−0.0257390	+	0.0257390i
$778$		0			0
$779$	−7.04309e6			−0.415834
$780$		0			0
$781$	−7.88763e6			−0.462721
$782$		0			0
$783$	2.97011e6	−	2.97011e6i	0.173128	−	0.173128i
$784$		0			0
$785$	−143289.	−	1.42809e6i	−0.00829925	−	0.0827145i
$786$		0			0
$787$	−7.86188e6	−	7.86188e6i	−0.452470	−	0.452470i	0.443704	−	0.896174i	$-0.353664\pi$
$787$	−7.86188e6	−	7.86188e6i	−0.452470	−	0.452470i	−0.896174	+	0.443704i	$0.853664\pi$
$788$		0			0
$789$		−	1.18982e6i		−	0.0680438i
$790$		0			0
$791$		−	701038.i		−	0.0398382i
$792$		0			0
$793$	2.46393e6	+	2.46393e6i	0.139138	+	0.139138i
$794$		0			0
$795$	1.41206e6	−	1.72702e6i	0.0792383	−	0.0969126i
$796$		0			0
$797$	−1.64771e6	+	1.64771e6i	−0.0918830	+	0.0918830i	−0.751554	−	0.659671i	$-0.770696\pi$
$797$	−1.64771e6	+	1.64771e6i	−0.0918830	+	0.0918830i	0.659671	+	0.751554i	$0.270696\pi$
$798$		0			0
$799$	−1.24163e7			−0.688056
$800$		0			0
$801$	−1.43345e7			−0.789409
$802$		0			0
$803$	1.08242e7	−	1.08242e7i	0.592388	−	0.592388i
$804$		0			0
$805$	−567478.	+	694055.i	−0.0308645	+	0.0377489i
$806$		0			0
$807$	−237977.	−	237977.i	−0.0128633	−	0.0128633i
$808$		0			0
$809$			1.20143e7i			0.645396i	0.946502	+	0.322698i	$0.104590\pi$
$809$			1.20143e7i			0.645396i	−0.946502	+	0.322698i	$0.895410\pi$
$810$		0			0
$811$		−	1.17390e7i		−	0.626727i	−0.949633	−	0.313364i	$-0.898544\pi$
$811$		−	1.17390e7i		−	0.626727i	0.949633	−	0.313364i	$-0.101456\pi$
$812$		0			0
$813$	−6.75535e6	−	6.75535e6i	−0.358444	−	0.358444i
$814$		0			0
$815$	−2.27444e6	−	2.26682e7i	−0.119944	−	1.19543i
$816$		0			0
$817$	−5.69834e6	+	5.69834e6i	−0.298671	+	0.298671i
$818$		0			0
$819$	−597451.			−0.0311238
$820$		0			0
$821$	2.76061e7			1.42938			0.714690	−	0.699441i	$-0.246568\pi$
$821$	2.76061e7			1.42938			0.714690	+	0.699441i	$0.246568\pi$
$822$		0			0
$823$	−2.25518e7	+	2.25518e7i	−1.16060	+	1.16060i	−0.176250	+	0.984345i	$0.556397\pi$
$823$	−2.25518e7	+	2.25518e7i	−1.16060	+	1.16060i	−0.984345	+	0.176250i	$0.943603\pi$
$824$		0			0
$825$	5.09901e6	−	7.69189e6i	0.260826	−	0.393458i
$826$		0			0
$827$	1.00811e7	+	1.00811e7i	0.512559	+	0.512559i	0.915310	−	0.402750i	$-0.131946\pi$
$827$	1.00811e7	+	1.00811e7i	0.512559	+	0.512559i	−0.402750	+	0.915310i	$0.631946\pi$
$828$		0			0
$829$		−	2.93364e7i		−	1.48259i	−0.671180	−	0.741294i	$-0.734212\pi$
$829$		−	2.93364e7i		−	1.48259i	0.671180	−	0.741294i	$-0.265788\pi$
$830$		0			0
$831$		−	6.31303e6i		−	0.317128i
$832$		0			0
$833$	−7.18300e6	−	7.18300e6i	−0.358669	−	0.358669i
$834$		0			0
$835$	−2.44961e6	+	245785.i	−0.121585	+	0.0121994i
$836$		0			0
$837$	−1.22611e7	+	1.22611e7i	−0.604944	+	0.604944i
$838$		0			0
$839$	1.26054e7			0.618230			0.309115	−	0.951025i	$-0.399967\pi$
$839$	1.26054e7			0.618230			0.309115	+	0.951025i	$0.399967\pi$
$840$		0			0
$841$	1.67378e7			0.816036
$842$		0			0
$843$	7.25235e6	−	7.25235e6i	0.351488	−	0.351488i
$844$		0			0
$845$	−1.16304e7	−	9.50935e6i	−0.560343	−	0.458151i
$846$		0			0
$847$	−1.43684e6	−	1.43684e6i	−0.0688176	−	0.0688176i
$848$		0			0
$849$			5.74759e6i			0.273663i
$850$		0			0
$851$			2.96837e7i			1.40506i
$852$		0			0
$853$	1.64758e7	+	1.64758e7i	0.775310	+	0.775310i	0.979029	−	0.203720i	$-0.0653031\pi$
$853$	1.64758e7	+	1.64758e7i	0.775310	+	0.775310i	−0.203720	+	0.979029i	$0.565303\pi$
$854$		0			0
$855$	−5.17855e6	−	4.23412e6i	−0.242266	−	0.198083i
$856$		0			0
$857$	1.84182e7	−	1.84182e7i	0.856635	−	0.856635i	−0.134305	−	0.990940i	$-0.542880\pi$
$857$	1.84182e7	−	1.84182e7i	0.856635	−	0.856635i	0.990940	+	0.134305i	$0.0428803\pi$
$858$		0			0
$859$	4.03573e7			1.86612			0.933060	−	0.359720i	$-0.117128\pi$
$859$	4.03573e7			1.86612			0.933060	+	0.359720i	$0.117128\pi$
$860$		0			0
$861$	−511404.			−0.0235102
$862$		0			0
$863$	1.37186e7	−	1.37186e7i	0.627020	−	0.627020i	−0.320297	−	0.947317i	$-0.603783\pi$
$863$	1.37186e7	−	1.37186e7i	0.627020	−	0.627020i	0.947317	+	0.320297i	$0.103783\pi$
$864$		0			0
$865$	1.25326e7	−	1.25747e6i	0.569510	−	0.0571424i
$866$		0			0
$867$	−3.46247e6	−	3.46247e6i	−0.156436	−	0.156436i
$868$		0			0
$869$			4.37898e7i			1.96709i
$870$		0			0
$871$			4.02470e6i			0.179758i
$872$		0			0
$873$	7.82172e6	+	7.82172e6i	0.347350	+	0.347350i
$874$		0			0
$875$	−435208.	−	1.40689e6i	−0.0192166	−	0.0621211i
$876$		0			0
$877$	−7.68375e6	+	7.68375e6i	−0.337345	+	0.337345i	−0.855367	−	0.518022i	$-0.826668\pi$
$877$	−7.68375e6	+	7.68375e6i	−0.337345	+	0.337345i	0.518022	+	0.855367i	$0.326668\pi$
$878$		0			0
$879$	5.34723e6			0.233430
$880$		0			0
$881$	−1.78611e7			−0.775298			−0.387649	−	0.921807i	$-0.626713\pi$
$881$	−1.78611e7			−0.775298			−0.387649	+	0.921807i	$0.626713\pi$
$882$		0			0
$883$	1.62792e7	−	1.62792e7i	0.702637	−	0.702637i	−0.262339	−	0.964976i	$-0.584494\pi$
$883$	1.62792e7	−	1.62792e7i	0.702637	−	0.702637i	0.964976	+	0.262339i	$0.0844937\pi$
$884$		0			0
$885$	10543.1	+	105078.i	0.000452491	+	0.00450975i
$886$		0			0
$887$	−5.07996e6	−	5.07996e6i	−0.216796	−	0.216796i	0.590351	−	0.807147i	$-0.298989\pi$
$887$	−5.07996e6	−	5.07996e6i	−0.216796	−	0.216796i	−0.807147	+	0.590351i	$0.798989\pi$
$888$		0			0
$889$		−	1.87102e6i		−	0.0794008i
$890$		0			0
$891$			2.77158e7i			1.16959i
$892$		0			0
$893$	7.82077e6	+	7.82077e6i	0.328187	+	0.328187i
$894$		0			0
$895$	−2.32757e7	+	2.84674e7i	−0.971281	+	1.18793i
$896$		0			0
$897$	2.00621e6	−	2.00621e6i	0.0832522	−	0.0832522i
$898$		0			0
$899$	1.55768e7			0.642805
$900$		0			0
$901$	−5.20106e6			−0.213442
$902$		0			0
$903$	−413761.	+	413761.i	−0.0168861	+	0.0168861i
$904$		0			0
$905$	−2.34363e7	+	2.86639e7i	−0.951192	+	1.16336i
$906$		0			0
$907$	−1.23719e7	−	1.23719e7i	−0.499367	−	0.499367i	0.411874	−	0.911241i	$-0.364874\pi$
$907$	−1.23719e7	−	1.23719e7i	−0.499367	−	0.499367i	−0.911241	+	0.411874i	$0.864874\pi$
$908$		0			0
$909$		−	2.30418e7i		−	0.924925i
$910$		0			0
$911$			1.71338e7i			0.684003i	0.939699	+	0.342002i	$0.111105\pi$
$911$			1.71338e7i			0.684003i	−0.939699	+	0.342002i	$0.888895\pi$
$912$		0			0
$913$	−2.57506e7	−	2.57506e7i	−1.02237	−	1.02237i
$914$		0			0
$915$	282812.	+	2.81865e6i	0.0111672	+	0.111298i
$916$		0			0
$917$	−1.95926e6	+	1.95926e6i	−0.0769428	+	0.0769428i
$918$		0			0
$919$	1.74717e6			0.0682411			0.0341206	−	0.999418i	$-0.489137\pi$
$919$	1.74717e6			0.0682411			0.0341206	+	0.999418i	$0.489137\pi$
$920$		0			0
$921$	−9.88636e6			−0.384050
$922$		0			0
$923$	2.81668e6	−	2.81668e6i	0.108826	−	0.108826i
$924$		0			0
$925$	−4.06411e7	−	2.69413e7i	−1.56175	−	1.03529i
$926$		0			0
$927$	−9.53132e6	−	9.53132e6i	−0.364296	−	0.364296i
$928$		0			0
$929$			3.80243e7i			1.44551i	0.691102	+	0.722757i	$0.257125\pi$
$929$			3.80243e7i			1.44551i	−0.691102	+	0.722757i	$0.742875\pi$
$930$		0			0
$931$			9.04887e6i			0.342153i
$932$		0			0
$933$	−9.87226e6	−	9.87226e6i	−0.371289	−	0.371289i
$934$		0			0
$935$	−2.14084e7	+	2.14804e6i	−0.800858	+	0.0803550i
$936$		0			0
$937$	−1.05384e7	+	1.05384e7i	−0.392127	+	0.392127i	−0.875445	−	0.483318i	$-0.839432\pi$
$937$	−1.05384e7	+	1.05384e7i	−0.392127	+	0.392127i	0.483318	+	0.875445i	$0.339432\pi$
$938$		0			0
$939$	−1.22588e6			−0.0453717
$940$		0			0
$941$	−4.44456e7			−1.63627			−0.818135	−	0.575026i	$-0.804992\pi$
$941$	−4.44456e7			−1.63627			−0.818135	+	0.575026i	$0.804992\pi$
$942$		0			0
$943$	−1.75230e7	+	1.75230e7i	−0.641697	+	0.641697i
$944$		0			0
$945$	−788887.	−	645015.i	−0.0287366	−	0.0234958i
$946$		0			0
$947$	1.69931e7	+	1.69931e7i	0.615740	+	0.615740i	0.944436	−	0.328696i	$-0.106609\pi$
$947$	1.69931e7	+	1.69931e7i	0.615740	+	0.615740i	−0.328696	+	0.944436i	$0.606609\pi$
$948$		0			0
$949$			7.73065e6i			0.278644i
$950$		0			0
$951$		−	1.77533e6i		−	0.0636544i
$952$		0			0
$953$	2.89702e7	+	2.89702e7i	1.03328	+	1.03328i	0.999427	+	0.0338563i	$0.0107788\pi$
$953$	2.89702e7	+	2.89702e7i	1.03328	+	1.03328i	0.0338563	+	0.999427i	$0.489221\pi$
$954$		0			0
$955$	1.79438e7	+	1.46713e7i	0.636656	+	0.520547i
$956$		0			0
$957$	−4.05627e6	+	4.05627e6i	−0.143168	+	0.143168i
$958$		0			0
$959$	−821914.			−0.0288589
$960$		0			0
$961$	−3.56744e7			−1.24609
$962$		0			0
$963$	−3.09760e7	+	3.09760e7i	−1.07636	+	1.07636i
$964$		0			0
$965$	5.41592e7	−	5.43413e6i	1.87221	−	0.187850i
$966$		0			0
$967$	1.69845e7	+	1.69845e7i	0.584101	+	0.584101i	0.936028	−	0.351927i	$-0.114473\pi$
$967$	1.69845e7	+	1.69845e7i	0.584101	+	0.584101i	−0.351927	+	0.936028i	$0.614473\pi$
$968$		0			0
$969$		−	1.52838e6i		−	0.0522905i
$970$		0			0
$971$			4.58022e7i			1.55897i	0.626419	+	0.779486i	$0.284520\pi$
$971$			4.58022e7i			1.55897i	−0.626419	+	0.779486i	$0.715480\pi$
$972$		0			0
$973$	2.13370e6	+	2.13370e6i	0.0722521	+	0.0722521i
$974$		0			0
$975$	925920.	+	4.56764e6i	0.0311934	+	0.153879i
$976$		0			0
$977$	−1.14731e7	+	1.14731e7i	−0.384544	+	0.384544i	−0.872736	−	0.488192i	$-0.837657\pi$
$977$	−1.14731e7	+	1.14731e7i	−0.384544	+	0.384544i	0.488192	+	0.872736i	$0.337657\pi$
$978$		0			0
$979$	4.10718e7			1.36958
$980$		0			0
$981$	−2.14375e7			−0.711215
$982$		0			0
$983$	2.41644e7	−	2.41644e7i	0.797613	−	0.797613i	−0.185106	−	0.982719i	$-0.559263\pi$
$983$	2.41644e7	−	2.41644e7i	0.797613	−	0.797613i	0.982719	+	0.185106i	$0.0592628\pi$
$984$		0			0
$985$	−5.39547e6	−	5.37739e7i	−0.177190	−	1.76596i
$986$		0			0
$987$	567872.	+	567872.i	0.0185549	+	0.0185549i
$988$		0			0
$989$			2.83546e7i			0.921792i
$990$		0			0
$991$			1.55838e7i			0.504067i	0.967719	+	0.252033i	$0.0810993\pi$
$991$			1.55838e7i			0.504067i	−0.967719	+	0.252033i	$0.918901\pi$
$992$		0			0
$993$	2.16164e6	+	2.16164e6i	0.0695680	+	0.0695680i
$994$		0			0
$995$	2.86239e7	−	3.50085e7i	0.916581	−	1.12103i
$996$		0			0
$997$	6.51999e6	−	6.51999e6i	0.207735	−	0.207735i	−0.595569	−	0.803304i	$-0.703073\pi$
$997$	6.51999e6	−	6.51999e6i	0.207735	−	0.207735i	0.803304	+	0.595569i	$0.203073\pi$
$998$		0			0
$999$	−3.37395e7			−1.06961

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.6.n.c.63.4	✓	16
4.3	odd	2		160.6.n.d.63.5	yes	16
5.2	odd	4		160.6.n.d.127.5	yes	16
20.7	even	4	inner	160.6.n.c.127.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.6.n.c.63.4	✓	16	1.1	even	1	trivial
160.6.n.c.127.4	yes	16	20.7	even	4	inner
160.6.n.d.63.5	yes	16	4.3	odd	2
160.6.n.d.127.5	yes	16	5.2	odd	4

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:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	160.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.29308 + 3.29308i) q^{3} +(35.3847 - 43.2773i) q^{5} +(5.96093 + 5.96093i) q^{7} +221.311i q^{9} +O(q^{10})\)	\(q+(-3.29308 + 3.29308i) q^{3} +(35.3847 - 43.2773i) q^{5} +(5.96093 + 5.96093i) q^{7} +221.311i q^{9} -634.109i q^{11} +(226.441 + 226.441i) q^{13} +(25.9911 + 259.040i) q^{15} +(429.196 - 429.196i) q^{17} -540.685 q^{19} -39.2596 q^{21} +(-1345.21 + 1345.21i) q^{23} +(-620.850 - 3062.71i) q^{25} +(-1529.01 - 1529.01i) q^{27} +1942.50i q^{29} -8018.95i q^{31} +(2088.17 + 2088.17i) q^{33} +(468.898 - 47.0474i) q^{35} +(11033.1 - 11033.1i) q^{37} -1491.37 q^{39} +13026.2 q^{41} +(10539.1 - 10539.1i) q^{43} +(9577.76 + 7831.03i) q^{45} +(-14464.6 - 14464.6i) q^{47} -16735.9i q^{49} +2826.75i q^{51} +(-6059.07 - 6059.07i) q^{53} +(-27442.5 - 22437.7i) q^{55} +(1780.52 - 1780.52i) q^{57} +405.643 q^{59} +10881.1 q^{61} +(-1319.22 + 1319.22i) q^{63} +(17812.3 - 1787.22i) q^{65} +(8886.87 + 8886.87i) q^{67} -8859.76i q^{69} -12438.9i q^{71} +(17069.9 + 17069.9i) q^{73} +(12130.2 + 8041.22i) q^{75} +(3779.87 - 3779.87i) q^{77} -69057.3 q^{79} -43708.3 q^{81} +(40609.1 - 40609.1i) q^{83} +(-3387.49 - 33761.4i) q^{85} +(-6396.80 - 6396.80i) q^{87} +64770.8i q^{89} +2699.59i q^{91} +(26407.0 + 26407.0i) q^{93} +(-19132.0 + 23399.4i) q^{95} +(35342.6 - 35342.6i) q^{97} +140335. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 10 q^{3} - 42 q^{5} + 86 q^{7}+O(q^{10}) \) 16 * q - 10 * q^3 - 42 * q^5 + 86 * q^7	\( 16 q - 10 q^{3} - 42 q^{5} + 86 q^{7} + 536 q^{13} + 698 q^{15} - 1828 q^{17} - 2512 q^{19} - 4284 q^{21} + 7642 q^{23} + 9140 q^{25} + 12272 q^{27} + 11876 q^{33} - 10518 q^{35} - 7620 q^{37} - 11244 q^{39} - 21284 q^{41} - 20002 q^{43} + 686 q^{45} - 25298 q^{47} + 12852 q^{53} + 10584 q^{55} + 55848 q^{57} + 142704 q^{59} - 20564 q^{61} + 115282 q^{63} - 38256 q^{65} + 10506 q^{67} + 15432 q^{73} - 256226 q^{75} + 133852 q^{77} + 159344 q^{79} - 236116 q^{81} + 61222 q^{83} + 7056 q^{85} - 162176 q^{87} + 122180 q^{93} - 267512 q^{95} - 17344 q^{97} - 107332 q^{99}+O(q^{100}) \) 16 * q - 10 * q^3 - 42 * q^5 + 86 * q^7 + 536 * q^13 + 698 * q^15 - 1828 * q^17 - 2512 * q^19 - 4284 * q^21 + 7642 * q^23 + 9140 * q^25 + 12272 * q^27 + 11876 * q^33 - 10518 * q^35 - 7620 * q^37 - 11244 * q^39 - 21284 * q^41 - 20002 * q^43 + 686 * q^45 - 25298 * q^47 + 12852 * q^53 + 10584 * q^55 + 55848 * q^57 + 142704 * q^59 - 20564 * q^61 + 115282 * q^63 - 38256 * q^65 + 10506 * q^67 + 15432 * q^73 - 256226 * q^75 + 133852 * q^77 + 159344 * q^79 - 236116 * q^81 + 61222 * q^83 + 7056 * q^85 - 162176 * q^87 + 122180 * q^93 - 267512 * q^95 - 17344 * q^97 - 107332 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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