LMFDB - Embedded newform 400.2.j.b.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(43,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 3]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("400.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.j (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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.1
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	400.43
Dual form			400.2.j.b.307.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} -0.517638i q^{3} +2.00000 q^{4} +0.732051i q^{6} +(3.34607 - 3.34607i) q^{7} -2.82843 q^{8} +2.73205 q^{9} +O(q^{10})$	\(q-1.41421 q^{2} -0.517638i q^{3} +2.00000 q^{4} +0.732051i q^{6} +(3.34607 - 3.34607i) q^{7} -2.82843 q^{8} +2.73205 q^{9} +(-1.09808 + 1.09808i) q^{11} -1.03528i q^{12} -4.89898 q^{13} +(-4.73205 + 4.73205i) q^{14} +4.00000 q^{16} +(0.707107 - 0.707107i) q^{17} -3.86370 q^{18} +(2.09808 - 2.09808i) q^{19} +(-1.73205 - 1.73205i) q^{21} +(1.55291 - 1.55291i) q^{22} +(4.38134 + 4.38134i) q^{23} +1.46410i q^{24} +6.92820 q^{26} -2.96713i q^{27} +(6.69213 - 6.69213i) q^{28} +(-4.73205 - 4.73205i) q^{29} -6.19615i q^{31} -5.65685 q^{32} +(0.568406 + 0.568406i) q^{33} +(-1.00000 + 1.00000i) q^{34} +5.46410 q^{36} +6.03579 q^{37} +(-2.96713 + 2.96713i) q^{38} +2.53590i q^{39} -0.464102i q^{41} +(2.44949 + 2.44949i) q^{42} +0.656339 q^{43} +(-2.19615 + 2.19615i) q^{44} +(-6.19615 - 6.19615i) q^{46} +(1.41421 + 1.41421i) q^{47} -2.07055i q^{48} -15.3923i q^{49} +(-0.366025 - 0.366025i) q^{51} -9.79796 q^{52} -9.89949i q^{53} +4.19615i q^{54} +(-9.46410 + 9.46410i) q^{56} +(-1.08604 - 1.08604i) q^{57} +(6.69213 + 6.69213i) q^{58} +(7.73205 + 7.73205i) q^{59} +(-3.19615 + 3.19615i) q^{61} +8.76268i q^{62} +(9.14162 - 9.14162i) q^{63} +8.00000 q^{64} +(-0.803848 - 0.803848i) q^{66} +5.79555 q^{67} +(1.41421 - 1.41421i) q^{68} +(2.26795 - 2.26795i) q^{69} +0.928203 q^{71} -7.72741 q^{72} +(-8.81345 + 8.81345i) q^{73} -8.53590 q^{74} +(4.19615 - 4.19615i) q^{76} +7.34847i q^{77} -3.58630i q^{78} -2.19615 q^{79} +6.66025 q^{81} +0.656339i q^{82} +17.3867i q^{83} +(-3.46410 - 3.46410i) q^{84} -0.928203 q^{86} +(-2.44949 + 2.44949i) q^{87} +(3.10583 - 3.10583i) q^{88} -10.2679 q^{89} +(-16.3923 + 16.3923i) q^{91} +(8.76268 + 8.76268i) q^{92} -3.20736 q^{93} +(-2.00000 - 2.00000i) q^{94} +2.92820i q^{96} +(-11.5911 + 11.5911i) q^{97} +21.7680i q^{98} +(-3.00000 + 3.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{4} + 8 q^{9}+O(q^{10}) $ 8 * q + 16 * q^4 + 8 * q^9	$ 8 q + 16 q^{4} + 8 q^{9} + 12 q^{11} - 24 q^{14} + 32 q^{16} - 4 q^{19} - 24 q^{29} - 8 q^{34} + 16 q^{36} + 24 q^{44} - 8 q^{46} + 4 q^{51} - 48 q^{56} + 48 q^{59} + 16 q^{61} + 64 q^{64} - 48 q^{66} + 32 q^{69} - 48 q^{71} - 96 q^{74} - 8 q^{76} + 24 q^{79} - 16 q^{81} + 48 q^{86} - 96 q^{89} - 48 q^{91} - 16 q^{94} - 24 q^{99}+O(q^{100}) $ 8 * q + 16 * q^4 + 8 * q^9 + 12 * q^11 - 24 * q^14 + 32 * q^16 - 4 * q^19 - 24 * q^29 - 8 * q^34 + 16 * q^36 + 24 * q^44 - 8 * q^46 + 4 * q^51 - 48 * q^56 + 48 * q^59 + 16 * q^61 + 64 * q^64 - 48 * q^66 + 32 * q^69 - 48 * q^71 - 96 * q^74 - 8 * q^76 + 24 * q^79 - 16 * q^81 + 48 * q^86 - 96 * q^89 - 48 * q^91 - 16 * q^94 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−1.41421			−1.00000
$2$	−1.41421			−1.00000
$3$		−	0.517638i		−	0.298858i	−0.988772	−	0.149429i	$-0.952256\pi$
$3$		−	0.517638i		−	0.298858i	0.988772	−	0.149429i	$-0.0477436\pi$
$4$	2.00000			1.00000
$5$		0			0
$5$		0			0
$6$			0.732051i			0.298858i
$7$	3.34607	−	3.34607i	1.26469	−	1.26469i	0.315902	−	0.948792i	$-0.397693\pi$
$7$	3.34607	−	3.34607i	1.26469	−	1.26469i	0.948792	−	0.315902i	$-0.102307\pi$
$8$	−2.82843			−1.00000
$9$	2.73205			0.910684
$10$		0			0
$11$	−1.09808	+	1.09808i	−0.331082	+	0.331082i	−0.852997	−	0.521915i	$-0.825218\pi$
$11$	−1.09808	+	1.09808i	−0.331082	+	0.331082i	0.521915	+	0.852997i	$0.325218\pi$
$12$		−	1.03528i		−	0.298858i
$13$	−4.89898			−1.35873			−0.679366	−	0.733799i	$-0.737745\pi$
$13$	−4.89898			−1.35873			−0.679366	+	0.733799i	$0.737745\pi$
$14$	−4.73205	+	4.73205i	−1.26469	+	1.26469i
$15$		0			0
$16$	4.00000			1.00000
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i	−0.616139	−	0.787638i	$-0.711304\pi$
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i	0.787638	+	0.616139i	$0.211304\pi$
$18$	−3.86370			−0.910684
$19$	2.09808	−	2.09808i	0.481332	−	0.481332i	−0.424225	−	0.905557i	$-0.639453\pi$
$19$	2.09808	−	2.09808i	0.481332	−	0.481332i	0.905557	+	0.424225i	$0.139453\pi$
$20$		0			0
$21$	−1.73205	−	1.73205i	−0.377964	−	0.377964i
$22$	1.55291	−	1.55291i	0.331082	−	0.331082i
$23$	4.38134	+	4.38134i	0.913573	+	0.913573i	0.996551	−	0.0829785i	$-0.0264433\pi$
$23$	4.38134	+	4.38134i	0.913573	+	0.913573i	−0.0829785	+	0.996551i	$0.526443\pi$
$24$			1.46410i			0.298858i
$25$		0			0
$26$	6.92820			1.35873
$27$		−	2.96713i		−	0.571024i
$28$	6.69213	−	6.69213i	1.26469	−	1.26469i
$29$	−4.73205	−	4.73205i	−0.878720	−	0.878720i	0.114682	−	0.993402i	$-0.463415\pi$
$29$	−4.73205	−	4.73205i	−0.878720	−	0.878720i	−0.993402	+	0.114682i	$0.963415\pi$
$30$		0			0
$31$		−	6.19615i		−	1.11286i	−0.830894	−	0.556431i	$-0.812170\pi$
$31$		−	6.19615i		−	1.11286i	0.830894	−	0.556431i	$-0.187830\pi$
$32$	−5.65685			−1.00000
$33$	0.568406	+	0.568406i	0.0989468	+	0.0989468i
$34$	−1.00000	+	1.00000i	−0.171499	+	0.171499i
$35$		0			0
$36$	5.46410			0.910684
$37$	6.03579			0.992278			0.496139	−	0.868243i	$-0.334751\pi$
$37$	6.03579			0.992278			0.496139	+	0.868243i	$0.334751\pi$
$38$	−2.96713	+	2.96713i	−0.481332	+	0.481332i
$39$			2.53590i			0.406069i
$40$		0			0
$41$		−	0.464102i		−	0.0724805i	−0.999343	−	0.0362402i	$-0.988462\pi$
$41$		−	0.464102i		−	0.0724805i	0.999343	−	0.0362402i	$-0.0115382\pi$
$42$	2.44949	+	2.44949i	0.377964	+	0.377964i
$43$	0.656339			0.100091			0.0500454	−	0.998747i	$-0.484063\pi$
$43$	0.656339			0.100091			0.0500454	+	0.998747i	$0.484063\pi$
$44$	−2.19615	+	2.19615i	−0.331082	+	0.331082i
$45$		0			0
$46$	−6.19615	−	6.19615i	−0.913573	−	0.913573i
$47$	1.41421	+	1.41421i	0.206284	+	0.206284i	0.802686	−	0.596402i	$-0.203403\pi$
$47$	1.41421	+	1.41421i	0.206284	+	0.206284i	−0.596402	+	0.802686i	$0.703403\pi$
$48$		−	2.07055i		−	0.298858i
$49$		−	15.3923i		−	2.19890i
$50$		0			0
$51$	−0.366025	−	0.366025i	−0.0512538	−	0.0512538i
$52$	−9.79796			−1.35873
$53$		−	9.89949i		−	1.35980i	−0.733305	−	0.679900i	$-0.762023\pi$
$53$		−	9.89949i		−	1.35980i	0.733305	−	0.679900i	$-0.237977\pi$
$54$			4.19615i			0.571024i
$55$		0			0
$56$	−9.46410	+	9.46410i	−1.26469	+	1.26469i
$57$	−1.08604	−	1.08604i	−0.143850	−	0.143850i
$58$	6.69213	+	6.69213i	0.878720	+	0.878720i
$59$	7.73205	+	7.73205i	1.00663	+	1.00663i	0.999978	+	0.00664938i	$0.00211658\pi$
$59$	7.73205	+	7.73205i	1.00663	+	1.00663i	0.00664938	+	0.999978i	$0.497883\pi$
$60$		0			0
$61$	−3.19615	+	3.19615i	−0.409225	+	0.409225i	−0.881468	−	0.472243i	$-0.843444\pi$
$61$	−3.19615	+	3.19615i	−0.409225	+	0.409225i	0.472243	+	0.881468i	$0.343444\pi$
$62$			8.76268i			1.11286i
$63$	9.14162	−	9.14162i	1.15174	−	1.15174i
$64$	8.00000			1.00000
$65$		0			0
$66$	−0.803848	−	0.803848i	−0.0989468	−	0.0989468i
$67$	5.79555			0.708040			0.354020	−	0.935238i	$-0.384815\pi$
$67$	5.79555			0.708040			0.354020	+	0.935238i	$0.384815\pi$
$68$	1.41421	−	1.41421i	0.171499	−	0.171499i
$69$	2.26795	−	2.26795i	0.273029	−	0.273029i
$70$		0			0
$71$	0.928203			0.110157			0.0550787	−	0.998482i	$-0.482459\pi$
$71$	0.928203			0.110157			0.0550787	+	0.998482i	$0.482459\pi$
$72$	−7.72741			−0.910684
$73$	−8.81345	+	8.81345i	−1.03154	+	1.03154i	−0.0320501	+	0.999486i	$0.510204\pi$
$73$	−8.81345	+	8.81345i	−1.03154	+	1.03154i	−0.999486	+	0.0320501i	$0.989796\pi$
$74$	−8.53590			−0.992278
$75$		0			0
$76$	4.19615	−	4.19615i	0.481332	−	0.481332i
$77$			7.34847i			0.837436i
$78$		−	3.58630i		−	0.406069i
$79$	−2.19615			−0.247086			−0.123543	−	0.992339i	$-0.539426\pi$
$79$	−2.19615			−0.247086			−0.123543	+	0.992339i	$0.539426\pi$
$80$		0			0
$81$	6.66025			0.740028
$82$			0.656339i			0.0724805i
$83$			17.3867i			1.90843i	0.299115	+	0.954217i	$0.403309\pi$
$83$			17.3867i			1.90843i	−0.299115	+	0.954217i	$0.596691\pi$
$84$	−3.46410	−	3.46410i	−0.377964	−	0.377964i
$85$		0			0
$86$	−0.928203			−0.100091
$87$	−2.44949	+	2.44949i	−0.262613	+	0.262613i
$88$	3.10583	−	3.10583i	0.331082	−	0.331082i
$89$	−10.2679			−1.08840			−0.544200	−	0.838955i	$-0.683167\pi$
$89$	−10.2679			−1.08840			−0.544200	+	0.838955i	$0.683167\pi$
$90$		0			0
$91$	−16.3923	+	16.3923i	−1.71838	+	1.71838i
$92$	8.76268	+	8.76268i	0.913573	+	0.913573i
$93$	−3.20736			−0.332588
$94$	−2.00000	−	2.00000i	−0.206284	−	0.206284i
$95$		0			0
$96$			2.92820i			0.298858i
$97$	−11.5911	+	11.5911i	−1.17690	+	1.17690i	−0.196369	+	0.980530i	$0.562915\pi$
$97$	−11.5911	+	11.5911i	−1.17690	+	1.17690i	−0.980530	+	0.196369i	$0.937085\pi$
$98$			21.7680i			2.19890i
$99$	−3.00000	+	3.00000i	−0.301511	+	0.301511i
$100$		0			0
$101$	−9.92820	−	9.92820i	−0.987893	−	0.987893i	0.0120344	−	0.999928i	$-0.496169\pi$
$101$	−9.92820	−	9.92820i	−0.987893	−	0.987893i	−0.999928	+	0.0120344i	$0.996169\pi$
$102$	0.517638	+	0.517638i	0.0512538	+	0.0512538i
$103$	2.44949	+	2.44949i	0.241355	+	0.241355i	0.817411	−	0.576055i	$-0.195409\pi$
$103$	2.44949	+	2.44949i	0.241355	+	0.241355i	−0.576055	+	0.817411i	$0.695409\pi$
$104$	13.8564			1.35873
$105$		0			0
$106$			14.0000i			1.35980i
$107$		−	5.79555i		−	0.560277i	−0.959960	−	0.280139i	$-0.909620\pi$
$107$		−	5.79555i		−	0.560277i	0.959960	−	0.280139i	$-0.0903805\pi$
$108$		−	5.93426i		−	0.571024i
$109$	9.39230	+	9.39230i	0.899620	+	0.899620i	0.995402	−	0.0957826i	$-0.0305354\pi$
$109$	9.39230	+	9.39230i	0.899620	+	0.899620i	−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$		−	3.12436i		−	0.296551i
$112$	13.3843	−	13.3843i	1.26469	−	1.26469i
$113$	1.98262	+	1.98262i	0.186509	+	0.186509i	0.794185	−	0.607676i	$-0.207898\pi$
$113$	1.98262	+	1.98262i	0.186509	+	0.186509i	−0.607676	+	0.794185i	$0.707898\pi$
$114$	1.53590	+	1.53590i	0.143850	+	0.143850i
$115$		0			0
$116$	−9.46410	−	9.46410i	−0.878720	−	0.878720i
$117$	−13.3843			−1.23738
$118$	−10.9348	−	10.9348i	−1.00663	−	1.00663i
$119$		−	4.73205i		−	0.433786i
$120$		0			0
$121$			8.58846i			0.780769i
$122$	4.52004	−	4.52004i	0.409225	−	0.409225i
$123$	−0.240237			−0.0216614
$124$		−	12.3923i		−	1.11286i
$125$		0			0
$126$	−12.9282	+	12.9282i	−1.15174	+	1.15174i
$127$	−5.79555	−	5.79555i	−0.514272	−	0.514272i	0.401560	−	0.915833i	$-0.368468\pi$
$127$	−5.79555	−	5.79555i	−0.514272	−	0.514272i	−0.915833	+	0.401560i	$0.868468\pi$
$128$	−11.3137			−1.00000
$129$		−	0.339746i		−	0.0299130i
$130$		0			0
$131$	3.92820	+	3.92820i	0.343209	+	0.343209i	0.857572	−	0.514364i	$-0.171972\pi$
$131$	3.92820	+	3.92820i	0.343209	+	0.343209i	−0.514364	+	0.857572i	$0.671972\pi$
$132$	1.13681	+	1.13681i	0.0989468	+	0.0989468i
$133$		−	14.0406i		−	1.21747i
$134$	−8.19615			−0.708040
$135$		0			0
$136$	−2.00000	+	2.00000i	−0.171499	+	0.171499i
$137$	9.33109	+	9.33109i	0.797209	+	0.797209i	0.982654	−	0.185446i	$-0.0593729\pi$
$137$	9.33109	+	9.33109i	0.797209	+	0.797209i	−0.185446	+	0.982654i	$0.559373\pi$
$138$	−3.20736	+	3.20736i	−0.273029	+	0.273029i
$139$	7.29423	+	7.29423i	0.618688	+	0.618688i	0.945195	−	0.326507i	$-0.105872\pi$
$139$	7.29423	+	7.29423i	0.618688	+	0.618688i	−0.326507	+	0.945195i	$0.605872\pi$
$140$		0			0
$141$	0.732051	−	0.732051i	0.0616498	−	0.0616498i
$142$	−1.31268			−0.110157
$143$	5.37945	−	5.37945i	0.449852	−	0.449852i
$144$	10.9282			0.910684
$145$		0			0
$146$	12.4641	−	12.4641i	1.03154	−	1.03154i
$147$	−7.96764			−0.657160
$148$	12.0716			0.992278
$149$	−15.1244	+	15.1244i	−1.23904	+	1.23904i	−0.278640	+	0.960396i	$0.589884\pi$
$149$	−15.1244	+	15.1244i	−1.23904	+	1.23904i	−0.960396	+	0.278640i	$0.910116\pi$
$150$		0			0
$151$	10.1962			0.829751			0.414876	−	0.909878i	$-0.363825\pi$
$151$	10.1962			0.829751			0.414876	+	0.909878i	$0.363825\pi$
$152$	−5.93426	+	5.93426i	−0.481332	+	0.481332i
$153$	1.93185	−	1.93185i	0.156181	−	0.156181i
$154$		−	10.3923i		−	0.837436i
$155$		0			0
$156$			5.07180i			0.406069i
$157$		−	9.14162i		−	0.729581i	−0.931090	−	0.364790i	$-0.881141\pi$
$157$		−	9.14162i		−	0.729581i	0.931090	−	0.364790i	$-0.118859\pi$
$158$	3.10583			0.247086
$159$	−5.12436			−0.406388
$160$		0			0
$161$	29.3205			2.31078
$162$	−9.41902			−0.740028
$163$		−	8.90138i		−	0.697210i	−0.937270	−	0.348605i	$-0.886655\pi$
$163$		−	8.90138i		−	0.697210i	0.937270	−	0.348605i	$-0.113345\pi$
$164$		−	0.928203i		−	0.0724805i
$165$		0			0
$166$		−	24.5885i		−	1.90843i
$167$	0.277401	−	0.277401i	0.0214660	−	0.0214660i	−0.696292	−	0.717758i	$-0.745168\pi$
$167$	0.277401	−	0.277401i	0.0214660	−	0.0214660i	0.717758	+	0.696292i	$0.245168\pi$
$168$	4.89898	+	4.89898i	0.377964	+	0.377964i
$169$	11.0000			0.846154
$170$		0			0
$171$	5.73205	−	5.73205i	0.438341	−	0.438341i
$172$	1.31268			0.100091
$173$	−5.93426			−0.451173			−0.225587	−	0.974223i	$-0.572430\pi$
$173$	−5.93426			−0.451173			−0.225587	+	0.974223i	$0.572430\pi$
$174$	3.46410	−	3.46410i	0.262613	−	0.262613i
$175$		0			0
$176$	−4.39230	+	4.39230i	−0.331082	+	0.331082i
$177$	4.00240	−	4.00240i	0.300839	−	0.300839i
$178$	14.5211			1.08840
$179$	−7.56218	+	7.56218i	−0.565224	+	0.565224i	−0.930787	−	0.365563i	$-0.880877\pi$
$179$	−7.56218	+	7.56218i	−0.565224	+	0.565224i	0.365563	+	0.930787i	$0.380877\pi$
$180$		0			0
$181$	2.80385	+	2.80385i	0.208408	+	0.208408i	0.803591	−	0.595182i	$-0.202920\pi$
$181$	2.80385	+	2.80385i	0.208408	+	0.208408i	−0.595182	+	0.803591i	$0.702920\pi$
$182$	23.1822	−	23.1822i	1.71838	−	1.71838i
$183$	1.65445	+	1.65445i	0.122300	+	0.122300i
$184$	−12.3923	−	12.3923i	−0.913573	−	0.913573i
$185$		0			0
$186$	4.53590			0.332588
$187$			1.55291i			0.113560i
$188$	2.82843	+	2.82843i	0.206284	+	0.206284i
$189$	−9.92820	−	9.92820i	−0.722171	−	0.722171i
$190$		0			0
$191$		−	17.6603i		−	1.27785i	−0.769269	−	0.638926i	$-0.779379\pi$
$191$		−	17.6603i		−	1.27785i	0.769269	−	0.638926i	$-0.220621\pi$
$192$		−	4.14110i		−	0.298858i
$193$	9.46979	+	9.46979i	0.681650	+	0.681650i	0.960372	−	0.278722i	$-0.0899107\pi$
$193$	9.46979	+	9.46979i	0.681650	+	0.681650i	−0.278722	+	0.960372i	$0.589911\pi$
$194$	16.3923	−	16.3923i	1.17690	−	1.17690i
$195$		0			0
$196$		−	30.7846i		−	2.19890i
$197$	10.4543			0.744838			0.372419	−	0.928065i	$-0.378528\pi$
$197$	10.4543			0.744838			0.372419	+	0.928065i	$0.378528\pi$
$198$	4.24264	−	4.24264i	0.301511	−	0.301511i
$199$			16.3923i			1.16202i	0.813897	+	0.581010i	$0.197342\pi$
$199$			16.3923i			1.16202i	−0.813897	+	0.581010i	$0.802658\pi$
$200$		0			0
$201$		−	3.00000i		−	0.211604i
$202$	14.0406	+	14.0406i	0.987893	+	0.987893i
$203$	−31.6675			−2.22262
$204$	−0.732051	−	0.732051i	−0.0512538	−	0.0512538i
$205$		0			0
$206$	−3.46410	−	3.46410i	−0.241355	−	0.241355i
$207$	11.9700	+	11.9700i	0.831976	+	0.831976i
$208$	−19.5959			−1.35873
$209$			4.60770i			0.318721i
$210$		0			0
$211$	11.2942	+	11.2942i	0.777527	+	0.777527i	0.979410	−	0.201883i	$-0.0647060\pi$
$211$	11.2942	+	11.2942i	0.777527	+	0.777527i	−0.201883	+	0.979410i	$0.564706\pi$
$212$		−	19.7990i		−	1.35980i
$213$		−	0.480473i		−	0.0329215i
$214$			8.19615i			0.560277i
$215$		0			0
$216$			8.39230i			0.571024i
$217$	−20.7327	−	20.7327i	−1.40743	−	1.40743i
$218$	−13.2827	−	13.2827i	−0.899620	−	0.899620i
$219$	4.56218	+	4.56218i	0.308283	+	0.308283i
$220$		0			0
$221$	−3.46410	+	3.46410i	−0.233021	+	0.233021i
$222$			4.41851i			0.296551i
$223$	2.44949	−	2.44949i	0.164030	−	0.164030i	−0.620319	−	0.784349i	$-0.712997\pi$
$223$	2.44949	−	2.44949i	0.164030	−	0.164030i	0.784349	+	0.620319i	$0.212997\pi$
$224$	−18.9282	+	18.9282i	−1.26469	+	1.26469i
$225$		0			0
$226$	−2.80385	−	2.80385i	−0.186509	−	0.186509i
$227$	−18.9396			−1.25706			−0.628532	−	0.777784i	$-0.716344\pi$
$227$	−18.9396			−1.25706			−0.628532	+	0.777784i	$0.716344\pi$
$228$	−2.17209	−	2.17209i	−0.143850	−	0.143850i
$229$	−4.00000	+	4.00000i	−0.264327	+	0.264327i	−0.826809	−	0.562482i	$-0.809847\pi$
$229$	−4.00000	+	4.00000i	−0.264327	+	0.264327i	0.562482	+	0.826809i	$0.309847\pi$
$230$		0			0
$231$	3.80385			0.250275
$232$	13.3843	+	13.3843i	0.878720	+	0.878720i
$233$	5.65685	−	5.65685i	0.370593	−	0.370593i	−0.497100	−	0.867693i	$-0.665602\pi$
$233$	5.65685	−	5.65685i	0.370593	−	0.370593i	0.867693	+	0.497100i	$0.165602\pi$
$234$	18.9282			1.23738
$235$		0			0
$236$	15.4641	+	15.4641i	1.00663	+	1.00663i
$237$			1.13681i			0.0738439i
$238$			6.69213i			0.433786i
$239$	−21.4641			−1.38840			−0.694199	−	0.719783i	$-0.744241\pi$
$239$	−21.4641			−1.38840			−0.694199	+	0.719783i	$0.744241\pi$
$240$		0			0
$241$	−12.8038			−0.824768			−0.412384	−	0.911010i	$-0.635304\pi$
$241$	−12.8038			−0.824768			−0.412384	+	0.911010i	$0.635304\pi$
$242$		−	12.1459i		−	0.780769i
$243$		−	12.3490i		−	0.792188i
$244$	−6.39230	+	6.39230i	−0.409225	+	0.409225i
$245$		0			0
$246$	0.339746			0.0216614
$247$	−10.2784	+	10.2784i	−0.654001	+	0.654001i
$248$			17.5254i			1.11286i
$249$	9.00000			0.570352
$250$		0			0
$251$	8.83013	−	8.83013i	0.557353	−	0.557353i	−0.371200	−	0.928553i	$-0.621054\pi$
$251$	8.83013	−	8.83013i	0.557353	−	0.557353i	0.928553	+	0.371200i	$0.121054\pi$
$252$	18.2832	−	18.2832i	1.15174	−	1.15174i
$253$	−9.62209			−0.604936
$254$	8.19615	+	8.19615i	0.514272	+	0.514272i
$255$		0			0
$256$	16.0000			1.00000
$257$	4.52004	−	4.52004i	0.281952	−	0.281952i	−0.551935	−	0.833887i	$-0.686110\pi$
$257$	4.52004	−	4.52004i	0.281952	−	0.281952i	0.833887	+	0.551935i	$0.186110\pi$
$258$			0.480473i			0.0299130i
$259$	20.1962	−	20.1962i	1.25493	−	1.25493i
$260$		0			0
$261$	−12.9282	−	12.9282i	−0.800236	−	0.800236i
$262$	−5.55532	−	5.55532i	−0.343209	−	0.343209i
$263$	8.62398	+	8.62398i	0.531778	+	0.531778i	0.921101	−	0.389324i	$-0.127291\pi$
$263$	8.62398	+	8.62398i	0.531778	+	0.531778i	−0.389324	+	0.921101i	$0.627291\pi$
$264$	−1.60770	−	1.60770i	−0.0989468	−	0.0989468i
$265$		0			0
$266$			19.8564i			1.21747i
$267$			5.31508i			0.325278i
$268$	11.5911			0.708040
$269$	7.26795	+	7.26795i	0.443135	+	0.443135i	0.893064	−	0.449929i	$-0.148551\pi$
$269$	7.26795	+	7.26795i	0.443135	+	0.443135i	−0.449929	+	0.893064i	$0.648551\pi$
$270$		0			0
$271$			0.588457i			0.0357462i	0.999840	+	0.0178731i	$0.00568949\pi$
$271$			0.588457i			0.0357462i	−0.999840	+	0.0178731i	$0.994311\pi$
$272$	2.82843	−	2.82843i	0.171499	−	0.171499i
$273$	8.48528	+	8.48528i	0.513553	+	0.513553i
$274$	−13.1962	−	13.1962i	−0.797209	−	0.797209i
$275$		0			0
$276$	4.53590	−	4.53590i	0.273029	−	0.273029i
$277$		0			0			−	1.00000i	$-0.5\pi$
$277$		0			0				1.00000i	$0.5\pi$
$278$	−10.3156	−	10.3156i	−0.618688	−	0.618688i
$279$		−	16.9282i		−	1.01347i
$280$		0			0
$281$			15.4641i			0.922511i	0.887267	+	0.461255i	$0.152601\pi$
$281$			15.4641i			0.922511i	−0.887267	+	0.461255i	$0.847399\pi$
$282$	−1.03528	+	1.03528i	−0.0616498	+	0.0616498i
$283$	−8.72552			−0.518678			−0.259339	−	0.965786i	$-0.583505\pi$
$283$	−8.72552			−0.518678			−0.259339	+	0.965786i	$0.583505\pi$
$284$	1.85641			0.110157
$285$		0			0
$286$	−7.60770	+	7.60770i	−0.449852	+	0.449852i
$287$	−1.55291	−	1.55291i	−0.0916656	−	0.0916656i
$288$	−15.4548			−0.910684
$289$			16.0000i			0.941176i
$290$		0			0
$291$	6.00000	+	6.00000i	0.351726	+	0.351726i
$292$	−17.6269	+	17.6269i	−1.03154	+	1.03154i
$293$			9.89949i			0.578335i	0.957279	+	0.289167i	$0.0933784\pi$
$293$			9.89949i			0.578335i	−0.957279	+	0.289167i	$0.906622\pi$
$294$	11.2679			0.657160
$295$		0			0
$296$	−17.0718			−0.992278
$297$	3.25813	+	3.25813i	0.189056	+	0.189056i
$298$	21.3891	−	21.3891i	1.23904	−	1.23904i
$299$	−21.4641	−	21.4641i	−1.24130	−	1.24130i
$300$		0			0
$301$	2.19615	−	2.19615i	0.126584	−	0.126584i
$302$	−14.4195			−0.829751
$303$	−5.13922	+	5.13922i	−0.295240	+	0.295240i
$304$	8.39230	−	8.39230i	0.481332	−	0.481332i
$305$		0			0
$306$	−2.73205	+	2.73205i	−0.156181	+	0.156181i
$307$	23.4225			1.33679			0.668395	−	0.743806i	$-0.266982\pi$
$307$	23.4225			1.33679			0.668395	+	0.743806i	$0.266982\pi$
$308$			14.6969i			0.837436i
$309$	1.26795	−	1.26795i	0.0721311	−	0.0721311i
$310$		0			0
$311$	−11.6603			−0.661192			−0.330596	−	0.943772i	$-0.607250\pi$
$311$	−11.6603			−0.661192			−0.330596	+	0.943772i	$0.607250\pi$
$312$		−	7.17260i		−	0.406069i
$313$	0.656339	−	0.656339i	0.0370985	−	0.0370985i	−0.688314	−	0.725413i	$-0.741649\pi$
$313$	0.656339	−	0.656339i	0.0370985	−	0.0370985i	0.725413	+	0.688314i	$0.241649\pi$
$314$			12.9282i			0.729581i
$315$		0			0
$316$	−4.39230			−0.247086
$317$		−	5.37945i		−	0.302140i	−0.988523	−	0.151070i	$-0.951728\pi$
$317$		−	5.37945i		−	0.302140i	0.988523	−	0.151070i	$-0.0482719\pi$
$318$	7.24693			0.406388
$319$	10.3923			0.581857
$320$		0			0
$321$	−3.00000			−0.167444
$322$	−41.4655			−2.31078
$323$		−	2.96713i		−	0.165095i
$324$	13.3205			0.740028
$325$		0			0
$326$			12.5885i			0.697210i
$327$	4.86181	−	4.86181i	0.268859	−	0.268859i
$328$			1.31268i			0.0724805i
$329$	9.46410			0.521773
$330$		0			0
$331$	−19.4904	+	19.4904i	−1.07129	+	1.07129i	−0.0740324	+	0.997256i	$0.523587\pi$
$331$	−19.4904	+	19.4904i	−1.07129	+	1.07129i	−0.997256	+	0.0740324i	$0.976413\pi$
$332$			34.7733i			1.90843i
$333$	16.4901			0.903651
$334$	−0.392305	+	0.392305i	−0.0214660	+	0.0214660i
$335$		0			0
$336$	−6.92820	−	6.92820i	−0.377964	−	0.377964i
$337$	7.26054	−	7.26054i	0.395507	−	0.395507i	−0.481138	−	0.876645i	$-0.659776\pi$
$337$	7.26054	−	7.26054i	0.395507	−	0.395507i	0.876645	+	0.481138i	$0.159776\pi$
$338$	−15.5563			−0.846154
$339$	1.02628	−	1.02628i	0.0557398	−	0.0557398i
$340$		0			0
$341$	6.80385	+	6.80385i	0.368449	+	0.368449i
$342$	−8.10634	+	8.10634i	−0.438341	+	0.438341i
$343$	−28.0812	−	28.0812i	−1.51624	−	1.51624i
$344$	−1.85641			−0.100091
$345$		0			0
$346$	8.39230			0.451173
$347$		−	2.96713i		−	0.159284i	−0.996824	−	0.0796419i	$-0.974622\pi$
$347$		−	2.96713i		−	0.159284i	0.996824	−	0.0796419i	$-0.0253777\pi$
$348$	−4.89898	+	4.89898i	−0.262613	+	0.262613i
$349$	23.5885	+	23.5885i	1.26266	+	1.26266i	0.949798	+	0.312863i	$0.101288\pi$
$349$	23.5885	+	23.5885i	1.26266	+	1.26266i	0.312863	+	0.949798i	$0.398712\pi$
$350$		0			0
$351$			14.5359i			0.775869i
$352$	6.21166	−	6.21166i	0.331082	−	0.331082i
$353$	4.79744	+	4.79744i	0.255342	+	0.255342i	0.823157	−	0.567814i	$-0.192211\pi$
$353$	4.79744	+	4.79744i	0.255342	+	0.255342i	−0.567814	+	0.823157i	$0.692211\pi$
$354$	−5.66025	+	5.66025i	−0.300839	+	0.300839i
$355$		0			0
$356$	−20.5359			−1.08840
$357$	−2.44949			−0.129641
$358$	10.6945	−	10.6945i	0.565224	−	0.565224i
$359$		−	24.5885i		−	1.29773i	−0.760904	−	0.648865i	$-0.775244\pi$
$359$		−	24.5885i		−	1.29773i	0.760904	−	0.648865i	$-0.224756\pi$
$360$		0			0
$361$			10.1962i			0.536640i
$362$	−3.96524	−	3.96524i	−0.208408	−	0.208408i
$363$	4.44571			0.233339
$364$	−32.7846	+	32.7846i	−1.71838	+	1.71838i
$365$		0			0
$366$	−2.33975	−	2.33975i	−0.122300	−	0.122300i
$367$	−2.92996	−	2.92996i	−0.152943	−	0.152943i	0.626488	−	0.779431i	$-0.284492\pi$
$367$	−2.92996	−	2.92996i	−0.152943	−	0.152943i	−0.779431	+	0.626488i	$0.784492\pi$
$368$	17.5254	+	17.5254i	0.913573	+	0.913573i
$369$		−	1.26795i		−	0.0660068i
$370$		0			0
$371$	−33.1244	−	33.1244i	−1.71973	−	1.71973i
$372$	−6.41473			−0.332588
$373$			15.8338i			0.819841i	0.912121	+	0.409920i	$0.134443\pi$
$373$			15.8338i			0.819841i	−0.912121	+	0.409920i	$0.865557\pi$
$374$		−	2.19615i		−	0.113560i
$375$		0			0
$376$	−4.00000	−	4.00000i	−0.206284	−	0.206284i
$377$	23.1822	+	23.1822i	1.19395	+	1.19395i
$378$	14.0406	+	14.0406i	0.722171	+	0.722171i
$379$	−10.2942	−	10.2942i	−0.528779	−	0.528779i	0.391429	−	0.920208i	$-0.371981\pi$
$379$	−10.2942	−	10.2942i	−0.528779	−	0.528779i	−0.920208	+	0.391429i	$0.871981\pi$
$380$		0			0
$381$	−3.00000	+	3.00000i	−0.153695	+	0.153695i
$382$			24.9754i			1.27785i
$383$	−0.138701	+	0.138701i	−0.00708728	+	0.00708728i	−0.710642	−	0.703554i	$-0.751595\pi$
$383$	−0.138701	+	0.138701i	−0.00708728	+	0.00708728i	0.703554	+	0.710642i	$0.251595\pi$
$384$			5.85641i			0.298858i
$385$		0			0
$386$	−13.3923	−	13.3923i	−0.681650	−	0.681650i
$387$	1.79315			0.0911510
$388$	−23.1822	+	23.1822i	−1.17690	+	1.17690i
$389$	8.32051	−	8.32051i	0.421867	−	0.421867i	−0.463979	−	0.885846i	$-0.653579\pi$
$389$	8.32051	−	8.32051i	0.421867	−	0.421867i	0.885846	+	0.463979i	$0.153579\pi$
$390$		0			0
$391$	6.19615			0.313353
$392$			43.5360i			2.19890i
$393$	2.03339	−	2.03339i	0.102571	−	0.102571i
$394$	−14.7846			−0.744838
$395$		0			0
$396$	−6.00000	+	6.00000i	−0.301511	+	0.301511i
$397$			3.58630i			0.179991i	0.995942	+	0.0899957i	$0.0286853\pi$
$397$			3.58630i			0.179991i	−0.995942	+	0.0899957i	$0.971315\pi$
$398$		−	23.1822i		−	1.16202i
$399$	−7.26795			−0.363853
$400$		0			0
$401$	−12.1244			−0.605461			−0.302731	−	0.953076i	$-0.597898\pi$
$401$	−12.1244			−0.605461			−0.302731	+	0.953076i	$0.597898\pi$
$402$			4.24264i			0.211604i
$403$			30.3548i			1.51208i
$404$	−19.8564	−	19.8564i	−0.987893	−	0.987893i
$405$		0			0
$406$	44.7846			2.22262
$407$	−6.62776	+	6.62776i	−0.328526	+	0.328526i
$408$	1.03528	+	1.03528i	0.0512538	+	0.0512538i
$409$	−25.3923			−1.25557			−0.627784	−	0.778387i	$-0.716038\pi$
$409$	−25.3923			−1.25557			−0.627784	+	0.778387i	$0.716038\pi$
$410$		0			0
$411$	4.83013	−	4.83013i	0.238253	−	0.238253i
$412$	4.89898	+	4.89898i	0.241355	+	0.241355i
$413$	51.7439			2.54615
$414$	−16.9282	−	16.9282i	−0.831976	−	0.831976i
$415$		0			0
$416$	27.7128			1.35873
$417$	3.77577	−	3.77577i	0.184900	−	0.184900i
$418$		−	6.51626i		−	0.318721i
$419$	4.43782	−	4.43782i	0.216802	−	0.216802i	−0.590347	−	0.807149i	$-0.701009\pi$
$419$	4.43782	−	4.43782i	0.216802	−	0.216802i	0.807149	+	0.590347i	$0.201009\pi$
$420$		0			0
$421$	−5.60770	−	5.60770i	−0.273302	−	0.273302i	0.557126	−	0.830428i	$-0.311904\pi$
$421$	−5.60770	−	5.60770i	−0.273302	−	0.273302i	−0.830428	+	0.557126i	$0.811904\pi$
$422$	−15.9725	−	15.9725i	−0.777527	−	0.777527i
$423$	3.86370	+	3.86370i	0.187860	+	0.187860i
$424$			28.0000i			1.35980i
$425$		0			0
$426$			0.679492i			0.0329215i
$427$			21.3891i			1.03509i
$428$		−	11.5911i		−	0.560277i
$429$	−2.78461	−	2.78461i	−0.134442	−	0.134442i
$430$		0			0
$431$		−	24.5885i		−	1.18438i	−0.805797	−	0.592192i	$-0.798263\pi$
$431$		−	24.5885i		−	1.18438i	0.805797	−	0.592192i	$-0.201737\pi$
$432$		−	11.8685i		−	0.571024i
$433$	0.328169	+	0.328169i	0.0157708	+	0.0157708i	0.714948	−	0.699177i	$-0.246450\pi$
$433$	0.328169	+	0.328169i	0.0157708	+	0.0157708i	−0.699177	+	0.714948i	$0.746450\pi$
$434$	29.3205	+	29.3205i	1.40743	+	1.40743i
$435$		0			0
$436$	18.7846	+	18.7846i	0.899620	+	0.899620i
$437$	18.3848			0.879463
$438$	−6.45189	−	6.45189i	−0.308283	−	0.308283i
$439$		−	19.6077i		−	0.935824i	−0.883775	−	0.467912i	$-0.845006\pi$
$439$		−	19.6077i		−	0.935824i	0.883775	−	0.467912i	$-0.154994\pi$
$440$		0			0
$441$		−	42.0526i		−	2.00250i
$442$	4.89898	−	4.89898i	0.233021	−	0.233021i
$443$	38.5999			1.83394			0.916968	−	0.398962i	$-0.130629\pi$
$443$	38.5999			1.83394			0.916968	+	0.398962i	$0.130629\pi$
$444$		−	6.24871i		−	0.296551i
$445$		0			0
$446$	−3.46410	+	3.46410i	−0.164030	+	0.164030i
$447$	7.82894	+	7.82894i	0.370296	+	0.370296i
$448$	26.7685	−	26.7685i	1.26469	−	1.26469i
$449$		−	18.1244i		−	0.855341i	−0.903935	−	0.427671i	$-0.859334\pi$
$449$		−	18.1244i		−	0.855341i	0.903935	−	0.427671i	$-0.140666\pi$
$450$		0			0
$451$	0.509619	+	0.509619i	0.0239970	+	0.0239970i
$452$	3.96524	+	3.96524i	0.186509	+	0.186509i
$453$		−	5.27792i		−	0.247978i
$454$	26.7846			1.25706
$455$		0			0
$456$	3.07180	+	3.07180i	0.143850	+	0.143850i
$457$	−15.7458	−	15.7458i	−0.736558	−	0.736558i	0.235352	−	0.971910i	$-0.424376\pi$
$457$	−15.7458	−	15.7458i	−0.736558	−	0.736558i	−0.971910	+	0.235352i	$0.924376\pi$
$458$	5.65685	−	5.65685i	0.264327	−	0.264327i
$459$	−2.09808	−	2.09808i	−0.0979298	−	0.0979298i
$460$		0			0
$461$	−16.7321	+	16.7321i	−0.779289	+	0.779289i	−0.979710	−	0.200421i	$-0.935769\pi$
$461$	−16.7321	+	16.7321i	−0.779289	+	0.779289i	0.200421	+	0.979710i	$0.435769\pi$
$462$	−5.37945			−0.250275
$463$	−16.4901	+	16.4901i	−0.766359	+	0.766359i	−0.977464	−	0.211104i	$-0.932294\pi$
$463$	−16.4901	+	16.4901i	−0.766359	+	0.766359i	0.211104	+	0.977464i	$0.432294\pi$
$464$	−18.9282	−	18.9282i	−0.878720	−	0.878720i
$465$		0			0
$466$	−8.00000	+	8.00000i	−0.370593	+	0.370593i
$467$	1.41421			0.0654420			0.0327210	−	0.999465i	$-0.489583\pi$
$467$	1.41421			0.0654420			0.0327210	+	0.999465i	$0.489583\pi$
$468$	−26.7685			−1.23738
$469$	19.3923	−	19.3923i	0.895453	−	0.895453i
$470$		0			0
$471$	−4.73205			−0.218041
$472$	−21.8695	−	21.8695i	−1.00663	−	1.00663i
$473$	−0.720710	+	0.720710i	−0.0331383	+	0.0331383i
$474$		−	1.60770i		−	0.0738439i
$475$		0			0
$476$		−	9.46410i		−	0.433786i
$477$		−	27.0459i		−	1.23835i
$478$	30.3548			1.38840
$479$	41.6603			1.90351			0.951753	−	0.306866i	$-0.0992803\pi$
$479$	41.6603			1.90351			0.951753	+	0.306866i	$0.0992803\pi$
$480$		0			0
$481$	−29.5692			−1.34824
$482$	18.1074			0.824768
$483$		−	15.1774i		−	0.690596i
$484$			17.1769i			0.780769i
$485$		0			0
$486$			17.4641i			0.792188i
$487$	−6.27603	+	6.27603i	−0.284394	+	0.284394i	−0.834859	−	0.550465i	$-0.814451\pi$
$487$	−6.27603	+	6.27603i	−0.284394	+	0.284394i	0.550465	+	0.834859i	$0.314451\pi$
$488$	9.04008	−	9.04008i	0.409225	−	0.409225i
$489$	−4.60770			−0.208367
$490$		0			0
$491$	20.3205	−	20.3205i	0.917052	−	0.917052i	−0.0797622	−	0.996814i	$-0.525416\pi$
$491$	20.3205	−	20.3205i	0.917052	−	0.917052i	0.996814	+	0.0797622i	$0.0254161\pi$
$492$	−0.480473			−0.0216614
$493$	−6.69213			−0.301398
$494$	14.5359	−	14.5359i	0.654001	−	0.654001i
$495$		0			0
$496$		−	24.7846i		−	1.11286i
$497$	3.10583	−	3.10583i	0.139315	−	0.139315i
$498$	−12.7279			−0.570352
$499$	−23.0000	+	23.0000i	−1.02962	+	1.02962i	−0.0300737	+	0.999548i	$0.509574\pi$
$499$	−23.0000	+	23.0000i	−1.02962	+	1.02962i	−0.999548	+	0.0300737i	$0.990426\pi$
$500$		0			0
$501$	−0.143594	−	0.143594i	−0.00641529	−	0.00641529i
$502$	−12.4877	+	12.4877i	−0.557353	+	0.557353i
$503$	−21.7680	−	21.7680i	−0.970587	−	0.970587i	0.0289922	−	0.999580i	$-0.490770\pi$
$503$	−21.7680	−	21.7680i	−0.970587	−	0.970587i	−0.999580	+	0.0289922i	$0.990770\pi$
$504$	−25.8564	+	25.8564i	−1.15174	+	1.15174i
$505$		0			0
$506$	13.6077			0.604936
$507$		−	5.69402i		−	0.252880i
$508$	−11.5911	−	11.5911i	−0.514272	−	0.514272i
$509$	−15.0000	−	15.0000i	−0.664863	−	0.664863i	0.291659	−	0.956522i	$-0.405793\pi$
$509$	−15.0000	−	15.0000i	−0.664863	−	0.664863i	−0.956522	+	0.291659i	$0.905793\pi$
$510$		0			0
$511$			58.9808i			2.60916i
$512$	−22.6274			−1.00000
$513$	−6.22526	−	6.22526i	−0.274852	−	0.274852i
$514$	−6.39230	+	6.39230i	−0.281952	+	0.281952i
$515$		0			0
$516$		−	0.679492i		−	0.0299130i
$517$	−3.10583			−0.136594
$518$	−28.5617	+	28.5617i	−1.25493	+	1.25493i
$519$			3.07180i			0.134837i
$520$		0			0
$521$		−	3.24871i		−	0.142329i	−0.997465	−	0.0711643i	$-0.977329\pi$
$521$		−	3.24871i		−	0.142329i	0.997465	−	0.0711643i	$-0.0226715\pi$
$522$	18.2832	+	18.2832i	0.800236	+	0.800236i
$523$	−30.2905			−1.32451			−0.662255	−	0.749279i	$-0.730400\pi$
$523$	−30.2905			−1.32451			−0.662255	+	0.749279i	$0.730400\pi$
$524$	7.85641	+	7.85641i	0.343209	+	0.343209i
$525$		0			0
$526$	−12.1962	−	12.1962i	−0.531778	−	0.531778i
$527$	−4.38134	−	4.38134i	−0.190854	−	0.190854i
$528$	2.27362	+	2.27362i	0.0989468	+	0.0989468i
$529$			15.3923i			0.669231i
$530$		0			0
$531$	21.1244	+	21.1244i	0.916719	+	0.916719i
$532$		−	28.0812i		−	1.21747i
$533$			2.27362i			0.0984816i
$534$		−	7.51666i		−	0.325278i
$535$		0			0
$536$	−16.3923			−0.708040
$537$	3.91447	+	3.91447i	0.168922	+	0.168922i
$538$	−10.2784	−	10.2784i	−0.443135	−	0.443135i
$539$	16.9019	+	16.9019i	0.728017	+	0.728017i
$540$		0			0
$541$	19.8038	−	19.8038i	0.851434	−	0.851434i	−0.138876	−	0.990310i	$-0.544349\pi$
$541$	19.8038	−	19.8038i	0.851434	−	0.851434i	0.990310	+	0.138876i	$0.0443489\pi$
$542$		−	0.832204i		−	0.0357462i
$543$	1.45138	−	1.45138i	0.0622846	−	0.0622846i
$544$	−4.00000	+	4.00000i	−0.171499	+	0.171499i
$545$		0			0
$546$	−12.0000	−	12.0000i	−0.513553	−	0.513553i
$547$	6.93237			0.296407			0.148203	−	0.988957i	$-0.452651\pi$
$547$	6.93237			0.296407			0.148203	+	0.988957i	$0.452651\pi$
$548$	18.6622	+	18.6622i	0.797209	+	0.797209i
$549$	−8.73205	+	8.73205i	−0.372675	+	0.372675i
$550$		0			0
$551$	−19.8564			−0.845911
$552$	−6.41473	+	6.41473i	−0.273029	+	0.273029i
$553$	−7.34847	+	7.34847i	−0.312489	+	0.312489i
$554$		0			0
$555$		0			0
$556$	14.5885	+	14.5885i	0.618688	+	0.618688i
$557$		−	26.0106i		−	1.10211i	−0.834470	−	0.551053i	$-0.814226\pi$
$557$		−	26.0106i		−	1.10211i	0.834470	−	0.551053i	$-0.185774\pi$
$558$			23.9401i			1.01347i
$559$	−3.21539			−0.135997
$560$		0			0
$561$	0.803848			0.0339385
$562$		−	21.8695i		−	0.922511i
$563$		−	23.7642i		−	1.00154i	−0.865580	−	0.500771i	$-0.833050\pi$
$563$		−	23.7642i		−	1.00154i	0.865580	−	0.500771i	$-0.166950\pi$
$564$	1.46410	−	1.46410i	0.0616498	−	0.0616498i
$565$		0			0
$566$	12.3397			0.518678
$567$	22.2856	−	22.2856i	0.935909	−	0.935909i
$568$	−2.62536			−0.110157
$569$	27.9282			1.17081			0.585406	−	0.810741i	$-0.300935\pi$
$569$	27.9282			1.17081			0.585406	+	0.810741i	$0.300935\pi$
$570$		0			0
$571$	21.3923	−	21.3923i	0.895240	−	0.895240i	−0.0997704	−	0.995010i	$-0.531811\pi$
$571$	21.3923	−	21.3923i	0.895240	−	0.895240i	0.995010	+	0.0997704i	$0.0318108\pi$
$572$	10.7589	−	10.7589i	0.449852	−	0.449852i
$573$	−9.14162			−0.381897
$574$	2.19615	+	2.19615i	0.0916656	+	0.0916656i
$575$		0			0
$576$	21.8564			0.910684
$577$	13.4722	−	13.4722i	0.560855	−	0.560855i	−0.368695	−	0.929550i	$-0.620195\pi$
$577$	13.4722	−	13.4722i	0.560855	−	0.560855i	0.929550	+	0.368695i	$0.120195\pi$
$578$		−	22.6274i		−	0.941176i
$579$	4.90192	−	4.90192i	0.203717	−	0.203717i
$580$		0			0
$581$	58.1769	+	58.1769i	2.41359	+	2.41359i
$582$	−8.48528	−	8.48528i	−0.351726	−	0.351726i
$583$	10.8704	+	10.8704i	0.450206	+	0.450206i
$584$	24.9282	−	24.9282i	1.03154	−	1.03154i
$585$		0			0
$586$		−	14.0000i		−	0.578335i
$587$			9.20599i			0.379972i	0.981787	+	0.189986i	$0.0608443\pi$
$587$			9.20599i			0.379972i	−0.981787	+	0.189986i	$0.939156\pi$
$588$	−15.9353			−0.657160
$589$	−13.0000	−	13.0000i	−0.535656	−	0.535656i
$590$		0			0
$591$		−	5.41154i		−	0.222601i
$592$	24.1432			0.992278
$593$	−25.4422	−	25.4422i	−1.04479	−	1.04479i	−0.998949	−	0.0458388i	$-0.985404\pi$
$593$	−25.4422	−	25.4422i	−1.04479	−	1.04479i	−0.0458388	−	0.998949i	$-0.514596\pi$
$594$	−4.60770	−	4.60770i	−0.189056	−	0.189056i
$595$		0			0
$596$	−30.2487	+	30.2487i	−1.23904	+	1.23904i
$597$	8.48528			0.347279
$598$	30.3548	+	30.3548i	1.24130	+	1.24130i
$599$			15.8038i			0.645728i	0.946445	+	0.322864i	$0.104646\pi$
$599$			15.8038i			0.645728i	−0.946445	+	0.322864i	$0.895354\pi$
$600$		0			0
$601$		−	12.8038i		−	0.522280i	−0.965301	−	0.261140i	$-0.915902\pi$
$601$		−	12.8038i		−	0.522280i	0.965301	−	0.261140i	$-0.0840984\pi$
$602$	−3.10583	+	3.10583i	−0.126584	+	0.126584i
$603$	15.8338			0.644800
$604$	20.3923			0.829751
$605$		0			0
$606$	7.26795	−	7.26795i	0.295240	−	0.295240i
$607$	−9.62209	−	9.62209i	−0.390549	−	0.390549i	0.484334	−	0.874883i	$-0.339062\pi$
$607$	−9.62209	−	9.62209i	−0.390549	−	0.390549i	−0.874883	+	0.484334i	$0.839062\pi$
$608$	−11.8685	+	11.8685i	−0.481332	+	0.481332i
$609$			16.3923i			0.664250i
$610$		0			0
$611$	−6.92820	−	6.92820i	−0.280285	−	0.280285i
$612$	3.86370	−	3.86370i	0.156181	−	0.156181i
$613$			30.5307i			1.23312i	0.787307	+	0.616561i	$0.211475\pi$
$613$			30.5307i			1.23312i	−0.787307	+	0.616561i	$0.788525\pi$
$614$	−33.1244			−1.33679
$615$		0			0
$616$		−	20.7846i		−	0.837436i
$617$	−8.20788	−	8.20788i	−0.330437	−	0.330437i	0.522316	−	0.852752i	$-0.325068\pi$
$617$	−8.20788	−	8.20788i	−0.330437	−	0.330437i	−0.852752	+	0.522316i	$0.825068\pi$
$618$	−1.79315	+	1.79315i	−0.0721311	+	0.0721311i
$619$	−25.7846	−	25.7846i	−1.03637	−	1.03637i	−0.999313	−	0.0370578i	$-0.988201\pi$
$619$	−25.7846	−	25.7846i	−1.03637	−	1.03637i	−0.0370578	−	0.999313i	$-0.511799\pi$
$620$		0			0
$621$	13.0000	−	13.0000i	0.521672	−	0.521672i
$622$	16.4901			0.661192
$623$	−34.3572	+	34.3572i	−1.37649	+	1.37649i
$624$			10.1436i			0.406069i
$625$		0			0
$626$	−0.928203	+	0.928203i	−0.0370985	+	0.0370985i
$627$	2.38512			0.0952525
$628$		−	18.2832i		−	0.729581i
$629$	4.26795	−	4.26795i	0.170174	−	0.170174i
$630$		0			0
$631$	12.5885			0.501139			0.250569	−	0.968099i	$-0.419382\pi$
$631$	12.5885			0.501139			0.250569	+	0.968099i	$0.419382\pi$
$632$	6.21166			0.247086
$633$	5.84632	−	5.84632i	0.232370	−	0.232370i
$634$			7.60770i			0.302140i
$635$		0			0
$636$	−10.2487			−0.406388
$637$			75.4066i			2.98772i
$638$	−14.6969			−0.581857
$639$	2.53590			0.100319
$640$		0			0
$641$	−12.9282			−0.510633			−0.255317	−	0.966857i	$-0.582180\pi$
$641$	−12.9282			−0.510633			−0.255317	+	0.966857i	$0.582180\pi$
$642$	4.24264			0.167444
$643$		−	6.86800i		−	0.270847i	−0.990788	−	0.135424i	$-0.956760\pi$
$643$		−	6.86800i		−	0.270847i	0.990788	−	0.135424i	$-0.0432395\pi$
$644$	58.6410			2.31078
$645$		0			0
$646$			4.19615i			0.165095i
$647$	18.6622	−	18.6622i	0.733686	−	0.733686i	−0.237662	−	0.971348i	$-0.576381\pi$
$647$	18.6622	−	18.6622i	0.733686	−	0.733686i	0.971348	+	0.237662i	$0.0763811\pi$
$648$	−18.8380			−0.740028
$649$	−16.9808			−0.666553
$650$		0			0
$651$	−10.7321	+	10.7321i	−0.420622	+	0.420622i
$652$		−	17.8028i		−	0.697210i
$653$	−21.7680			−0.851848			−0.425924	−	0.904759i	$-0.640051\pi$
$653$	−21.7680			−0.851848			−0.425924	+	0.904759i	$0.640051\pi$
$654$	−6.87564	+	6.87564i	−0.268859	+	0.268859i
$655$		0			0
$656$		−	1.85641i		−	0.0724805i
$657$	−24.0788	+	24.0788i	−0.939403	+	0.939403i
$658$	−13.3843			−0.521773
$659$	0.509619	−	0.509619i	0.0198519	−	0.0198519i	−0.697111	−	0.716963i	$-0.745532\pi$
$659$	0.509619	−	0.509619i	0.0198519	−	0.0198519i	0.716963	+	0.697111i	$0.245532\pi$
$660$		0			0
$661$	−8.00000	−	8.00000i	−0.311164	−	0.311164i	0.534196	−	0.845360i	$-0.320614\pi$
$661$	−8.00000	−	8.00000i	−0.311164	−	0.311164i	−0.845360	+	0.534196i	$0.820614\pi$
$662$	27.5636	−	27.5636i	1.07129	−	1.07129i
$663$	1.79315	+	1.79315i	0.0696402	+	0.0696402i
$664$		−	49.1769i		−	1.90843i
$665$		0			0
$666$	−23.3205			−0.903651
$667$		−	41.4655i		−	1.60555i
$668$	0.554803	−	0.554803i	0.0214660	−	0.0214660i
$669$	−1.26795	−	1.26795i	−0.0490217	−	0.0490217i
$670$		0			0
$671$		−	7.01924i		−	0.270975i
$672$	9.79796	+	9.79796i	0.377964	+	0.377964i
$673$	−26.7685	−	26.7685i	−1.03185	−	1.03185i	−0.999476	−	0.0323749i	$-0.989693\pi$
$673$	−26.7685	−	26.7685i	−1.03185	−	1.03185i	−0.0323749	−	0.999476i	$-0.510307\pi$
$674$	−10.2679	+	10.2679i	−0.395507	+	0.395507i
$675$		0			0
$676$	22.0000			0.846154
$677$	−31.1127			−1.19576			−0.597879	−	0.801586i	$-0.703990\pi$
$677$	−31.1127			−1.19576			−0.597879	+	0.801586i	$0.703990\pi$
$678$	−1.45138	+	1.45138i	−0.0557398	+	0.0557398i
$679$			77.5692i			2.97683i
$680$		0			0
$681$			9.80385i			0.375684i
$682$	−9.62209	−	9.62209i	−0.368449	−	0.368449i
$683$	34.0798			1.30403			0.652014	−	0.758207i	$-0.273924\pi$
$683$	34.0798			1.30403			0.652014	+	0.758207i	$0.273924\pi$
$684$	11.4641	−	11.4641i	0.438341	−	0.438341i
$685$		0			0
$686$	39.7128	+	39.7128i	1.51624	+	1.51624i
$687$	2.07055	+	2.07055i	0.0789965	+	0.0789965i
$688$	2.62536			0.100091
$689$			48.4974i			1.84760i
$690$		0			0
$691$	−20.8827	−	20.8827i	−0.794415	−	0.794415i	0.187794	−	0.982208i	$-0.439866\pi$
$691$	−20.8827	−	20.8827i	−0.794415	−	0.794415i	−0.982208	+	0.187794i	$0.939866\pi$
$692$	−11.8685			−0.451173
$693$			20.0764i			0.762639i
$694$			4.19615i			0.159284i
$695$		0			0
$696$	6.92820	−	6.92820i	0.262613	−	0.262613i
$697$	−0.328169	−	0.328169i	−0.0124303	−	0.0124303i
$698$	−33.3591	−	33.3591i	−1.26266	−	1.26266i
$699$	−2.92820	−	2.92820i	−0.110755	−	0.110755i
$700$		0			0
$701$	18.5885	−	18.5885i	0.702076	−	0.702076i	−0.262780	−	0.964856i	$-0.584639\pi$
$701$	18.5885	−	18.5885i	0.702076	−	0.702076i	0.964856	+	0.262780i	$0.0846392\pi$
$702$		−	20.5569i		−	0.775869i
$703$	12.6636	−	12.6636i	0.477615	−	0.477615i
$704$	−8.78461	+	8.78461i	−0.331082	+	0.331082i
$705$		0			0
$706$	−6.78461	−	6.78461i	−0.255342	−	0.255342i
$707$	−66.4408			−2.49876
$708$	8.00481	−	8.00481i	0.300839	−	0.300839i
$709$	−2.00000	+	2.00000i	−0.0751116	+	0.0751116i	−0.743665	−	0.668553i	$-0.766914\pi$
$709$	−2.00000	+	2.00000i	−0.0751116	+	0.0751116i	0.668553	+	0.743665i	$0.266914\pi$
$710$		0			0
$711$	−6.00000			−0.225018
$712$	29.0421			1.08840
$713$	27.1475	−	27.1475i	1.01668	−	1.01668i
$714$	3.46410			0.129641
$715$		0			0
$716$	−15.1244	+	15.1244i	−0.565224	+	0.565224i
$717$			11.1106i			0.414934i
$718$			34.7733i			1.29773i
$719$	−1.26795			−0.0472865			−0.0236433	−	0.999720i	$-0.507527\pi$
$719$	−1.26795			−0.0472865			−0.0236433	+	0.999720i	$0.507527\pi$
$720$		0			0
$721$	16.3923			0.610481
$722$		−	14.4195i		−	0.536640i
$723$			6.62776i			0.246489i
$724$	5.60770	+	5.60770i	0.208408	+	0.208408i
$725$		0			0
$726$	−6.28719			−0.233339
$727$	−7.34847	+	7.34847i	−0.272540	+	0.272540i	−0.830122	−	0.557582i	$-0.811729\pi$
$727$	−7.34847	+	7.34847i	−0.272540	+	0.272540i	0.557582	+	0.830122i	$0.311729\pi$
$728$	46.3644	−	46.3644i	1.71838	−	1.71838i
$729$	13.5885			0.503276
$730$		0			0
$731$	0.464102	−	0.464102i	0.0171654	−	0.0171654i
$732$	3.30890	+	3.30890i	0.122300	+	0.122300i
$733$	−30.7066			−1.13417			−0.567086	−	0.823658i	$-0.691929\pi$
$733$	−30.7066			−1.13417			−0.567086	+	0.823658i	$0.691929\pi$
$734$	4.14359	+	4.14359i	0.152943	+	0.152943i
$735$		0			0
$736$	−24.7846	−	24.7846i	−0.913573	−	0.913573i
$737$	−6.36396	+	6.36396i	−0.234420	+	0.234420i
$738$			1.79315i			0.0660068i
$739$	21.3923	−	21.3923i	0.786929	−	0.786929i	−0.194061	−	0.980989i	$-0.562166\pi$
$739$	21.3923	−	21.3923i	0.786929	−	0.786929i	0.980989	+	0.194061i	$0.0621659\pi$
$740$		0			0
$741$	5.32051	+	5.32051i	0.195454	+	0.195454i
$742$	46.8449	+	46.8449i	1.71973	+	1.71973i
$743$	25.0125	+	25.0125i	0.917621	+	0.917621i	0.996856	−	0.0792350i	$-0.0252478\pi$
$743$	25.0125	+	25.0125i	0.917621	+	0.917621i	−0.0792350	+	0.996856i	$0.525248\pi$
$744$	9.07180			0.332588
$745$		0			0
$746$		−	22.3923i		−	0.819841i
$747$			47.5013i			1.73798i
$748$			3.10583i			0.113560i
$749$	−19.3923	−	19.3923i	−0.708579	−	0.708579i
$750$		0			0
$751$			44.3923i			1.61990i	0.586500	+	0.809949i	$0.300505\pi$
$751$			44.3923i			1.61990i	−0.586500	+	0.809949i	$0.699495\pi$
$752$	5.65685	+	5.65685i	0.206284	+	0.206284i
$753$	−4.57081	−	4.57081i	−0.166570	−	0.166570i
$754$	−32.7846	−	32.7846i	−1.19395	−	1.19395i
$755$		0			0
$756$	−19.8564	−	19.8564i	−0.722171	−	0.722171i
$757$	−20.0764			−0.729689			−0.364844	−	0.931068i	$-0.618878\pi$
$757$	−20.0764			−0.729689			−0.364844	+	0.931068i	$0.618878\pi$
$758$	14.5582	+	14.5582i	0.528779	+	0.528779i
$759$			4.98076i			0.180790i
$760$		0			0
$761$			4.60770i			0.167029i	0.996507	+	0.0835144i	$0.0266145\pi$
$761$			4.60770i			0.167029i	−0.996507	+	0.0835144i	$0.973386\pi$
$762$	4.24264	−	4.24264i	0.153695	−	0.153695i
$763$	62.8545			2.27549
$764$		−	35.3205i		−	1.27785i
$765$		0			0
$766$	0.196152	−	0.196152i	0.00708728	−	0.00708728i
$767$	−37.8792	−	37.8792i	−1.36774	−	1.36774i
$768$		−	8.28221i		−	0.298858i
$769$		−	35.1962i		−	1.26921i	−0.772838	−	0.634603i	$-0.781164\pi$
$769$		−	35.1962i		−	1.26921i	0.772838	−	0.634603i	$-0.218836\pi$
$770$		0			0
$771$	−2.33975	−	2.33975i	−0.0842639	−	0.0842639i
$772$	18.9396	+	18.9396i	0.681650	+	0.681650i
$773$		−	32.4997i		−	1.16893i	−0.811418	−	0.584467i	$-0.801304\pi$
$773$		−	32.4997i		−	1.16893i	0.811418	−	0.584467i	$-0.198696\pi$
$774$	−2.53590			−0.0911510
$775$		0			0
$776$	32.7846	−	32.7846i	1.17690	−	1.17690i
$777$	−10.4543	−	10.4543i	−0.375046	−	0.375046i
$778$	−11.7670	+	11.7670i	−0.421867	+	0.421867i
$779$	−0.973721	−	0.973721i	−0.0348872	−	0.0348872i
$780$		0			0
$781$	−1.01924	+	1.01924i	−0.0364712	+	0.0364712i
$782$	−8.76268			−0.313353
$783$	−14.0406	+	14.0406i	−0.501770	+	0.501770i
$784$		−	61.5692i		−	2.19890i
$785$		0			0
$786$	−2.87564	+	2.87564i	−0.102571	+	0.102571i
$787$	49.2944			1.75716			0.878578	−	0.477599i	$-0.158493\pi$
$787$	49.2944			1.75716			0.878578	+	0.477599i	$0.158493\pi$
$788$	20.9086			0.744838
$789$	4.46410	−	4.46410i	0.158926	−	0.158926i
$790$		0			0
$791$	13.2679			0.471754
$792$	8.48528	−	8.48528i	0.301511	−	0.301511i
$793$	15.6579	−	15.6579i	0.556028	−	0.556028i
$794$		−	5.07180i		−	0.179991i
$795$		0			0
$796$			32.7846i			1.16202i
$797$			22.0454i			0.780888i	0.920627	+	0.390444i	$0.127679\pi$
$797$			22.0454i			0.780888i	−0.920627	+	0.390444i	$0.872321\pi$
$798$	10.2784			0.363853
$799$	2.00000			0.0707549
$800$		0			0
$801$	−28.0526			−0.991188
$802$	17.1464			0.605461
$803$		−	19.3557i		−	0.683047i
$804$		−	6.00000i		−	0.211604i
$805$		0			0
$806$		−	42.9282i		−	1.51208i
$807$	3.76217	−	3.76217i	0.132435	−	0.132435i
$808$	28.0812	+	28.0812i	0.987893	+	0.987893i
$809$	−42.2487			−1.48539			−0.742693	−	0.669632i	$-0.766452\pi$
$809$	−42.2487			−1.48539			−0.742693	+	0.669632i	$0.766452\pi$
$810$		0			0
$811$	37.7846	−	37.7846i	1.32680	−	1.32680i	0.418649	−	0.908148i	$-0.362504\pi$
$811$	37.7846	−	37.7846i	1.32680	−	1.32680i	0.908148	−	0.418649i	$-0.137496\pi$
$812$	−63.3350			−2.22262
$813$	0.304608			0.0106831
$814$	9.37307	−	9.37307i	0.328526	−	0.328526i
$815$		0			0
$816$	−1.46410	−	1.46410i	−0.0512538	−	0.0512538i
$817$	1.37705	−	1.37705i	0.0481768	−	0.0481768i
$818$	35.9101			1.25557
$819$	−44.7846	+	44.7846i	−1.56490	+	1.56490i
$820$		0			0
$821$	11.5359	+	11.5359i	0.402606	+	0.402606i	0.879150	−	0.476545i	$-0.158111\pi$
$821$	11.5359	+	11.5359i	0.402606	+	0.402606i	−0.476545	+	0.879150i	$0.658111\pi$
$822$	−6.83083	+	6.83083i	−0.238253	+	0.238253i
$823$	3.10583	+	3.10583i	0.108262	+	0.108262i	0.759163	−	0.650901i	$-0.225609\pi$
$823$	3.10583	+	3.10583i	0.108262	+	0.108262i	−0.650901	+	0.759163i	$0.725609\pi$
$824$	−6.92820	−	6.92820i	−0.241355	−	0.241355i
$825$		0			0
$826$	−73.1769			−2.54615
$827$			4.10394i			0.142708i	0.997451	+	0.0713540i	$0.0227320\pi$
$827$			4.10394i			0.142708i	−0.997451	+	0.0713540i	$0.977268\pi$
$828$	23.9401	+	23.9401i	0.831976	+	0.831976i
$829$	16.5885	+	16.5885i	0.576141	+	0.576141i	0.933838	−	0.357697i	$-0.116438\pi$
$829$	16.5885	+	16.5885i	0.576141	+	0.576141i	−0.357697	+	0.933838i	$0.616438\pi$
$830$		0			0
$831$		0			0
$832$	−39.1918			−1.35873
$833$	−10.8840	−	10.8840i	−0.377108	−	0.377108i
$834$	−5.33975	+	5.33975i	−0.184900	+	0.184900i
$835$		0			0
$836$			9.21539i			0.318721i
$837$	−18.3848			−0.635471
$838$	−6.27603	+	6.27603i	−0.216802	+	0.216802i
$839$			20.5359i			0.708978i	0.935060	+	0.354489i	$0.115345\pi$
$839$			20.5359i			0.708978i	−0.935060	+	0.354489i	$0.884655\pi$
$840$		0			0
$841$			15.7846i			0.544297i
$842$	7.93048	+	7.93048i	0.273302	+	0.273302i
$843$	8.00481			0.275700
$844$	22.5885	+	22.5885i	0.777527	+	0.777527i
$845$		0			0
$846$	−5.46410	−	5.46410i	−0.187860	−	0.187860i
$847$	28.7375	+	28.7375i	0.987433	+	0.987433i
$848$		−	39.5980i		−	1.35980i
$849$			4.51666i			0.155011i
$850$		0			0
$851$	26.4449	+	26.4449i	0.906518	+	0.906518i
$852$		−	0.960947i		−	0.0329215i
$853$			46.1886i			1.58147i	0.612161	+	0.790733i	$0.290301\pi$
$853$			46.1886i			1.58147i	−0.612161	+	0.790733i	$0.709699\pi$
$854$		−	30.2487i		−	1.03509i
$855$		0			0
$856$			16.3923i			0.560277i
$857$	26.5791	+	26.5791i	0.907923	+	0.907923i	0.996104	−	0.0881813i	$-0.0281055\pi$
$857$	26.5791	+	26.5791i	0.907923	+	0.907923i	−0.0881813	+	0.996104i	$0.528105\pi$
$858$	3.93803	+	3.93803i	0.134442	+	0.134442i
$859$	33.0981	+	33.0981i	1.12929	+	1.12929i	0.990292	+	0.138999i	$0.0443886\pi$
$859$	33.0981	+	33.0981i	1.12929	+	1.12929i	0.138999	+	0.990292i	$0.455611\pi$
$860$		0			0
$861$	−0.803848	+	0.803848i	−0.0273951	+	0.0273951i
$862$			34.7733i			1.18438i
$863$	17.5254	−	17.5254i	0.596570	−	0.596570i	−0.342828	−	0.939398i	$-0.611385\pi$
$863$	17.5254	−	17.5254i	0.596570	−	0.596570i	0.939398	+	0.342828i	$0.111385\pi$
$864$			16.7846i			0.571024i
$865$		0			0
$866$	−0.464102	−	0.464102i	−0.0157708	−	0.0157708i
$867$	8.28221			0.281279
$868$	−41.4655	−	41.4655i	−1.40743	−	1.40743i
$869$	2.41154	−	2.41154i	0.0818060	−	0.0818060i
$870$		0			0
$871$	−28.3923			−0.962037
$872$	−26.5654	−	26.5654i	−0.899620	−	0.899620i
$873$	−31.6675	+	31.6675i	−1.07178	+	1.07178i
$874$	−26.0000			−0.879463
$875$		0			0
$876$	9.12436	+	9.12436i	0.308283	+	0.308283i
$877$		−	24.9754i		−	0.843358i	−0.906745	−	0.421679i	$-0.861441\pi$
$877$		−	24.9754i		−	0.843358i	0.906745	−	0.421679i	$-0.138559\pi$
$878$			27.7295i			0.935824i
$879$	5.12436			0.172840
$880$		0			0
$881$	−13.8564			−0.466834			−0.233417	−	0.972377i	$-0.574991\pi$
$881$	−13.8564			−0.466834			−0.233417	+	0.972377i	$0.574991\pi$
$882$			59.4713i			2.00250i
$883$			12.6636i			0.426162i	0.977034	+	0.213081i	$0.0683499\pi$
$883$			12.6636i			0.426162i	−0.977034	+	0.213081i	$0.931650\pi$
$884$	−6.92820	+	6.92820i	−0.233021	+	0.233021i
$885$		0			0
$886$	−54.5885			−1.83394
$887$	−31.3901	+	31.3901i	−1.05398	+	1.05398i	−0.0555188	+	0.998458i	$0.517681\pi$
$887$	−31.3901	+	31.3901i	−1.05398	+	1.05398i	−0.998458	+	0.0555188i	$0.982319\pi$
$888$			8.83701i			0.296551i
$889$	−38.7846			−1.30079
$890$		0			0
$891$	−7.31347	+	7.31347i	−0.245010	+	0.245010i
$892$	4.89898	−	4.89898i	0.164030	−	0.164030i
$893$	5.93426			0.198582
$894$	−11.0718	−	11.0718i	−0.370296	−	0.370296i
$895$		0			0
$896$	−37.8564	+	37.8564i	−1.26469	+	1.26469i
$897$	−11.1106	+	11.1106i	−0.370973	+	0.370973i
$898$			25.6317i			0.855341i
$899$	−29.3205	+	29.3205i	−0.977894	+	0.977894i
$900$		0			0
$901$	−7.00000	−	7.00000i	−0.233204	−	0.233204i
$902$	−0.720710	−	0.720710i	−0.0239970	−	0.0239970i
$903$	−1.13681	−	1.13681i	−0.0378307	−	0.0378307i
$904$	−5.60770	−	5.60770i	−0.186509	−	0.186509i
$905$		0			0
$906$			7.46410i			0.247978i
$907$		−	23.4868i		−	0.779867i	−0.920843	−	0.389934i	$-0.872498\pi$
$907$		−	23.4868i		−	0.779867i	0.920843	−	0.389934i	$-0.127502\pi$
$908$	−37.8792			−1.25706
$909$	−27.1244	−	27.1244i	−0.899658	−	0.899658i
$910$		0			0
$911$			24.2487i			0.803396i	0.915772	+	0.401698i	$0.131580\pi$
$911$			24.2487i			0.803396i	−0.915772	+	0.401698i	$0.868420\pi$
$912$	−4.34418	−	4.34418i	−0.143850	−	0.143850i
$913$	−19.0919	−	19.0919i	−0.631849	−	0.631849i
$914$	22.2679	+	22.2679i	0.736558	+	0.736558i
$915$		0			0
$916$	−8.00000	+	8.00000i	−0.264327	+	0.264327i
$917$	26.2880			0.868108
$918$	2.96713	+	2.96713i	0.0979298	+	0.0979298i
$919$			6.19615i			0.204392i	0.994764	+	0.102196i	$0.0325869\pi$
$919$			6.19615i			0.204392i	−0.994764	+	0.102196i	$0.967413\pi$
$920$		0			0
$921$		−	12.1244i		−	0.399511i
$922$	23.6627	−	23.6627i	0.779289	−	0.779289i
$923$	−4.54725			−0.149675
$924$	7.60770			0.250275
$925$		0			0
$926$	23.3205	−	23.3205i	0.766359	−	0.766359i
$927$	6.69213	+	6.69213i	0.219798	+	0.219798i
$928$	26.7685	+	26.7685i	0.878720	+	0.878720i
$929$		−	36.0000i		−	1.18112i	−0.806993	−	0.590561i	$-0.798907\pi$
$929$		−	36.0000i		−	1.18112i	0.806993	−	0.590561i	$-0.201093\pi$
$930$		0			0
$931$	−32.2942	−	32.2942i	−1.05840	−	1.05840i
$932$	11.3137	−	11.3137i	0.370593	−	0.370593i
$933$			6.03579i			0.197603i
$934$	−2.00000			−0.0654420
$935$		0			0
$936$	37.8564			1.23738
$937$	−9.95026	−	9.95026i	−0.325061	−	0.325061i	0.525644	−	0.850705i	$-0.323824\pi$
$937$	−9.95026	−	9.95026i	−0.325061	−	0.325061i	−0.850705	+	0.525644i	$0.823824\pi$
$938$	−27.4249	+	27.4249i	−0.895453	+	0.895453i
$939$	−0.339746	−	0.339746i	−0.0110872	−	0.0110872i
$940$		0			0
$941$	−14.7846	+	14.7846i	−0.481965	+	0.481965i	−0.905759	−	0.423794i	$-0.860698\pi$
$941$	−14.7846	+	14.7846i	−0.481965	+	0.481965i	0.423794	+	0.905759i	$0.360698\pi$
$942$	6.69213			0.218041
$943$	2.03339	−	2.03339i	0.0662162	−	0.0662162i
$944$	30.9282	+	30.9282i	1.00663	+	1.00663i
$945$		0			0
$946$	1.01924	−	1.01924i	0.0331383	−	0.0331383i
$947$	1.13681			0.0369414			0.0184707	−	0.999829i	$-0.494120\pi$
$947$	1.13681			0.0369414			0.0184707	+	0.999829i	$0.494120\pi$
$948$			2.27362i			0.0738439i
$949$	43.1769	−	43.1769i	1.40158	−	1.40158i
$950$		0			0
$951$	−2.78461			−0.0902972
$952$			13.3843i			0.433786i
$953$	−20.9222	+	20.9222i	−0.677736	+	0.677736i	−0.959488	−	0.281751i	$-0.909085\pi$
$953$	−20.9222	+	20.9222i	−0.677736	+	0.677736i	0.281751	+	0.959488i	$0.409085\pi$
$954$			38.2487i			1.23835i
$955$		0			0
$956$	−42.9282			−1.38840
$957$		−	5.37945i		−	0.173893i
$958$	−58.9165			−1.90351
$959$	62.4449			2.01645
$960$		0			0
$961$	−7.39230			−0.238461
$962$	41.8172			1.34824
$963$		−	15.8338i		−	0.510235i
$964$	−25.6077			−0.824768
$965$		0			0
$966$			21.4641i			0.690596i
$967$	−23.0064	+	23.0064i	−0.739834	+	0.739834i	−0.972546	−	0.232711i	$-0.925240\pi$
$967$	−23.0064	+	23.0064i	−0.739834	+	0.739834i	0.232711	+	0.972546i	$0.425240\pi$
$968$		−	24.2918i		−	0.780769i
$969$	−1.53590			−0.0493402
$970$		0			0
$971$	2.36603	−	2.36603i	0.0759294	−	0.0759294i	−0.668122	−	0.744052i	$-0.732902\pi$
$971$	2.36603	−	2.36603i	0.0759294	−	0.0759294i	0.744052	+	0.668122i	$0.232902\pi$
$972$		−	24.6980i		−	0.792188i
$973$	48.8139			1.56490
$974$	8.87564	−	8.87564i	0.284394	−	0.284394i
$975$		0			0
$976$	−12.7846	+	12.7846i	−0.409225	+	0.409225i
$977$	−25.0261	+	25.0261i	−0.800657	+	0.800657i	−0.983198	−	0.182541i	$-0.941568\pi$
$977$	−25.0261	+	25.0261i	−0.800657	+	0.800657i	0.182541	+	0.983198i	$0.441568\pi$
$978$	6.51626			0.208367
$979$	11.2750	−	11.2750i	0.360350	−	0.360350i
$980$		0			0
$981$	25.6603	+	25.6603i	0.819269	+	0.819269i
$982$	−28.7375	+	28.7375i	−0.917052	+	0.917052i
$983$	−14.5582	−	14.5582i	−0.464336	−	0.464336i	0.435738	−	0.900074i	$-0.356487\pi$
$983$	−14.5582	−	14.5582i	−0.464336	−	0.464336i	−0.900074	+	0.435738i	$0.856487\pi$
$984$	0.679492			0.0216614
$985$		0			0
$986$	9.46410			0.301398
$987$		−	4.89898i		−	0.155936i
$988$	−20.5569	+	20.5569i	−0.654001	+	0.654001i
$989$	2.87564	+	2.87564i	0.0914402	+	0.0914402i
$990$		0			0
$991$			12.5885i			0.399886i	0.979808	+	0.199943i	$0.0640756\pi$
$991$			12.5885i			0.399886i	−0.979808	+	0.199943i	$0.935924\pi$
$992$			35.0507i			1.11286i
$993$	10.0890	+	10.0890i	0.320164	+	0.320164i
$994$	−4.39230	+	4.39230i	−0.139315	+	0.139315i
$995$		0			0
$996$	18.0000			0.570352
$997$	−28.9134			−0.915697			−0.457848	−	0.889030i	$-0.651380\pi$
$997$	−28.9134			−0.915697			−0.457848	+	0.889030i	$0.651380\pi$
$998$	32.5269	−	32.5269i	1.02962	−	1.02962i
$999$		−	17.9090i		−	0.566615i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.j.b.43.1	✓	8
4.3	odd	2		1600.2.j.b.143.3		8
5.2	odd	4		400.2.s.b.107.1	yes	8
5.3	odd	4		400.2.s.b.107.4	yes	8
5.4	even	2	inner	400.2.j.b.43.4	yes	8
16.3	odd	4		400.2.s.b.243.3	yes	8
16.13	even	4		1600.2.s.b.943.3		8
20.3	even	4		1600.2.s.b.207.2		8
20.7	even	4		1600.2.s.b.207.3		8
20.19	odd	2		1600.2.j.b.143.2		8
80.3	even	4	inner	400.2.j.b.307.3	yes	8
80.13	odd	4		1600.2.j.b.1007.3		8
80.19	odd	4		400.2.s.b.243.2	yes	8
80.29	even	4		1600.2.s.b.943.2		8
80.67	even	4	inner	400.2.j.b.307.2	yes	8
80.77	odd	4		1600.2.j.b.1007.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.j.b.43.1	✓	8	1.1	even	1	trivial
400.2.j.b.43.4	yes	8	5.4	even	2	inner
400.2.j.b.307.2	yes	8	80.67	even	4	inner
400.2.j.b.307.3	yes	8	80.3	even	4	inner
400.2.s.b.107.1	yes	8	5.2	odd	4
400.2.s.b.107.4	yes	8	5.3	odd	4
400.2.s.b.243.2	yes	8	80.19	odd	4
400.2.s.b.243.3	yes	8	16.3	odd	4
1600.2.j.b.143.2		8	20.19	odd	2
1600.2.j.b.143.3		8	4.3	odd	2
1600.2.j.b.1007.2		8	80.77	odd	4
1600.2.j.b.1007.3		8	80.13	odd	4
1600.2.s.b.207.2		8	20.3	even	4
1600.2.s.b.207.3		8	20.7	even	4
1600.2.s.b.943.2		8	80.29	even	4
1600.2.s.b.943.3		8	16.13	even	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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} -0.517638i q^{3} +2.00000 q^{4} +0.732051i q^{6} +(3.34607 - 3.34607i) q^{7} -2.82843 q^{8} +2.73205 q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} -0.517638i q^{3} +2.00000 q^{4} +0.732051i q^{6} +(3.34607 - 3.34607i) q^{7} -2.82843 q^{8} +2.73205 q^{9} +(-1.09808 + 1.09808i) q^{11} -1.03528i q^{12} -4.89898 q^{13} +(-4.73205 + 4.73205i) q^{14} +4.00000 q^{16} +(0.707107 - 0.707107i) q^{17} -3.86370 q^{18} +(2.09808 - 2.09808i) q^{19} +(-1.73205 - 1.73205i) q^{21} +(1.55291 - 1.55291i) q^{22} +(4.38134 + 4.38134i) q^{23} +1.46410i q^{24} +6.92820 q^{26} -2.96713i q^{27} +(6.69213 - 6.69213i) q^{28} +(-4.73205 - 4.73205i) q^{29} -6.19615i q^{31} -5.65685 q^{32} +(0.568406 + 0.568406i) q^{33} +(-1.00000 + 1.00000i) q^{34} +5.46410 q^{36} +6.03579 q^{37} +(-2.96713 + 2.96713i) q^{38} +2.53590i q^{39} -0.464102i q^{41} +(2.44949 + 2.44949i) q^{42} +0.656339 q^{43} +(-2.19615 + 2.19615i) q^{44} +(-6.19615 - 6.19615i) q^{46} +(1.41421 + 1.41421i) q^{47} -2.07055i q^{48} -15.3923i q^{49} +(-0.366025 - 0.366025i) q^{51} -9.79796 q^{52} -9.89949i q^{53} +4.19615i q^{54} +(-9.46410 + 9.46410i) q^{56} +(-1.08604 - 1.08604i) q^{57} +(6.69213 + 6.69213i) q^{58} +(7.73205 + 7.73205i) q^{59} +(-3.19615 + 3.19615i) q^{61} +8.76268i q^{62} +(9.14162 - 9.14162i) q^{63} +8.00000 q^{64} +(-0.803848 - 0.803848i) q^{66} +5.79555 q^{67} +(1.41421 - 1.41421i) q^{68} +(2.26795 - 2.26795i) q^{69} +0.928203 q^{71} -7.72741 q^{72} +(-8.81345 + 8.81345i) q^{73} -8.53590 q^{74} +(4.19615 - 4.19615i) q^{76} +7.34847i q^{77} -3.58630i q^{78} -2.19615 q^{79} +6.66025 q^{81} +0.656339i q^{82} +17.3867i q^{83} +(-3.46410 - 3.46410i) q^{84} -0.928203 q^{86} +(-2.44949 + 2.44949i) q^{87} +(3.10583 - 3.10583i) q^{88} -10.2679 q^{89} +(-16.3923 + 16.3923i) q^{91} +(8.76268 + 8.76268i) q^{92} -3.20736 q^{93} +(-2.00000 - 2.00000i) q^{94} +2.92820i q^{96} +(-11.5911 + 11.5911i) q^{97} +21.7680i q^{98} +(-3.00000 + 3.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{4} + 8 q^{9}+O(q^{10}) \) 8 * q + 16 * q^4 + 8 * q^9	\( 8 q + 16 q^{4} + 8 q^{9} + 12 q^{11} - 24 q^{14} + 32 q^{16} - 4 q^{19} - 24 q^{29} - 8 q^{34} + 16 q^{36} + 24 q^{44} - 8 q^{46} + 4 q^{51} - 48 q^{56} + 48 q^{59} + 16 q^{61} + 64 q^{64} - 48 q^{66} + 32 q^{69} - 48 q^{71} - 96 q^{74} - 8 q^{76} + 24 q^{79} - 16 q^{81} + 48 q^{86} - 96 q^{89} - 48 q^{91} - 16 q^{94} - 24 q^{99}+O(q^{100}) \) 8 * q + 16 * q^4 + 8 * q^9 + 12 * q^11 - 24 * q^14 + 32 * q^16 - 4 * q^19 - 24 * q^29 - 8 * q^34 + 16 * q^36 + 24 * q^44 - 8 * q^46 + 4 * q^51 - 48 * q^56 + 48 * q^59 + 16 * q^61 + 64 * q^64 - 48 * q^66 + 32 * q^69 - 48 * q^71 - 96 * q^74 - 8 * q^76 + 24 * q^79 - 16 * q^81 + 48 * q^86 - 96 * q^89 - 48 * q^91 - 16 * q^94 - 24 * q^99

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