LMFDB - Embedded newform 400.2.l.d.101.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [400,2,Mod(101,400)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(400, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("400.101"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-4,-2,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{11})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 9 $ x^4 - 5*x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			101.1
Root			$-1.65831 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	400.101
Dual form			400.2.l.d.301.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 + 1.00000i) q^{2} +(-2.15831 + 2.15831i) q^{3} -2.00000i q^{4} -4.31662i q^{6} -2.31662i q^{7} +(2.00000 + 2.00000i) q^{8} -6.31662i q^{9} +(3.15831 + 3.15831i) q^{11} +(4.31662 + 4.31662i) q^{12} +(4.31662 - 4.31662i) q^{13} +(2.31662 + 2.31662i) q^{14} -4.00000 q^{16} -1.31662 q^{17} +(6.31662 + 6.31662i) q^{18} +(-0.158312 + 0.158312i) q^{19} +(5.00000 + 5.00000i) q^{21} -6.31662 q^{22} -0.316625i q^{23} -8.63325 q^{24} +8.63325i q^{26} +(7.15831 + 7.15831i) q^{27} -4.63325 q^{28} +(2.00000 - 2.00000i) q^{29} -2.31662 q^{31} +(4.00000 - 4.00000i) q^{32} -13.6332 q^{33} +(1.31662 - 1.31662i) q^{34} -12.6332 q^{36} +(-0.683375 - 0.683375i) q^{37} -0.316625i q^{38} +18.6332i q^{39} +5.00000i q^{41} -10.0000 q^{42} +(7.63325 + 7.63325i) q^{43} +(6.31662 - 6.31662i) q^{44} +(0.316625 + 0.316625i) q^{46} +8.00000 q^{47} +(8.63325 - 8.63325i) q^{48} +1.63325 q^{49} +(2.84169 - 2.84169i) q^{51} +(-8.63325 - 8.63325i) q^{52} +(3.31662 + 3.31662i) q^{53} -14.3166 q^{54} +(4.63325 - 4.63325i) q^{56} -0.683375i q^{57} +4.00000i q^{58} +(-1.31662 - 1.31662i) q^{59} +(9.63325 - 9.63325i) q^{61} +(2.31662 - 2.31662i) q^{62} -14.6332 q^{63} +8.00000i q^{64} +(13.6332 - 13.6332i) q^{66} +(-9.15831 + 9.15831i) q^{67} +2.63325i q^{68} +(0.683375 + 0.683375i) q^{69} -8.63325i q^{71} +(12.6332 - 12.6332i) q^{72} -6.68338i q^{73} +1.36675 q^{74} +(0.316625 + 0.316625i) q^{76} +(7.31662 - 7.31662i) q^{77} +(-18.6332 - 18.6332i) q^{78} +4.31662 q^{79} -11.9499 q^{81} +(-5.00000 - 5.00000i) q^{82} +(7.15831 - 7.15831i) q^{83} +(10.0000 - 10.0000i) q^{84} -15.2665 q^{86} +8.63325i q^{87} +12.6332i q^{88} +3.94987i q^{89} +(-10.0000 - 10.0000i) q^{91} -0.633250 q^{92} +(5.00000 - 5.00000i) q^{93} +(-8.00000 + 8.00000i) q^{94} +17.2665i q^{96} +6.63325 q^{97} +(-1.63325 + 1.63325i) q^{98} +(19.9499 - 19.9499i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 2 q^{3} + 8 q^{8} + 6 q^{11} + 4 q^{12} + 4 q^{13} - 4 q^{14} - 16 q^{16} + 8 q^{17} + 12 q^{18} + 6 q^{19} + 20 q^{21} - 12 q^{22} - 8 q^{24} + 22 q^{27} + 8 q^{28} + 8 q^{29} + 4 q^{31}+ \cdots + 40 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 2 * q^3 + 8 * q^8 + 6 * q^11 + 4 * q^12 + 4 * q^13 - 4 * q^14 - 16 * q^16 + 8 * q^17 + 12 * q^18 + 6 * q^19 + 20 * q^21 - 12 * q^22 - 8 * q^24 + 22 * q^27 + 8 * q^28 + 8 * q^29 + 4 * q^31 + 16 * q^32 - 28 * q^33 - 8 * q^34 - 24 * q^36 - 16 * q^37 - 40 * q^42 + 4 * q^43 + 12 * q^44 - 12 * q^46 + 32 * q^47 + 8 * q^48 - 20 * q^49 + 18 * q^51 - 8 * q^52 - 44 * q^54 - 8 * q^56 + 8 * q^59 + 12 * q^61 - 4 * q^62 - 32 * q^63 + 28 * q^66 - 30 * q^67 + 16 * q^69 + 24 * q^72 + 32 * q^74 - 12 * q^76 + 16 * q^77 - 48 * q^78 + 4 * q^79 - 8 * q^81 - 20 * q^82 + 22 * q^83 + 40 * q^84 - 8 * q^86 - 40 * q^91 + 24 * q^92 + 20 * q^93 - 32 * q^94 + 20 * q^98 + 40 * q^99

Character values

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

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

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 $

$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$3$	−2.15831	+	2.15831i	−1.24610	+	1.24610i	−0.288675	+	0.957427i	$0.593215\pi$
$3$	−2.15831	+	2.15831i	−1.24610	+	1.24610i	−0.957427	+	0.288675i	$0.906785\pi$
$4$		−	2.00000i		−	1.00000i
$5$		0			0
$5$		0			0
$6$		−	4.31662i		−	1.76225i
$7$		−	2.31662i		−	0.875602i	−0.899072	−	0.437801i	$-0.855757\pi$
$7$		−	2.31662i		−	0.875602i	0.899072	−	0.437801i	$-0.144243\pi$
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$		−	6.31662i		−	2.10554i
$10$		0			0
$11$	3.15831	+	3.15831i	0.952267	+	0.952267i	0.998912	−	0.0466445i	$-0.0148528\pi$
$11$	3.15831	+	3.15831i	0.952267	+	0.952267i	−0.0466445	+	0.998912i	$0.514853\pi$
$12$	4.31662	+	4.31662i	1.24610	+	1.24610i
$13$	4.31662	−	4.31662i	1.19722	−	1.19722i	0.222220	−	0.974997i	$-0.428670\pi$
$13$	4.31662	−	4.31662i	1.19722	−	1.19722i	0.974997	−	0.222220i	$-0.0713302\pi$
$14$	2.31662	+	2.31662i	0.619144	+	0.619144i
$15$		0			0
$16$	−4.00000			−1.00000
$17$	−1.31662			−0.319328			−0.159664	−	0.987171i	$-0.551041\pi$
$17$	−1.31662			−0.319328			−0.159664	+	0.987171i	$0.551041\pi$
$18$	6.31662	+	6.31662i	1.48884	+	1.48884i
$19$	−0.158312	+	0.158312i	−0.0363194	+	0.0363194i	−0.725033	−	0.688714i	$-0.758176\pi$
$19$	−0.158312	+	0.158312i	−0.0363194	+	0.0363194i	0.688714	+	0.725033i	$0.258176\pi$
$20$		0			0
$21$	5.00000	+	5.00000i	1.09109	+	1.09109i
$22$	−6.31662			−1.34671
$23$		−	0.316625i		−	0.0660208i	−0.999455	−	0.0330104i	$-0.989491\pi$
$23$		−	0.316625i		−	0.0660208i	0.999455	−	0.0330104i	$-0.0105095\pi$
$24$	−8.63325			−1.76225
$25$		0			0
$26$			8.63325i			1.69312i
$27$	7.15831	+	7.15831i	1.37762	+	1.37762i
$28$	−4.63325			−0.875602
$29$	2.00000	−	2.00000i	0.371391	−	0.371391i	−0.496593	−	0.867984i	$-0.665416\pi$
$29$	2.00000	−	2.00000i	0.371391	−	0.371391i	0.867984	+	0.496593i	$0.165416\pi$
$30$		0			0
$31$	−2.31662			−0.416078			−0.208039	−	0.978121i	$-0.566708\pi$
$31$	−2.31662			−0.416078			−0.208039	+	0.978121i	$0.566708\pi$
$32$	4.00000	−	4.00000i	0.707107	−	0.707107i
$33$	−13.6332			−2.37324
$34$	1.31662	−	1.31662i	0.225799	−	0.225799i
$35$		0			0
$36$	−12.6332			−2.10554
$37$	−0.683375	−	0.683375i	−0.112346	−	0.112346i	0.648699	−	0.761045i	$-0.275313\pi$
$37$	−0.683375	−	0.683375i	−0.112346	−	0.112346i	−0.761045	+	0.648699i	$0.775313\pi$
$38$		−	0.316625i		−	0.0513633i
$39$			18.6332i			2.98371i
$40$		0			0
$41$			5.00000i			0.780869i	0.920631	+	0.390434i	$0.127675\pi$
$41$			5.00000i			0.780869i	−0.920631	+	0.390434i	$0.872325\pi$
$42$	−10.0000			−1.54303
$43$	7.63325	+	7.63325i	1.16406	+	1.16406i	0.983578	+	0.180481i	$0.0577655\pi$
$43$	7.63325	+	7.63325i	1.16406	+	1.16406i	0.180481	+	0.983578i	$0.442234\pi$
$44$	6.31662	−	6.31662i	0.952267	−	0.952267i
$45$		0			0
$46$	0.316625	+	0.316625i	0.0466838	+	0.0466838i
$47$	8.00000			1.16692			0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000			1.16692			0.583460	+	0.812142i	$0.301699\pi$
$48$	8.63325	−	8.63325i	1.24610	−	1.24610i
$49$	1.63325			0.233321
$50$		0			0
$51$	2.84169	−	2.84169i	0.397916	−	0.397916i
$52$	−8.63325	−	8.63325i	−1.19722	−	1.19722i
$53$	3.31662	+	3.31662i	0.455573	+	0.455573i	0.897199	−	0.441626i	$-0.145598\pi$
$53$	3.31662	+	3.31662i	0.455573	+	0.455573i	−0.441626	+	0.897199i	$0.645598\pi$
$54$	−14.3166			−1.94825
$55$		0			0
$56$	4.63325	−	4.63325i	0.619144	−	0.619144i
$57$		−	0.683375i		−	0.0905153i
$58$			4.00000i			0.525226i
$59$	−1.31662	−	1.31662i	−0.171410	−	0.171410i	0.616189	−	0.787599i	$-0.288676\pi$
$59$	−1.31662	−	1.31662i	−0.171410	−	0.171410i	−0.787599	+	0.616189i	$0.788676\pi$
$60$		0			0
$61$	9.63325	−	9.63325i	1.23341	−	1.23341i	0.270766	−	0.962645i	$-0.412723\pi$
$61$	9.63325	−	9.63325i	1.23341	−	1.23341i	0.962645	−	0.270766i	$-0.0872770\pi$
$62$	2.31662	−	2.31662i	0.294212	−	0.294212i
$63$	−14.6332			−1.84362
$64$			8.00000i			1.00000i
$65$		0			0
$66$	13.6332	−	13.6332i	1.67814	−	1.67814i
$67$	−9.15831	+	9.15831i	−1.11887	+	1.11887i	−0.126958	+	0.991908i	$0.540521\pi$
$67$	−9.15831	+	9.15831i	−1.11887	+	1.11887i	−0.991908	+	0.126958i	$0.959479\pi$
$68$			2.63325i			0.319328i
$69$	0.683375	+	0.683375i	0.0822687	+	0.0822687i
$70$		0			0
$71$		−	8.63325i		−	1.02458i	−0.858813	−	0.512289i	$-0.828798\pi$
$71$		−	8.63325i		−	1.02458i	0.858813	−	0.512289i	$-0.171202\pi$
$72$	12.6332	−	12.6332i	1.48884	−	1.48884i
$73$		−	6.68338i		−	0.782230i	−0.920342	−	0.391115i	$-0.872089\pi$
$73$		−	6.68338i		−	0.782230i	0.920342	−	0.391115i	$-0.127911\pi$
$74$	1.36675			0.158882
$75$		0			0
$76$	0.316625	+	0.316625i	0.0363194	+	0.0363194i
$77$	7.31662	−	7.31662i	0.833807	−	0.833807i
$78$	−18.6332	−	18.6332i	−2.10980	−	2.10980i
$79$	4.31662			0.485658			0.242829	−	0.970069i	$-0.421925\pi$
$79$	4.31662			0.485658			0.242829	+	0.970069i	$0.421925\pi$
$80$		0			0
$81$	−11.9499			−1.32776
$82$	−5.00000	−	5.00000i	−0.552158	−	0.552158i
$83$	7.15831	−	7.15831i	0.785727	−	0.785727i	−0.195064	−	0.980791i	$-0.562491\pi$
$83$	7.15831	−	7.15831i	0.785727	−	0.785727i	0.980791	+	0.195064i	$0.0624914\pi$
$84$	10.0000	−	10.0000i	1.09109	−	1.09109i
$85$		0			0
$86$	−15.2665			−1.64623
$87$			8.63325i			0.925582i
$88$			12.6332i			1.34671i
$89$			3.94987i			0.418686i	0.977842	+	0.209343i	$0.0671325\pi$
$89$			3.94987i			0.418686i	−0.977842	+	0.209343i	$0.932868\pi$
$90$		0			0
$91$	−10.0000	−	10.0000i	−1.04828	−	1.04828i
$92$	−0.633250			−0.0660208
$93$	5.00000	−	5.00000i	0.518476	−	0.518476i
$94$	−8.00000	+	8.00000i	−0.825137	+	0.825137i
$95$		0			0
$96$			17.2665i			1.76225i
$97$	6.63325			0.673504			0.336752	−	0.941593i	$-0.390672\pi$
$97$	6.63325			0.673504			0.336752	+	0.941593i	$0.390672\pi$
$98$	−1.63325	+	1.63325i	−0.164983	+	0.164983i
$99$	19.9499	−	19.9499i	2.00504	−	2.00504i
$100$		0			0
$101$	5.31662	+	5.31662i	0.529024	+	0.529024i	0.920281	−	0.391257i	$-0.127960\pi$
$101$	5.31662	+	5.31662i	0.529024	+	0.529024i	−0.391257	+	0.920281i	$0.627960\pi$
$102$			5.68338i			0.562738i
$103$		−	4.63325i		−	0.456528i	−0.973599	−	0.228264i	$-0.926695\pi$
$103$		−	4.63325i		−	0.456528i	0.973599	−	0.228264i	$-0.0733049\pi$
$104$	17.2665			1.69312
$105$		0			0
$106$	−6.63325			−0.644278
$107$	2.84169	+	2.84169i	0.274716	+	0.274716i	0.830995	−	0.556279i	$-0.187771\pi$
$107$	2.84169	+	2.84169i	0.274716	+	0.274716i	−0.556279	+	0.830995i	$0.687771\pi$
$108$	14.3166	−	14.3166i	1.37762	−	1.37762i
$109$	−5.94987	+	5.94987i	−0.569895	+	0.569895i	−0.932099	−	0.362204i	$-0.882024\pi$
$109$	−5.94987	+	5.94987i	−0.569895	+	0.569895i	0.362204	+	0.932099i	$0.382024\pi$
$110$		0			0
$111$	2.94987			0.279990
$112$			9.26650i			0.875602i
$113$	−2.36675			−0.222645			−0.111323	−	0.993784i	$-0.535509\pi$
$113$	−2.36675			−0.222645			−0.111323	+	0.993784i	$0.535509\pi$
$114$	0.683375	+	0.683375i	0.0640040	+	0.0640040i
$115$		0			0
$116$	−4.00000	−	4.00000i	−0.371391	−	0.371391i
$117$	−27.2665	−	27.2665i	−2.52079	−	2.52079i
$118$	2.63325			0.242410
$119$			3.05013i			0.279605i
$120$		0			0
$121$			8.94987i			0.813625i
$122$			19.2665i			1.74431i
$123$	−10.7916	−	10.7916i	−0.973042	−	0.973042i
$124$			4.63325i			0.416078i
$125$		0			0
$126$	14.6332	−	14.6332i	1.30363	−	1.30363i
$127$	−6.31662			−0.560510			−0.280255	−	0.959926i	$-0.590419\pi$
$127$	−6.31662			−0.560510			−0.280255	+	0.959926i	$0.590419\pi$
$128$	−8.00000	−	8.00000i	−0.707107	−	0.707107i
$129$	−32.9499			−2.90107
$130$		0			0
$131$	1.00000	−	1.00000i	0.0873704	−	0.0873704i	−0.662071	−	0.749441i	$-0.730322\pi$
$131$	1.00000	−	1.00000i	0.0873704	−	0.0873704i	0.749441	+	0.662071i	$0.230322\pi$
$132$			27.2665i			2.37324i
$133$	0.366750	+	0.366750i	0.0318013	+	0.0318013i
$134$		−	18.3166i		−	1.58232i
$135$		0			0
$136$	−2.63325	−	2.63325i	−0.225799	−	0.225799i
$137$		−	11.6332i		−	0.993896i	−0.867780	−	0.496948i	$-0.834454\pi$
$137$		−	11.6332i		−	0.993896i	0.867780	−	0.496948i	$-0.165546\pi$
$138$	−1.36675			−0.116346
$139$	−9.15831	−	9.15831i	−0.776798	−	0.776798i	0.202487	−	0.979285i	$-0.435098\pi$
$139$	−9.15831	−	9.15831i	−0.776798	−	0.776798i	−0.979285	+	0.202487i	$0.935098\pi$
$140$		0			0
$141$	−17.2665	+	17.2665i	−1.45410	+	1.45410i
$142$	8.63325	+	8.63325i	0.724486	+	0.724486i
$143$	27.2665			2.28014
$144$			25.2665i			2.10554i
$145$		0			0
$146$	6.68338	+	6.68338i	0.553120	+	0.553120i
$147$	−3.52506	+	3.52506i	−0.290742	+	0.290742i
$148$	−1.36675	+	1.36675i	−0.112346	+	0.112346i
$149$	16.6332	+	16.6332i	1.36265	+	1.36265i	0.870525	+	0.492124i	$0.163779\pi$
$149$	16.6332	+	16.6332i	1.36265	+	1.36265i	0.492124	+	0.870525i	$0.336221\pi$
$150$		0			0
$151$			4.31662i			0.351282i	0.984454	+	0.175641i	$0.0561998\pi$
$151$			4.31662i			0.351282i	−0.984454	+	0.175641i	$0.943800\pi$
$152$	−0.633250			−0.0513633
$153$			8.31662i			0.672359i
$154$			14.6332i			1.17918i
$155$		0			0
$156$	37.2665			2.98371
$157$	−11.3166	+	11.3166i	−0.903165	+	0.903165i	−0.995709	−	0.0925436i	$-0.970500\pi$
$157$	−11.3166	+	11.3166i	−0.903165	+	0.903165i	0.0925436	+	0.995709i	$0.470500\pi$
$158$	−4.31662	+	4.31662i	−0.343412	+	0.343412i
$159$	−14.3166			−1.13538
$160$		0			0
$161$	−0.733501			−0.0578080
$162$	11.9499	−	11.9499i	0.938871	−	0.938871i
$163$	7.15831	−	7.15831i	0.560682	−	0.560682i	−0.368819	−	0.929501i	$-0.620238\pi$
$163$	7.15831	−	7.15831i	0.560682	−	0.560682i	0.929501	+	0.368819i	$0.120238\pi$
$164$	10.0000			0.780869
$165$		0			0
$166$			14.3166i			1.11119i
$167$		−	18.0000i		−	1.39288i	−0.717614	−	0.696441i	$-0.754766\pi$
$167$		−	18.0000i		−	1.39288i	0.717614	−	0.696441i	$-0.245234\pi$
$168$			20.0000i			1.54303i
$169$		−	24.2665i		−	1.86665i
$170$		0			0
$171$	1.00000	+	1.00000i	0.0764719	+	0.0764719i
$172$	15.2665	−	15.2665i	1.16406	−	1.16406i
$173$	−12.9499	+	12.9499i	−0.984561	+	0.984561i	−0.999883	−	0.0153219i	$-0.995123\pi$
$173$	−12.9499	+	12.9499i	−0.984561	+	0.984561i	0.0153219	+	0.999883i	$0.495123\pi$
$174$	−8.63325	−	8.63325i	−0.654485	−	0.654485i
$175$		0			0
$176$	−12.6332	−	12.6332i	−0.952267	−	0.952267i
$177$	5.68338			0.427189
$178$	−3.94987	−	3.94987i	−0.296056	−	0.296056i
$179$	−8.79156	+	8.79156i	−0.657112	+	0.657112i	−0.954696	−	0.297584i	$-0.903819\pi$
$179$	−8.79156	+	8.79156i	−0.657112	+	0.657112i	0.297584	+	0.954696i	$0.403819\pi$
$180$		0			0
$181$	−3.31662	−	3.31662i	−0.246523	−	0.246523i	0.573019	−	0.819542i	$-0.305772\pi$
$181$	−3.31662	−	3.31662i	−0.246523	−	0.246523i	−0.819542	+	0.573019i	$0.805772\pi$
$182$	20.0000			1.48250
$183$			41.5831i			3.07391i
$184$	0.633250	−	0.633250i	0.0466838	−	0.0466838i
$185$		0			0
$186$			10.0000i			0.733236i
$187$	−4.15831	−	4.15831i	−0.304086	−	0.304086i
$188$		−	16.0000i		−	1.16692i
$189$	16.5831	−	16.5831i	1.20624	−	1.20624i
$190$		0			0
$191$	−20.9499			−1.51588			−0.757940	−	0.652324i	$-0.773794\pi$
$191$	−20.9499			−1.51588			−0.757940	+	0.652324i	$0.773794\pi$
$192$	−17.2665	−	17.2665i	−1.24610	−	1.24610i
$193$	4.68338			0.337117			0.168558	−	0.985692i	$-0.446089\pi$
$193$	4.68338			0.337117			0.168558	+	0.985692i	$0.446089\pi$
$194$	−6.63325	+	6.63325i	−0.476240	+	0.476240i
$195$		0			0
$196$		−	3.26650i		−	0.233321i
$197$	16.5831	+	16.5831i	1.18150	+	1.18150i	0.979356	+	0.202143i	$0.0647904\pi$
$197$	16.5831	+	16.5831i	1.18150	+	1.18150i	0.202143	+	0.979356i	$0.435210\pi$
$198$			39.8997i			2.83555i
$199$		−	12.6332i		−	0.895547i	−0.894147	−	0.447774i	$-0.852217\pi$
$199$		−	12.6332i		−	0.895547i	0.894147	−	0.447774i	$-0.147783\pi$
$200$		0			0
$201$		−	39.5330i		−	2.78844i
$202$	−10.6332			−0.748153
$203$	−4.63325	−	4.63325i	−0.325190	−	0.325190i
$204$	−5.68338	−	5.68338i	−0.397916	−	0.397916i
$205$		0			0
$206$	4.63325	+	4.63325i	0.322814	+	0.322814i
$207$	−2.00000			−0.139010
$208$	−17.2665	+	17.2665i	−1.19722	+	1.19722i
$209$	−1.00000			−0.0691714
$210$		0			0
$211$	11.7916	−	11.7916i	0.811765	−	0.811765i	−0.173134	−	0.984898i	$-0.555389\pi$
$211$	11.7916	−	11.7916i	0.811765	−	0.811765i	0.984898	+	0.173134i	$0.0553893\pi$
$212$	6.63325	−	6.63325i	0.455573	−	0.455573i
$213$	18.6332	+	18.6332i	1.27673	+	1.27673i
$214$	−5.68338			−0.388508
$215$		0			0
$216$			28.6332i			1.94825i
$217$			5.36675i			0.364319i
$218$		−	11.8997i		−	0.805953i
$219$	14.4248	+	14.4248i	0.974738	+	0.974738i
$220$		0			0
$221$	−5.68338	+	5.68338i	−0.382305	+	0.382305i
$222$	−2.94987	+	2.94987i	−0.197983	+	0.197983i
$223$	−6.00000			−0.401790			−0.200895	−	0.979613i	$-0.564385\pi$
$223$	−6.00000			−0.401790			−0.200895	+	0.979613i	$0.564385\pi$
$224$	−9.26650	−	9.26650i	−0.619144	−	0.619144i
$225$		0			0
$226$	2.36675	−	2.36675i	0.157434	−	0.157434i
$227$	4.36675	−	4.36675i	0.289831	−	0.289831i	−0.547182	−	0.837014i	$-0.684300\pi$
$227$	4.36675	−	4.36675i	0.289831	−	0.289831i	0.837014	+	0.547182i	$0.184300\pi$
$228$	−1.36675			−0.0905153
$229$	−2.00000	−	2.00000i	−0.132164	−	0.132164i	0.637930	−	0.770094i	$-0.279791\pi$
$229$	−2.00000	−	2.00000i	−0.132164	−	0.132164i	−0.770094	+	0.637930i	$0.779791\pi$
$230$		0			0
$231$			31.5831i			2.07802i
$232$	8.00000			0.525226
$233$		−	11.8997i		−	0.779578i	−0.920904	−	0.389789i	$-0.872548\pi$
$233$		−	11.8997i		−	0.779578i	0.920904	−	0.389789i	$-0.127452\pi$
$234$	54.5330			3.56493
$235$		0			0
$236$	−2.63325	+	2.63325i	−0.171410	+	0.171410i
$237$	−9.31662	+	9.31662i	−0.605180	+	0.605180i
$238$	−3.05013	−	3.05013i	−0.197710	−	0.197710i
$239$	−18.6332			−1.20528			−0.602642	−	0.798011i	$-0.705885\pi$
$239$	−18.6332			−1.20528			−0.602642	+	0.798011i	$0.705885\pi$
$240$		0			0
$241$	18.5831			1.19704			0.598522	−	0.801106i	$-0.295755\pi$
$241$	18.5831			1.19704			0.598522	+	0.801106i	$0.295755\pi$
$242$	−8.94987	−	8.94987i	−0.575320	−	0.575320i
$243$	4.31662	−	4.31662i	0.276912	−	0.276912i
$244$	−19.2665	−	19.2665i	−1.23341	−	1.23341i
$245$		0			0
$246$	21.5831			1.37609
$247$			1.36675i			0.0869642i
$248$	−4.63325	−	4.63325i	−0.294212	−	0.294212i
$249$			30.8997i			1.95819i
$250$		0			0
$251$	−9.10819	−	9.10819i	−0.574904	−	0.574904i	0.358591	−	0.933495i	$-0.383257\pi$
$251$	−9.10819	−	9.10819i	−0.574904	−	0.574904i	−0.933495	+	0.358591i	$0.883257\pi$
$252$			29.2665i			1.84362i
$253$	1.00000	−	1.00000i	0.0628695	−	0.0628695i
$254$	6.31662	−	6.31662i	0.396340	−	0.396340i
$255$		0			0
$256$	16.0000			1.00000
$257$	16.6332			1.03755			0.518777	−	0.854910i	$-0.326388\pi$
$257$	16.6332			1.03755			0.518777	+	0.854910i	$0.326388\pi$
$258$	32.9499	−	32.9499i	2.05137	−	2.05137i
$259$	−1.58312	+	1.58312i	−0.0983705	+	0.0983705i
$260$		0			0
$261$	−12.6332	−	12.6332i	−0.781979	−	0.781979i
$262$			2.00000i			0.123560i
$263$			15.5831i			0.960897i	0.877023	+	0.480448i	$0.159526\pi$
$263$			15.5831i			0.960897i	−0.877023	+	0.480448i	$0.840474\pi$
$264$	−27.2665	−	27.2665i	−1.67814	−	1.67814i
$265$		0			0
$266$	−0.733501			−0.0449738
$267$	−8.52506	−	8.52506i	−0.521725	−	0.521725i
$268$	18.3166	+	18.3166i	1.11887	+	1.11887i
$269$	6.31662	−	6.31662i	0.385131	−	0.385131i	−0.487815	−	0.872947i	$-0.662206\pi$
$269$	6.31662	−	6.31662i	0.385131	−	0.385131i	0.872947	+	0.487815i	$0.162206\pi$
$270$		0			0
$271$	−0.949874			−0.0577008			−0.0288504	−	0.999584i	$-0.509185\pi$
$271$	−0.949874			−0.0577008			−0.0288504	+	0.999584i	$0.509185\pi$
$272$	5.26650			0.319328
$273$	43.1662			2.61254
$274$	11.6332	+	11.6332i	0.702790	+	0.702790i
$275$		0			0
$276$	1.36675	−	1.36675i	0.0822687	−	0.0822687i
$277$	14.3166	+	14.3166i	0.860203	+	0.860203i	0.991361	−	0.131159i	$-0.0418698\pi$
$277$	14.3166	+	14.3166i	0.860203	+	0.860203i	−0.131159	+	0.991361i	$0.541870\pi$
$278$	18.3166			1.09856
$279$			14.6332i			0.876070i
$280$		0			0
$281$			7.26650i			0.433483i	0.976229	+	0.216741i	$0.0695429\pi$
$281$			7.26650i			0.433483i	−0.976229	+	0.216741i	$0.930457\pi$
$282$		−	34.5330i		−	2.05641i
$283$	−3.84169	−	3.84169i	−0.228365	−	0.228365i	0.583645	−	0.812009i	$-0.301626\pi$
$283$	−3.84169	−	3.84169i	−0.228365	−	0.228365i	−0.812009	+	0.583645i	$0.801626\pi$
$284$	−17.2665			−1.02458
$285$		0			0
$286$	−27.2665	+	27.2665i	−1.61230	+	1.61230i
$287$	11.5831			0.683730
$288$	−25.2665	−	25.2665i	−1.48884	−	1.48884i
$289$	−15.2665			−0.898029
$290$		0			0
$291$	−14.3166	+	14.3166i	−0.839255	+	0.839255i
$292$	−13.3668			−0.782230
$293$	−18.2665	−	18.2665i	−1.06714	−	1.06714i	−0.997578	−	0.0695627i	$-0.977840\pi$
$293$	−18.2665	−	18.2665i	−1.06714	−	1.06714i	−0.0695627	−	0.997578i	$-0.522160\pi$
$294$		−	7.05013i		−	0.411172i
$295$		0			0
$296$		−	2.73350i		−	0.158882i
$297$			45.2164i			2.62372i
$298$	−33.2665			−1.92708
$299$	−1.36675	−	1.36675i	−0.0790412	−	0.0790412i
$300$		0			0
$301$	17.6834	−	17.6834i	1.01925	−	1.01925i
$302$	−4.31662	−	4.31662i	−0.248394	−	0.248394i
$303$	−22.9499			−1.31844
$304$	0.633250	−	0.633250i	0.0363194	−	0.0363194i
$305$		0			0
$306$	−8.31662	−	8.31662i	−0.475430	−	0.475430i
$307$	−14.1583	+	14.1583i	−0.808058	+	0.808058i	−0.984340	−	0.176282i	$-0.943593\pi$
$307$	−14.1583	+	14.1583i	−0.808058	+	0.808058i	0.176282	+	0.984340i	$0.443593\pi$
$308$	−14.6332	−	14.6332i	−0.833807	−	0.833807i
$309$	10.0000	+	10.0000i	0.568880	+	0.568880i
$310$		0			0
$311$			12.9499i			0.734320i	0.930158	+	0.367160i	$0.119670\pi$
$311$			12.9499i			0.734320i	−0.930158	+	0.367160i	$0.880330\pi$
$312$	−37.2665	+	37.2665i	−2.10980	+	2.10980i
$313$		−	16.0000i		−	0.904373i	−0.891923	−	0.452187i	$-0.850644\pi$
$313$		−	16.0000i		−	0.904373i	0.891923	−	0.452187i	$-0.149356\pi$
$314$		−	22.6332i		−	1.27727i
$315$		0			0
$316$		−	8.63325i		−	0.485658i
$317$	−14.9499	+	14.9499i	−0.839669	+	0.839669i	−0.988815	−	0.149147i	$-0.952347\pi$
$317$	−14.9499	+	14.9499i	−0.839669	+	0.839669i	0.149147	+	0.988815i	$0.452347\pi$
$318$	14.3166	−	14.3166i	0.802836	−	0.802836i
$319$	12.6332			0.707326
$320$		0			0
$321$	−12.2665			−0.684649
$322$	0.733501	−	0.733501i	0.0408764	−	0.0408764i
$323$	0.208438	−	0.208438i	0.0115978	−	0.0115978i
$324$			23.8997i			1.32776i
$325$		0			0
$326$			14.3166i			0.792925i
$327$		−	25.6834i		−	1.42029i
$328$	−10.0000	+	10.0000i	−0.552158	+	0.552158i
$329$		−	18.5330i		−	1.02176i
$330$		0			0
$331$	−1.15831	−	1.15831i	−0.0636666	−	0.0636666i	0.674557	−	0.738223i	$-0.264335\pi$
$331$	−1.15831	−	1.15831i	−0.0636666	−	0.0636666i	−0.738223	+	0.674557i	$0.764335\pi$
$332$	−14.3166	−	14.3166i	−0.785727	−	0.785727i
$333$	−4.31662	+	4.31662i	−0.236550	+	0.236550i
$334$	18.0000	+	18.0000i	0.984916	+	0.984916i
$335$		0			0
$336$	−20.0000	−	20.0000i	−1.09109	−	1.09109i
$337$	−22.8997			−1.24743			−0.623714	−	0.781652i	$-0.714377\pi$
$337$	−22.8997			−1.24743			−0.623714	+	0.781652i	$0.714377\pi$
$338$	24.2665	+	24.2665i	1.31992	+	1.31992i
$339$	5.10819	−	5.10819i	0.277439	−	0.277439i
$340$		0			0
$341$	−7.31662	−	7.31662i	−0.396217	−	0.396217i
$342$	−2.00000			−0.108148
$343$		−	20.0000i		−	1.07990i
$344$			30.5330i			1.64623i
$345$		0			0
$346$		−	25.8997i		−	1.39238i
$347$	−14.4248	−	14.4248i	−0.774364	−	0.774364i	0.204502	−	0.978866i	$-0.434443\pi$
$347$	−14.4248	−	14.4248i	−0.774364	−	0.774364i	−0.978866	+	0.204502i	$0.934443\pi$
$348$	17.2665			0.925582
$349$	24.2665	−	24.2665i	1.29896	−	1.29896i	0.369874	−	0.929082i	$-0.379401\pi$
$349$	24.2665	−	24.2665i	1.29896	−	1.29896i	0.929082	−	0.369874i	$-0.120599\pi$
$350$		0			0
$351$	61.7995			3.29861
$352$	25.2665			1.34671
$353$	−33.2665			−1.77060			−0.885299	−	0.465023i	$-0.846046\pi$
$353$	−33.2665			−1.77060			−0.885299	+	0.465023i	$0.846046\pi$
$354$	−5.68338	+	5.68338i	−0.302068	+	0.302068i
$355$		0			0
$356$	7.89975			0.418686
$357$	−6.58312	−	6.58312i	−0.348416	−	0.348416i
$358$		−	17.5831i		−	0.929297i
$359$		−	9.68338i		−	0.511069i	−0.966800	−	0.255534i	$-0.917749\pi$
$359$		−	9.68338i		−	0.511069i	0.966800	−	0.255534i	$-0.0822514\pi$
$360$		0			0
$361$			18.9499i			0.997362i
$362$	6.63325			0.348636
$363$	−19.3166	−	19.3166i	−1.01386	−	1.01386i
$364$	−20.0000	+	20.0000i	−1.04828	+	1.04828i
$365$		0			0
$366$	−41.5831	−	41.5831i	−2.17358	−	2.17358i
$367$	26.6332			1.39024			0.695122	−	0.718892i	$-0.255350\pi$
$367$	26.6332			1.39024			0.695122	+	0.718892i	$0.255350\pi$
$368$			1.26650i			0.0660208i
$369$	31.5831			1.64415
$370$		0			0
$371$	7.68338	−	7.68338i	0.398901	−	0.398901i
$372$	−10.0000	−	10.0000i	−0.518476	−	0.518476i
$373$	−2.36675	−	2.36675i	−0.122546	−	0.122546i	0.643174	−	0.765720i	$-0.277617\pi$
$373$	−2.36675	−	2.36675i	−0.122546	−	0.122546i	−0.765720	+	0.643174i	$0.777617\pi$
$374$	8.31662			0.430042
$375$		0			0
$376$	16.0000	+	16.0000i	0.825137	+	0.825137i
$377$		−	17.2665i		−	0.889270i
$378$			33.1662i			1.70589i
$379$	−11.4248	−	11.4248i	−0.586853	−	0.586853i	0.349925	−	0.936778i	$-0.386207\pi$
$379$	−11.4248	−	11.4248i	−0.586853	−	0.586853i	−0.936778	+	0.349925i	$0.886207\pi$
$380$		0			0
$381$	13.6332	−	13.6332i	0.698453	−	0.698453i
$382$	20.9499	−	20.9499i	1.07189	−	1.07189i
$383$	16.9499			0.866098			0.433049	−	0.901370i	$-0.357438\pi$
$383$	16.9499			0.866098			0.433049	+	0.901370i	$0.357438\pi$
$384$	34.5330			1.76225
$385$		0			0
$386$	−4.68338	+	4.68338i	−0.238378	+	0.238378i
$387$	48.2164	−	48.2164i	2.45098	−	2.45098i
$388$		−	13.2665i		−	0.673504i
$389$	−4.26650	−	4.26650i	−0.216320	−	0.216320i	0.590626	−	0.806946i	$-0.298881\pi$
$389$	−4.26650	−	4.26650i	−0.216320	−	0.216320i	−0.806946	+	0.590626i	$0.798881\pi$
$390$		0			0
$391$			0.416876i			0.0210823i
$392$	3.26650	+	3.26650i	0.164983	+	0.164983i
$393$			4.31662i			0.217745i
$394$	−33.1662			−1.67089
$395$		0			0
$396$	−39.8997	−	39.8997i	−2.00504	−	2.00504i
$397$	25.2665	−	25.2665i	1.26809	−	1.26809i	0.321015	−	0.947074i	$-0.395976\pi$
$397$	25.2665	−	25.2665i	1.26809	−	1.26809i	0.947074	−	0.321015i	$-0.104024\pi$
$398$	12.6332	+	12.6332i	0.633248	+	0.633248i
$399$	−1.58312			−0.0792553
$400$		0			0
$401$	2.68338			0.134001			0.0670007	−	0.997753i	$-0.478657\pi$
$401$	2.68338			0.134001			0.0670007	+	0.997753i	$0.478657\pi$
$402$	39.5330	+	39.5330i	1.97173	+	1.97173i
$403$	−10.0000	+	10.0000i	−0.498135	+	0.498135i
$404$	10.6332	−	10.6332i	0.529024	−	0.529024i
$405$		0			0
$406$	9.26650			0.459889
$407$		−	4.31662i		−	0.213967i
$408$	11.3668			0.562738
$409$			19.6332i			0.970802i	0.874292	+	0.485401i	$0.161326\pi$
$409$			19.6332i			0.970802i	−0.874292	+	0.485401i	$0.838674\pi$
$410$		0			0
$411$	25.1082	+	25.1082i	1.23850	+	1.23850i
$412$	−9.26650			−0.456528
$413$	−3.05013	+	3.05013i	−0.150087	+	0.150087i
$414$	2.00000	−	2.00000i	0.0982946	−	0.0982946i
$415$		0			0
$416$		−	34.5330i		−	1.69312i
$417$	39.5330			1.93594
$418$	1.00000	−	1.00000i	0.0489116	−	0.0489116i
$419$	−11.5251	+	11.5251i	−0.563036	+	0.563036i	−0.930169	−	0.367132i	$-0.880340\pi$
$419$	−11.5251	+	11.5251i	−0.563036	+	0.563036i	0.367132	+	0.930169i	$0.380340\pi$
$420$		0			0
$421$	4.63325	+	4.63325i	0.225811	+	0.225811i	0.810940	−	0.585129i	$-0.198956\pi$
$421$	4.63325	+	4.63325i	0.225811	+	0.225811i	−0.585129	+	0.810940i	$0.698956\pi$
$422$			23.5831i			1.14801i
$423$		−	50.5330i		−	2.45700i
$424$			13.2665i			0.644278i
$425$		0			0
$426$	−37.2665			−1.80557
$427$	−22.3166	−	22.3166i	−1.07998	−	1.07998i
$428$	5.68338	−	5.68338i	0.274716	−	0.274716i
$429$	−58.8496	+	58.8496i	−2.84129	+	2.84129i
$430$		0			0
$431$	−10.9499			−0.527437			−0.263718	−	0.964600i	$-0.584949\pi$
$431$	−10.9499			−0.527437			−0.263718	+	0.964600i	$0.584949\pi$
$432$	−28.6332	−	28.6332i	−1.37762	−	1.37762i
$433$	−12.5831			−0.604706			−0.302353	−	0.953196i	$-0.597772\pi$
$433$	−12.5831			−0.604706			−0.302353	+	0.953196i	$0.597772\pi$
$434$	−5.36675	−	5.36675i	−0.257612	−	0.257612i
$435$		0			0
$436$	11.8997	+	11.8997i	0.569895	+	0.569895i
$437$	0.0501256	+	0.0501256i	0.00239783	+	0.00239783i
$438$	−28.8496			−1.37849
$439$		−	5.36675i		−	0.256141i	−0.991765	−	0.128071i	$-0.959122\pi$
$439$		−	5.36675i		−	0.256141i	0.991765	−	0.128071i	$-0.0408784\pi$
$440$		0			0
$441$		−	10.3166i		−	0.491268i
$442$		−	11.3668i		−	0.540661i
$443$	19.1082	+	19.1082i	0.907857	+	0.907857i	0.996099	−	0.0882417i	$-0.0281248\pi$
$443$	19.1082	+	19.1082i	0.907857	+	0.907857i	−0.0882417	+	0.996099i	$0.528125\pi$
$444$		−	5.89975i		−	0.279990i
$445$		0			0
$446$	6.00000	−	6.00000i	0.284108	−	0.284108i
$447$	−71.7995			−3.39600
$448$	18.5330			0.875602
$449$	20.6834			0.976109			0.488054	−	0.872813i	$-0.337707\pi$
$449$	20.6834			0.976109			0.488054	+	0.872813i	$0.337707\pi$
$450$		0			0
$451$	−15.7916	+	15.7916i	−0.743596	+	0.743596i
$452$			4.73350i			0.222645i
$453$	−9.31662	−	9.31662i	−0.437733	−	0.437733i
$454$			8.73350i			0.409884i
$455$		0			0
$456$	1.36675	−	1.36675i	0.0640040	−	0.0640040i
$457$			17.0000i			0.795226i	0.917553	+	0.397613i	$0.130161\pi$
$457$			17.0000i			0.795226i	−0.917553	+	0.397613i	$0.869839\pi$
$458$	4.00000			0.186908
$459$	−9.42481	−	9.42481i	−0.439913	−	0.439913i
$460$		0			0
$461$	−19.6834	+	19.6834i	−0.916746	+	0.916746i	−0.996791	−	0.0800451i	$-0.974494\pi$
$461$	−19.6834	+	19.6834i	−0.916746	+	0.916746i	0.0800451	+	0.996791i	$0.474494\pi$
$462$	−31.5831	−	31.5831i	−1.46938	−	1.46938i
$463$	−24.6332			−1.14480			−0.572402	−	0.819973i	$-0.693988\pi$
$463$	−24.6332			−1.14480			−0.572402	+	0.819973i	$0.693988\pi$
$464$	−8.00000	+	8.00000i	−0.371391	+	0.371391i
$465$		0			0
$466$	11.8997	+	11.8997i	0.551245	+	0.551245i
$467$	−14.2665	+	14.2665i	−0.660175	+	0.660175i	−0.955421	−	0.295246i	$-0.904598\pi$
$467$	−14.2665	+	14.2665i	−0.660175	+	0.660175i	0.295246	+	0.955421i	$0.404598\pi$
$468$	−54.5330	+	54.5330i	−2.52079	+	2.52079i
$469$	21.2164	+	21.2164i	0.979681	+	0.979681i
$470$		0			0
$471$		−	48.8496i		−	2.25087i
$472$		−	5.26650i		−	0.242410i
$473$			48.2164i			2.21699i
$474$		−	18.6332i		−	0.855853i
$475$		0			0
$476$	6.10025			0.279605
$477$	20.9499	−	20.9499i	0.959229	−	0.959229i
$478$	18.6332	−	18.6332i	0.852265	−	0.852265i
$479$	10.2164			0.466798			0.233399	−	0.972381i	$-0.425015\pi$
$479$	10.2164			0.466798			0.233399	+	0.972381i	$0.425015\pi$
$480$		0			0
$481$	−5.89975			−0.269005
$482$	−18.5831	+	18.5831i	−0.846438	+	0.846438i
$483$	1.58312	−	1.58312i	0.0720346	−	0.0720346i
$484$	17.8997			0.813625
$485$		0			0
$486$			8.63325i			0.391612i
$487$			32.2164i			1.45986i	0.683520	+	0.729932i	$0.260448\pi$
$487$			32.2164i			1.45986i	−0.683520	+	0.729932i	$0.739552\pi$
$488$	38.5330			1.74431
$489$			30.8997i			1.39733i
$490$		0			0
$491$	29.6332	+	29.6332i	1.33733	+	1.33733i	0.898637	+	0.438693i	$0.144558\pi$
$491$	29.6332	+	29.6332i	1.33733	+	1.33733i	0.438693	+	0.898637i	$0.355442\pi$
$492$	−21.5831	+	21.5831i	−0.973042	+	0.973042i
$493$	−2.63325	+	2.63325i	−0.118596	+	0.118596i
$494$	−1.36675	−	1.36675i	−0.0614930	−	0.0614930i
$495$		0			0
$496$	9.26650			0.416078
$497$	−20.0000			−0.897123
$498$	−30.8997	−	30.8997i	−1.38465	−	1.38465i
$499$	22.8997	−	22.8997i	1.02513	−	1.02513i	0.0254576	−	0.999676i	$-0.491896\pi$
$499$	22.8997	−	22.8997i	1.02513	−	1.02513i	0.999676	−	0.0254576i	$-0.00810429\pi$
$500$		0			0
$501$	38.8496	+	38.8496i	1.73567	+	1.73567i
$502$	18.2164			0.813037
$503$		−	31.8997i		−	1.42234i	−0.703020	−	0.711170i	$-0.748166\pi$
$503$		−	31.8997i		−	1.42234i	0.703020	−	0.711170i	$-0.251834\pi$
$504$	−29.2665	−	29.2665i	−1.30363	−	1.30363i
$505$		0			0
$506$			2.00000i			0.0889108i
$507$	52.3747	+	52.3747i	2.32604	+	2.32604i
$508$			12.6332i			0.560510i
$509$	−20.2665	+	20.2665i	−0.898297	+	0.898297i	−0.995285	−	0.0969887i	$-0.969079\pi$
$509$	−20.2665	+	20.2665i	−0.898297	+	0.898297i	0.0969887	+	0.995285i	$0.469079\pi$
$510$		0			0
$511$	−15.4829			−0.684922
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$	−2.26650			−0.100068
$514$	−16.6332	+	16.6332i	−0.733661	+	0.733661i
$515$		0			0
$516$			65.8997i			2.90107i
$517$	25.2665	+	25.2665i	1.11122	+	1.11122i
$518$		−	3.16625i		−	0.139117i
$519$		−	55.8997i		−	2.45373i
$520$		0			0
$521$		−	13.6332i		−	0.597284i	−0.954365	−	0.298642i	$-0.903466\pi$
$521$		−	13.6332i		−	0.597284i	0.954365	−	0.298642i	$-0.0965336\pi$
$522$	25.2665			1.10588
$523$	−7.47494	−	7.47494i	−0.326856	−	0.326856i	0.524534	−	0.851390i	$-0.324240\pi$
$523$	−7.47494	−	7.47494i	−0.326856	−	0.326856i	−0.851390	+	0.524534i	$0.824240\pi$
$524$	−2.00000	−	2.00000i	−0.0873704	−	0.0873704i
$525$		0			0
$526$	−15.5831	−	15.5831i	−0.679456	−	0.679456i
$527$	3.05013			0.132866
$528$	54.5330			2.37324
$529$	22.8997			0.995641
$530$		0			0
$531$	−8.31662	+	8.31662i	−0.360911	+	0.360911i
$532$	0.733501	−	0.733501i	0.0318013	−	0.0318013i
$533$	21.5831	+	21.5831i	0.934869	+	0.934869i
$534$	17.0501			0.737831
$535$		0			0
$536$	−36.6332			−1.58232
$537$		−	37.9499i		−	1.63766i
$538$			12.6332i			0.544658i
$539$	5.15831	+	5.15831i	0.222184	+	0.222184i
$540$		0			0
$541$	11.6834	−	11.6834i	0.502308	−	0.502308i	−0.409847	−	0.912154i	$-0.634418\pi$
$541$	11.6834	−	11.6834i	0.502308	−	0.502308i	0.912154	+	0.409847i	$0.134418\pi$
$542$	0.949874	−	0.949874i	0.0408006	−	0.0408006i
$543$	14.3166			0.614385
$544$	−5.26650	+	5.26650i	−0.225799	+	0.225799i
$545$		0			0
$546$	−43.1662	+	43.1662i	−1.84734	+	1.84734i
$547$	−15.7414	+	15.7414i	−0.673055	+	0.673055i	−0.958419	−	0.285364i	$-0.907886\pi$
$547$	−15.7414	+	15.7414i	−0.673055	+	0.673055i	0.285364	+	0.958419i	$0.407886\pi$
$548$	−23.2665			−0.993896
$549$	−60.8496	−	60.8496i	−2.59700	−	2.59700i
$550$		0			0
$551$			0.633250i			0.0269773i
$552$			2.73350i			0.116346i
$553$		−	10.0000i		−	0.425243i
$554$	−28.6332			−1.21651
$555$		0			0
$556$	−18.3166	+	18.3166i	−0.776798	+	0.776798i
$557$	−26.3166	+	26.3166i	−1.11507	+	1.11507i	−0.122617	+	0.992454i	$0.539129\pi$
$557$	−26.3166	+	26.3166i	−1.11507	+	1.11507i	−0.992454	+	0.122617i	$0.960871\pi$
$558$	−14.6332	−	14.6332i	−0.619475	−	0.619475i
$559$	65.8997			2.78726
$560$		0			0
$561$	17.9499			0.757844
$562$	−7.26650	−	7.26650i	−0.306519	−	0.306519i
$563$	−17.9499	+	17.9499i	−0.756497	+	0.756497i	−0.975683	−	0.219186i	$-0.929660\pi$
$563$	−17.9499	+	17.9499i	−0.756497	+	0.756497i	0.219186	+	0.975683i	$0.429660\pi$
$564$	34.5330	+	34.5330i	1.45410	+	1.45410i
$565$		0			0
$566$	7.68338			0.322956
$567$			27.6834i			1.16259i
$568$	17.2665	−	17.2665i	0.724486	−	0.724486i
$569$		−	9.00000i		−	0.377300i	−0.982044	−	0.188650i	$-0.939589\pi$
$569$		−	9.00000i		−	0.377300i	0.982044	−	0.188650i	$-0.0604111\pi$
$570$		0			0
$571$	−1.73350	−	1.73350i	−0.0725448	−	0.0725448i	0.669903	−	0.742448i	$-0.266335\pi$
$571$	−1.73350	−	1.73350i	−0.0725448	−	0.0725448i	−0.742448	+	0.669903i	$0.766335\pi$
$572$		−	54.5330i		−	2.28014i
$573$	45.2164	−	45.2164i	1.88894	−	1.88894i
$574$	−11.5831	+	11.5831i	−0.483470	+	0.483470i
$575$		0			0
$576$	50.5330			2.10554
$577$	−15.6332			−0.650821			−0.325410	−	0.945573i	$-0.605502\pi$
$577$	−15.6332			−0.650821			−0.325410	+	0.945573i	$0.605502\pi$
$578$	15.2665	−	15.2665i	0.635003	−	0.635003i
$579$	−10.1082	+	10.1082i	−0.420082	+	0.420082i
$580$		0			0
$581$	−16.5831	−	16.5831i	−0.687984	−	0.687984i
$582$		−	28.6332i		−	1.18689i
$583$			20.9499i			0.867655i
$584$	13.3668	−	13.3668i	0.553120	−	0.553120i
$585$		0			0
$586$	36.5330			1.50916
$587$	9.42481	+	9.42481i	0.389004	+	0.389004i	0.874332	−	0.485328i	$-0.161300\pi$
$587$	9.42481	+	9.42481i	0.389004	+	0.389004i	−0.485328	+	0.874332i	$0.661300\pi$
$588$	7.05013	+	7.05013i	0.290742	+	0.290742i
$589$	0.366750	−	0.366750i	0.0151117	−	0.0151117i
$590$		0			0
$591$	−71.5831			−2.94454
$592$	2.73350	+	2.73350i	0.112346	+	0.112346i
$593$	−35.5330			−1.45917			−0.729583	−	0.683893i	$-0.760286\pi$
$593$	−35.5330			−1.45917			−0.729583	+	0.683893i	$0.760286\pi$
$594$	−45.2164	−	45.2164i	−1.85525	−	1.85525i
$595$		0			0
$596$	33.2665	−	33.2665i	1.36265	−	1.36265i
$597$	27.2665	+	27.2665i	1.11594	+	1.11594i
$598$	2.73350			0.111781
$599$			36.2164i			1.47976i	0.672738	+	0.739880i	$0.265118\pi$
$599$			36.2164i			1.47976i	−0.672738	+	0.739880i	$0.734882\pi$
$600$		0			0
$601$			22.0501i			0.899443i	0.893169	+	0.449722i	$0.148477\pi$
$601$			22.0501i			0.899443i	−0.893169	+	0.449722i	$0.851523\pi$
$602$			35.3668i			1.44144i
$603$	57.8496	+	57.8496i	2.35582	+	2.35582i
$604$	8.63325			0.351282
$605$		0			0
$606$	22.9499	−	22.9499i	0.932275	−	0.932275i
$607$	21.1662			0.859112			0.429556	−	0.903040i	$-0.358670\pi$
$607$	21.1662			0.859112			0.429556	+	0.903040i	$0.358670\pi$
$608$			1.26650i			0.0513633i
$609$	20.0000			0.810441
$610$		0			0
$611$	34.5330	−	34.5330i	1.39706	−	1.39706i
$612$	16.6332			0.672359
$613$	16.2665	+	16.2665i	0.656998	+	0.656998i	0.954669	−	0.297671i	$-0.0962098\pi$
$613$	16.2665	+	16.2665i	0.656998	+	0.656998i	−0.297671	+	0.954669i	$0.596210\pi$
$614$		−	28.3166i		−	1.14277i
$615$		0			0
$616$	29.2665			1.17918
$617$		−	0.733501i		−	0.0295296i	−0.999891	−	0.0147648i	$-0.995300\pi$
$617$		−	0.733501i		−	0.0295296i	0.999891	−	0.0147648i	$-0.00469996\pi$
$618$	−20.0000			−0.804518
$619$	−8.36675	−	8.36675i	−0.336288	−	0.336288i	0.518680	−	0.854968i	$-0.326424\pi$
$619$	−8.36675	−	8.36675i	−0.336288	−	0.336288i	−0.854968	+	0.518680i	$0.826424\pi$
$620$		0			0
$621$	2.26650	−	2.26650i	0.0909515	−	0.0909515i
$622$	−12.9499	−	12.9499i	−0.519243	−	0.519243i
$623$	9.15038			0.366602
$624$		−	74.5330i		−	2.98371i
$625$		0			0
$626$	16.0000	+	16.0000i	0.639489	+	0.639489i
$627$	2.15831	−	2.15831i	0.0861947	−	0.0861947i
$628$	22.6332	+	22.6332i	0.903165	+	0.903165i
$629$	0.899749	+	0.899749i	0.0358753	+	0.0358753i
$630$		0			0
$631$		−	24.3166i		−	0.968030i	−0.875060	−	0.484015i	$-0.839178\pi$
$631$		−	24.3166i		−	0.968030i	0.875060	−	0.484015i	$-0.160822\pi$
$632$	8.63325	+	8.63325i	0.343412	+	0.343412i
$633$			50.8997i			2.02308i
$634$		−	29.8997i		−	1.18747i
$635$		0			0
$636$			28.6332i			1.13538i
$637$	7.05013	−	7.05013i	0.279336	−	0.279336i
$638$	−12.6332	+	12.6332i	−0.500155	+	0.500155i
$639$	−54.5330			−2.15729
$640$		0			0
$641$	−23.8997			−0.943983			−0.471992	−	0.881603i	$-0.656465\pi$
$641$	−23.8997			−0.943983			−0.471992	+	0.881603i	$0.656465\pi$
$642$	12.2665	−	12.2665i	0.484120	−	0.484120i
$643$	−2.26650	+	2.26650i	−0.0893820	+	0.0893820i	−0.750384	−	0.661002i	$-0.770131\pi$
$643$	−2.26650	+	2.26650i	−0.0893820	+	0.0893820i	0.661002	+	0.750384i	$0.270131\pi$
$644$			1.46700i			0.0578080i
$645$		0			0
$646$			0.416876i			0.0164018i
$647$		−	21.1662i		−	0.832131i	−0.909335	−	0.416066i	$-0.863409\pi$
$647$		−	21.1662i		−	0.832131i	0.909335	−	0.416066i	$-0.136591\pi$
$648$	−23.8997	−	23.8997i	−0.938871	−	0.938871i
$649$		−	8.31662i		−	0.326456i
$650$		0			0
$651$	−11.5831	−	11.5831i	−0.453978	−	0.453978i
$652$	−14.3166	−	14.3166i	−0.560682	−	0.560682i
$653$	−16.3668	+	16.3668i	−0.640480	+	0.640480i	−0.950674	−	0.310193i	$-0.899606\pi$
$653$	−16.3668	+	16.3668i	−0.640480	+	0.640480i	0.310193	+	0.950674i	$0.399606\pi$
$654$	25.6834	+	25.6834i	1.00430	+	1.00430i
$655$		0			0
$656$		−	20.0000i		−	0.780869i
$657$	−42.2164			−1.64702
$658$	18.5330	+	18.5330i	0.722491	+	0.722491i
$659$	−25.1583	+	25.1583i	−0.980029	+	0.980029i	−0.999804	−	0.0197757i	$-0.993705\pi$
$659$	−25.1583	+	25.1583i	−0.980029	+	0.980029i	0.0197757	+	0.999804i	$0.493705\pi$
$660$		0			0
$661$	−35.5831	−	35.5831i	−1.38402	−	1.38402i	−0.837339	−	0.546684i	$-0.815890\pi$
$661$	−35.5831	−	35.5831i	−1.38402	−	1.38402i	−0.546684	−	0.837339i	$-0.684110\pi$
$662$	2.31662			0.0900382
$663$		−	24.5330i		−	0.952783i
$664$	28.6332			1.11119
$665$		0			0
$666$		−	8.63325i		−	0.334532i
$667$	−0.633250	−	0.633250i	−0.0245195	−	0.0245195i
$668$	−36.0000			−1.39288
$669$	12.9499	−	12.9499i	0.500671	−	0.500671i
$670$		0			0
$671$	60.8496			2.34907
$672$	40.0000			1.54303
$673$	42.6332			1.64339			0.821696	−	0.569927i	$-0.193028\pi$
$673$	42.6332			1.64339			0.821696	+	0.569927i	$0.193028\pi$
$674$	22.8997	−	22.8997i	0.882065	−	0.882065i
$675$		0			0
$676$	−48.5330			−1.86665
$677$	−11.3668	−	11.3668i	−0.436860	−	0.436860i	0.454094	−	0.890954i	$-0.349963\pi$
$677$	−11.3668	−	11.3668i	−0.436860	−	0.436860i	−0.890954	+	0.454094i	$0.849963\pi$
$678$			10.2164i			0.392357i
$679$		−	15.3668i		−	0.589722i
$680$		0			0
$681$			18.8496i			0.722319i
$682$	14.6332			0.560336
$683$	5.47494	+	5.47494i	0.209493	+	0.209493i	0.804052	−	0.594559i	$-0.202673\pi$
$683$	5.47494	+	5.47494i	0.209493	+	0.209493i	−0.594559	+	0.804052i	$0.702673\pi$
$684$	2.00000	−	2.00000i	0.0764719	−	0.0764719i
$685$		0			0
$686$	20.0000	+	20.0000i	0.763604	+	0.763604i
$687$	8.63325			0.329379
$688$	−30.5330	−	30.5330i	−1.16406	−	1.16406i
$689$	28.6332			1.09084
$690$		0			0
$691$	−26.1583	+	26.1583i	−0.995109	+	0.995109i	−0.999988	−	0.00487900i	$-0.998447\pi$
$691$	−26.1583	+	26.1583i	−0.995109	+	0.995109i	0.00487900	+	0.999988i	$0.498447\pi$
$692$	25.8997	+	25.8997i	0.984561	+	0.984561i
$693$	−46.2164	−	46.2164i	−1.75561	−	1.75561i
$694$	28.8496			1.09512
$695$		0			0
$696$	−17.2665	+	17.2665i	−0.654485	+	0.654485i
$697$		−	6.58312i		−	0.249354i
$698$			48.5330i			1.83700i
$699$	25.6834	+	25.6834i	0.971434	+	0.971434i
$700$		0			0
$701$	−21.2665	+	21.2665i	−0.803225	+	0.803225i	−0.983598	−	0.180374i	$-0.942269\pi$
$701$	−21.2665	+	21.2665i	−0.803225	+	0.803225i	0.180374	+	0.983598i	$0.442269\pi$
$702$	−61.7995	+	61.7995i	−2.33247	+	2.33247i
$703$	0.216374			0.00816068
$704$	−25.2665	+	25.2665i	−0.952267	+	0.952267i
$705$		0			0
$706$	33.2665	−	33.2665i	1.25200	−	1.25200i
$707$	12.3166	−	12.3166i	0.463214	−	0.463214i
$708$		−	11.3668i		−	0.427189i
$709$	−22.0000	−	22.0000i	−0.826227	−	0.826227i	0.160765	−	0.986993i	$-0.448604\pi$
$709$	−22.0000	−	22.0000i	−0.826227	−	0.826227i	−0.986993	+	0.160765i	$0.948604\pi$
$710$		0			0
$711$		−	27.2665i		−	1.02257i
$712$	−7.89975	+	7.89975i	−0.296056	+	0.296056i
$713$			0.733501i			0.0274698i
$714$	13.1662			0.492734
$715$		0			0
$716$	17.5831	+	17.5831i	0.657112	+	0.657112i
$717$	40.2164	−	40.2164i	1.50191	−	1.50191i
$718$	9.68338	+	9.68338i	0.361380	+	0.361380i
$719$	2.94987			0.110012			0.0550059	−	0.998486i	$-0.482482\pi$
$719$	2.94987			0.110012			0.0550059	+	0.998486i	$0.482482\pi$
$720$		0			0
$721$	−10.7335			−0.399736
$722$	−18.9499	−	18.9499i	−0.705241	−	0.705241i
$723$	−40.1082	+	40.1082i	−1.49164	+	1.49164i
$724$	−6.63325	+	6.63325i	−0.246523	+	0.246523i
$725$		0			0
$726$	38.6332			1.43381
$727$		−	2.53300i		−	0.0939437i	−0.998896	−	0.0469719i	$-0.985043\pi$
$727$		−	2.53300i		−	0.0939437i	0.998896	−	0.0469719i	$-0.0149571\pi$
$728$		−	40.0000i		−	1.48250i
$729$		−	17.2164i		−	0.637643i
$730$		0			0
$731$	−10.0501	−	10.0501i	−0.371717	−	0.371717i
$732$	83.1662			3.07391
$733$	−5.68338	+	5.68338i	−0.209920	+	0.209920i	−0.804234	−	0.594313i	$-0.797424\pi$
$733$	−5.68338	+	5.68338i	−0.209920	+	0.209920i	0.594313	+	0.804234i	$0.297424\pi$
$734$	−26.6332	+	26.6332i	−0.983051	+	0.983051i
$735$		0			0
$736$	−1.26650	−	1.26650i	−0.0466838	−	0.0466838i
$737$	−57.8496			−2.13092
$738$	−31.5831	+	31.5831i	−1.16259	+	1.16259i
$739$	−14.3668	+	14.3668i	−0.528489	+	0.528489i	−0.920122	−	0.391632i	$-0.871911\pi$
$739$	−14.3668	+	14.3668i	−0.528489	+	0.528489i	0.391632	+	0.920122i	$0.371911\pi$
$740$		0			0
$741$	−2.94987	−	2.94987i	−0.108366	−	0.108366i
$742$			15.3668i			0.564131i
$743$		−	20.3166i		−	0.745345i	−0.927963	−	0.372672i	$-0.878442\pi$
$743$		−	20.3166i		−	0.745345i	0.927963	−	0.372672i	$-0.121558\pi$
$744$	20.0000			0.733236
$745$		0			0
$746$	4.73350			0.173306
$747$	−45.2164	−	45.2164i	−1.65438	−	1.65438i
$748$	−8.31662	+	8.31662i	−0.304086	+	0.304086i
$749$	6.58312	−	6.58312i	0.240542	−	0.240542i
$750$		0			0
$751$	42.4327			1.54839			0.774196	−	0.632945i	$-0.218154\pi$
$751$	42.4327			1.54839			0.774196	+	0.632945i	$0.218154\pi$
$752$	−32.0000			−1.16692
$753$	39.3166			1.43278
$754$	17.2665	+	17.2665i	0.628809	+	0.628809i
$755$		0			0
$756$	−33.1662	−	33.1662i	−1.20624	−	1.20624i
$757$	−34.3166	−	34.3166i	−1.24726	−	1.24726i	−0.956926	−	0.290333i	$-0.906234\pi$
$757$	−34.3166	−	34.3166i	−1.24726	−	1.24726i	−0.290333	−	0.956926i	$-0.593766\pi$
$758$	22.8496			0.829936
$759$			4.31662i			0.156684i
$760$		0			0
$761$			32.2665i			1.16966i	0.811156	+	0.584830i	$0.198839\pi$
$761$			32.2665i			1.16966i	−0.811156	+	0.584830i	$0.801161\pi$
$762$			27.2665i			0.987761i
$763$	13.7836	+	13.7836i	0.499001	+	0.499001i
$764$			41.8997i			1.51588i
$765$		0			0
$766$	−16.9499	+	16.9499i	−0.612424	+	0.612424i
$767$	−11.3668			−0.410430
$768$	−34.5330	+	34.5330i	−1.24610	+	1.24610i
$769$	−32.4829			−1.17136			−0.585681	−	0.810542i	$-0.699173\pi$
$769$	−32.4829			−1.17136			−0.585681	+	0.810542i	$0.699173\pi$
$770$		0			0
$771$	−35.8997	+	35.8997i	−1.29290	+	1.29290i
$772$		−	9.36675i		−	0.337117i
$773$	−17.3668	−	17.3668i	−0.624639	−	0.624639i	0.322075	−	0.946714i	$-0.395620\pi$
$773$	−17.3668	−	17.3668i	−0.624639	−	0.624639i	−0.946714	+	0.322075i	$0.895620\pi$
$774$			96.4327i			3.46620i
$775$		0			0
$776$	13.2665	+	13.2665i	0.476240	+	0.476240i
$777$		−	6.83375i		−	0.245159i
$778$	8.53300			0.305923
$779$	−0.791562	−	0.791562i	−0.0283607	−	0.0283607i
$780$		0			0
$781$	27.2665	−	27.2665i	0.975672	−	0.975672i
$782$	−0.416876	−	0.416876i	−0.0149075	−	0.0149075i
$783$	28.6332			1.02327
$784$	−6.53300			−0.233321
$785$		0			0
$786$	−4.31662	−	4.31662i	−0.153969	−	0.153969i
$787$	−7.00000	+	7.00000i	−0.249523	+	0.249523i	−0.820775	−	0.571252i	$-0.806458\pi$
$787$	−7.00000	+	7.00000i	−0.249523	+	0.249523i	0.571252	+	0.820775i	$0.306458\pi$
$788$	33.1662	−	33.1662i	1.18150	−	1.18150i
$789$	−33.6332	−	33.6332i	−1.19738	−	1.19738i
$790$		0			0
$791$			5.48287i			0.194949i
$792$	79.7995			2.83555
$793$		−	83.1662i		−	2.95332i
$794$			50.5330i			1.79335i
$795$		0			0
$796$	−25.2665			−0.895547
$797$	−15.6332	+	15.6332i	−0.553758	+	0.553758i	−0.927523	−	0.373765i	$-0.878067\pi$
$797$	−15.6332	+	15.6332i	−0.553758	+	0.553758i	0.373765	+	0.927523i	$0.378067\pi$
$798$	1.58312	−	1.58312i	0.0560420	−	0.0560420i
$799$	−10.5330			−0.372631
$800$		0			0
$801$	24.9499			0.881560
$802$	−2.68338	+	2.68338i	−0.0947533	+	0.0947533i
$803$	21.1082	−	21.1082i	0.744892	−	0.744892i
$804$	−79.0660			−2.78844
$805$		0			0
$806$		−	20.0000i		−	0.704470i
$807$			27.2665i			0.959826i
$808$			21.2665i			0.748153i
$809$		−	38.5330i		−	1.35475i	−0.735639	−	0.677374i	$-0.763118\pi$
$809$		−	38.5330i		−	1.35475i	0.735639	−	0.677374i	$-0.236882\pi$
$810$		0			0
$811$	−37.6332	−	37.6332i	−1.32148	−	1.32148i	−0.912577	−	0.408905i	$-0.865911\pi$
$811$	−37.6332	−	37.6332i	−1.32148	−	1.32148i	−0.408905	−	0.912577i	$-0.634089\pi$
$812$	−9.26650	+	9.26650i	−0.325190	+	0.325190i
$813$	2.05013	−	2.05013i	0.0719010	−	0.0719010i
$814$	4.31662	+	4.31662i	0.151298	+	0.151298i
$815$		0			0
$816$	−11.3668	+	11.3668i	−0.397916	+	0.397916i
$817$	−2.41688			−0.0845558
$818$	−19.6332	−	19.6332i	−0.686460	−	0.686460i
$819$	−63.1662	+	63.1662i	−2.20721	+	2.20721i
$820$		0			0
$821$	−1.73350	−	1.73350i	−0.0604996	−	0.0604996i	0.676210	−	0.736709i	$-0.263621\pi$
$821$	−1.73350	−	1.73350i	−0.0604996	−	0.0604996i	−0.736709	+	0.676210i	$0.763621\pi$
$822$	−50.2164			−1.75150
$823$			9.89975i			0.345084i	0.985002	+	0.172542i	$0.0551980\pi$
$823$			9.89975i			0.345084i	−0.985002	+	0.172542i	$0.944802\pi$
$824$	9.26650	−	9.26650i	0.322814	−	0.322814i
$825$		0			0
$826$		−	6.10025i		−	0.212255i
$827$	7.84169	+	7.84169i	0.272682	+	0.272682i	0.830179	−	0.557497i	$-0.188238\pi$
$827$	7.84169	+	7.84169i	0.272682	+	0.272682i	−0.557497	+	0.830179i	$0.688238\pi$
$828$			4.00000i			0.139010i
$829$	−0.733501	+	0.733501i	−0.0254755	+	0.0254755i	−0.719730	−	0.694254i	$-0.755734\pi$
$829$	−0.733501	+	0.733501i	−0.0254755	+	0.0254755i	0.694254	+	0.719730i	$0.255734\pi$
$830$		0			0
$831$	−61.7995			−2.14380
$832$	34.5330	+	34.5330i	1.19722	+	1.19722i
$833$	−2.15038			−0.0745061
$834$	−39.5330	+	39.5330i	−1.36892	+	1.36892i
$835$		0			0
$836$			2.00000i			0.0691714i
$837$	−16.5831	−	16.5831i	−0.573197	−	0.573197i
$838$		−	23.0501i		−	0.796253i
$839$		−	2.63325i		−	0.0909099i	−0.998966	−	0.0454549i	$-0.985526\pi$
$839$		−	2.63325i		−	0.0909099i	0.998966	−	0.0454549i	$-0.0144737\pi$
$840$		0			0
$841$			21.0000i			0.724138i
$842$	−9.26650			−0.319345
$843$	−15.6834	−	15.6834i	−0.540164	−	0.540164i
$844$	−23.5831	−	23.5831i	−0.811765	−	0.811765i
$845$		0			0
$846$	50.5330	+	50.5330i	1.73736	+	1.73736i
$847$	20.7335			0.712412
$848$	−13.2665	−	13.2665i	−0.455573	−	0.455573i
$849$	16.5831			0.569131
$850$		0			0
$851$	−0.216374	+	0.216374i	−0.00741719	+	0.00741719i
$852$	37.2665	−	37.2665i	1.27673	−	1.27673i
$853$	20.3668	+	20.3668i	0.697344	+	0.697344i	0.963837	−	0.266493i	$-0.0858648\pi$
$853$	20.3668	+	20.3668i	0.697344	+	0.697344i	−0.266493	+	0.963837i	$0.585865\pi$
$854$	44.6332			1.52732
$855$		0			0
$856$			11.3668i			0.388508i
$857$		−	21.6332i		−	0.738978i	−0.929235	−	0.369489i	$-0.879533\pi$
$857$		−	21.6332i		−	0.738978i	0.929235	−	0.369489i	$-0.120467\pi$
$858$		−	117.699i		−	4.01819i
$859$	22.4248	+	22.4248i	0.765125	+	0.765125i	0.977244	−	0.212119i	$-0.0680365\pi$
$859$	22.4248	+	22.4248i	0.765125	+	0.765125i	−0.212119	+	0.977244i	$0.568036\pi$
$860$		0			0
$861$	−25.0000	+	25.0000i	−0.851998	+	0.851998i
$862$	10.9499	−	10.9499i	0.372954	−	0.372954i
$863$	−20.5330			−0.698951			−0.349476	−	0.936945i	$-0.613640\pi$
$863$	−20.5330			−0.698951			−0.349476	+	0.936945i	$0.613640\pi$
$864$	57.2665			1.94825
$865$		0			0
$866$	12.5831	−	12.5831i	0.427592	−	0.427592i
$867$	32.9499	−	32.9499i	1.11904	−	1.11904i
$868$	10.7335			0.364319
$869$	13.6332	+	13.6332i	0.462476	+	0.462476i
$870$		0			0
$871$			79.0660i			2.67905i
$872$	−23.7995			−0.805953
$873$		−	41.8997i		−	1.41809i
$874$	−0.100251			−0.00339105
$875$		0			0
$876$	28.8496	−	28.8496i	0.974738	−	0.974738i
$877$	6.41688	−	6.41688i	0.216683	−	0.216683i	−0.590416	−	0.807099i	$-0.701036\pi$
$877$	6.41688	−	6.41688i	0.216683	−	0.216683i	0.807099	+	0.590416i	$0.201036\pi$
$878$	5.36675	+	5.36675i	0.181119	+	0.181119i
$879$	78.8496			2.65953
$880$		0			0
$881$	37.8997			1.27687			0.638437	−	0.769674i	$-0.279581\pi$
$881$	37.8997			1.27687			0.638437	+	0.769674i	$0.279581\pi$
$882$	10.3166	+	10.3166i	0.347379	+	0.347379i
$883$	−22.1583	+	22.1583i	−0.745687	+	0.745687i	−0.973666	−	0.227979i	$-0.926788\pi$
$883$	−22.1583	+	22.1583i	−0.745687	+	0.745687i	0.227979	+	0.973666i	$0.426788\pi$
$884$	11.3668	+	11.3668i	0.382305	+	0.382305i
$885$		0			0
$886$	−38.2164			−1.28390
$887$			46.5330i			1.56243i	0.624265	+	0.781213i	$0.285399\pi$
$887$			46.5330i			1.56243i	−0.624265	+	0.781213i	$0.714601\pi$
$888$	5.89975	+	5.89975i	0.197983	+	0.197983i
$889$			14.6332i			0.490783i
$890$		0			0
$891$	−37.7414	−	37.7414i	−1.26439	−	1.26439i
$892$			12.0000i			0.401790i
$893$	−1.26650	+	1.26650i	−0.0423818	+	0.0423818i
$894$	71.7995	−	71.7995i	2.40133	−	2.40133i
$895$		0			0
$896$	−18.5330	+	18.5330i	−0.619144	+	0.619144i
$897$	5.89975			0.196987
$898$	−20.6834	+	20.6834i	−0.690213	+	0.690213i
$899$	−4.63325	+	4.63325i	−0.154528	+	0.154528i
$900$		0			0
$901$	−4.36675	−	4.36675i	−0.145478	−	0.145478i
$902$		−	31.5831i		−	1.05160i
$903$			76.3325i			2.54019i
$904$	−4.73350	−	4.73350i	−0.157434	−	0.157434i
$905$		0			0
$906$	18.6332			0.619048
$907$	−13.6332	−	13.6332i	−0.452685	−	0.452685i	0.443560	−	0.896245i	$-0.353715\pi$
$907$	−13.6332	−	13.6332i	−0.452685	−	0.452685i	−0.896245	+	0.443560i	$0.853715\pi$
$908$	−8.73350	−	8.73350i	−0.289831	−	0.289831i
$909$	33.5831	−	33.5831i	1.11388	−	1.11388i
$910$		0			0
$911$	−41.1662			−1.36390			−0.681949	−	0.731399i	$-0.738868\pi$
$911$	−41.1662			−1.36390			−0.681949	+	0.731399i	$0.738868\pi$
$912$			2.73350i			0.0905153i
$913$	45.2164			1.49644
$914$	−17.0000	−	17.0000i	−0.562310	−	0.562310i
$915$		0			0
$916$	−4.00000	+	4.00000i	−0.132164	+	0.132164i
$917$	−2.31662	−	2.31662i	−0.0765017	−	0.0765017i
$918$	18.8496			0.622130
$919$			4.41688i			0.145699i	0.997343	+	0.0728496i	$0.0232093\pi$
$919$			4.41688i			0.145699i	−0.997343	+	0.0728496i	$0.976791\pi$
$920$		0			0
$921$		−	61.1161i		−	2.01384i
$922$		−	39.3668i		−	1.29647i
$923$	−37.2665	−	37.2665i	−1.22664	−	1.22664i
$924$	63.1662			2.07802
$925$		0			0
$926$	24.6332	−	24.6332i	0.809499	−	0.809499i
$927$	−29.2665			−0.961238
$928$		−	16.0000i		−	0.525226i
$929$	−20.0000			−0.656179			−0.328089	−	0.944647i	$-0.606405\pi$
$929$	−20.0000			−0.656179			−0.328089	+	0.944647i	$0.606405\pi$
$930$		0			0
$931$	−0.258564	+	0.258564i	−0.00847408	+	0.00847408i
$932$	−23.7995			−0.779578
$933$	−27.9499	−	27.9499i	−0.915038	−	0.915038i
$934$		−	28.5330i		−	0.933628i
$935$		0			0
$936$		−	109.066i		−	3.56493i
$937$		−	35.9499i		−	1.17443i	−0.809431	−	0.587216i	$-0.800224\pi$
$937$		−	35.9499i		−	1.17443i	0.809431	−	0.587216i	$-0.199776\pi$
$938$	−42.4327			−1.38548
$939$	34.5330	+	34.5330i	1.12694	+	1.12694i
$940$		0			0
$941$	8.94987	−	8.94987i	0.291758	−	0.291758i	−0.546017	−	0.837774i	$-0.683856\pi$
$941$	8.94987	−	8.94987i	0.291758	−	0.291758i	0.837774	+	0.546017i	$0.183856\pi$
$942$	48.8496	+	48.8496i	1.59161	+	1.59161i
$943$	1.58312			0.0515536
$944$	5.26650	+	5.26650i	0.171410	+	0.171410i
$945$		0			0
$946$	−48.2164	−	48.2164i	−1.56765	−	1.56765i
$947$	−5.41688	+	5.41688i	−0.176025	+	0.176025i	−0.789620	−	0.613596i	$-0.789723\pi$
$947$	−5.41688	+	5.41688i	−0.176025	+	0.176025i	0.613596	+	0.789620i	$0.289723\pi$
$948$	18.6332	+	18.6332i	0.605180	+	0.605180i
$949$	−28.8496	−	28.8496i	−0.936498	−	0.936498i
$950$		0			0
$951$		−	64.5330i		−	2.09263i
$952$	−6.10025	+	6.10025i	−0.197710	+	0.197710i
$953$		−	2.36675i		−	0.0766666i	−0.999265	−	0.0383333i	$-0.987795\pi$
$953$		−	2.36675i		−	0.0766666i	0.999265	−	0.0383333i	$-0.0122049\pi$
$954$			41.8997i			1.35655i
$955$		0			0
$956$			37.2665i			1.20528i
$957$	−27.2665	+	27.2665i	−0.881401	+	0.881401i
$958$	−10.2164	+	10.2164i	−0.330076	+	0.330076i
$959$	−26.9499			−0.870257
$960$		0			0
$961$	−25.6332			−0.826879
$962$	5.89975	−	5.89975i	0.190216	−	0.190216i
$963$	17.9499	−	17.9499i	0.578427	−	0.578427i
$964$		−	37.1662i		−	1.19704i
$965$		0			0
$966$			3.16625i			0.101872i
$967$		−	26.6332i		−	0.856468i	−0.903668	−	0.428234i	$-0.859136\pi$
$967$		−	26.6332i		−	0.856468i	0.903668	−	0.428234i	$-0.140864\pi$
$968$	−17.8997	+	17.8997i	−0.575320	+	0.575320i
$969$			0.899749i			0.0289041i
$970$		0			0
$971$	37.4749	+	37.4749i	1.20263	+	1.20263i	0.973364	+	0.229264i	$0.0736318\pi$
$971$	37.4749	+	37.4749i	1.20263	+	1.20263i	0.229264	+	0.973364i	$0.426368\pi$
$972$	−8.63325	−	8.63325i	−0.276912	−	0.276912i
$973$	−21.2164	+	21.2164i	−0.680166	+	0.680166i
$974$	−32.2164	−	32.2164i	−1.03228	−	1.03228i
$975$		0			0
$976$	−38.5330	+	38.5330i	−1.23341	+	1.23341i
$977$	56.3826			1.80384			0.901920	−	0.431903i	$-0.142158\pi$
$977$	56.3826			1.80384			0.901920	+	0.431903i	$0.142158\pi$
$978$	−30.8997	−	30.8997i	−0.988065	−	0.988065i
$979$	−12.4749	+	12.4749i	−0.398701	+	0.398701i
$980$		0			0
$981$	37.5831	+	37.5831i	1.19994	+	1.19994i
$982$	−59.2665			−1.89127
$983$			28.3166i			0.903160i	0.892231	+	0.451580i	$0.149139\pi$
$983$			28.3166i			0.903160i	−0.892231	+	0.451580i	$0.850861\pi$
$984$		−	43.1662i		−	1.37609i
$985$		0			0
$986$		−	5.26650i		−	0.167720i
$987$	40.0000	+	40.0000i	1.27321	+	1.27321i
$988$	2.73350			0.0869642
$989$	2.41688	−	2.41688i	0.0768522	−	0.0768522i
$990$		0			0
$991$	49.4829			1.57188			0.785938	−	0.618306i	$-0.212181\pi$
$991$	49.4829			1.57188			0.785938	+	0.618306i	$0.212181\pi$
$992$	−9.26650	+	9.26650i	−0.294212	+	0.294212i
$993$	5.00000			0.158670
$994$	20.0000	−	20.0000i	0.634361	−	0.634361i
$995$		0			0
$996$	61.7995			1.95819
$997$	−2.94987	−	2.94987i	−0.0934235	−	0.0934235i	0.658850	−	0.752274i	$-0.271043\pi$
$997$	−2.94987	−	2.94987i	−0.0934235	−	0.0934235i	−0.752274	+	0.658850i	$0.771043\pi$
$998$			45.7995i			1.44976i
$999$		−	9.78363i		−	0.309540i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.l.d.101.1	✓	4
4.3	odd	2		1600.2.l.e.1201.2		4
5.2	odd	4		400.2.q.c.149.2		4
5.3	odd	4		400.2.q.d.149.1		4
5.4	even	2		400.2.l.e.101.2	yes	4
16.3	odd	4		1600.2.l.e.401.2		4
16.13	even	4	inner	400.2.l.d.301.1	yes	4
20.3	even	4		1600.2.q.d.49.2		4
20.7	even	4		1600.2.q.c.49.1		4
20.19	odd	2		1600.2.l.d.1201.1		4
80.3	even	4		1600.2.q.c.849.1		4
80.13	odd	4		400.2.q.c.349.2		4
80.19	odd	4		1600.2.l.d.401.1		4
80.29	even	4		400.2.l.e.301.2	yes	4
80.67	even	4		1600.2.q.d.849.2		4
80.77	odd	4		400.2.q.d.349.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.l.d.101.1	✓	4	1.1	even	1	trivial
400.2.l.d.301.1	yes	4	16.13	even	4	inner
400.2.l.e.101.2	yes	4	5.4	even	2
400.2.l.e.301.2	yes	4	80.29	even	4
400.2.q.c.149.2		4	5.2	odd	4
400.2.q.c.349.2		4	80.13	odd	4
400.2.q.d.149.1		4	5.3	odd	4
400.2.q.d.349.1		4	80.77	odd	4
1600.2.l.d.401.1		4	80.19	odd	4
1600.2.l.d.1201.1		4	20.19	odd	2
1600.2.l.e.401.2		4	16.3	odd	4
1600.2.l.e.1201.2		4	4.3	odd	2
1600.2.q.c.49.1		4	20.7	even	4
1600.2.q.c.849.1		4	80.3	even	4
1600.2.q.d.49.2		4	20.3	even	4
1600.2.q.d.849.2		4	80.67	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-2.15831 + 2.15831i) q^{3} -2.00000i q^{4} -4.31662i q^{6} -2.31662i q^{7} +(2.00000 + 2.00000i) q^{8} -6.31662i q^{9} +(3.15831 + 3.15831i) q^{11} +(4.31662 + 4.31662i) q^{12} +(4.31662 - 4.31662i) q^{13} +(2.31662 + 2.31662i) q^{14} -4.00000 q^{16} -1.31662 q^{17} +(6.31662 + 6.31662i) q^{18} +(-0.158312 + 0.158312i) q^{19} +(5.00000 + 5.00000i) q^{21} -6.31662 q^{22} -0.316625i q^{23} -8.63325 q^{24} +8.63325i q^{26} +(7.15831 + 7.15831i) q^{27} -4.63325 q^{28} +(2.00000 - 2.00000i) q^{29} -2.31662 q^{31} +(4.00000 - 4.00000i) q^{32} -13.6332 q^{33} +(1.31662 - 1.31662i) q^{34} -12.6332 q^{36} +(-0.683375 - 0.683375i) q^{37} -0.316625i q^{38} +18.6332i q^{39} +5.00000i q^{41} -10.0000 q^{42} +(7.63325 + 7.63325i) q^{43} +(6.31662 - 6.31662i) q^{44} +(0.316625 + 0.316625i) q^{46} +8.00000 q^{47} +(8.63325 - 8.63325i) q^{48} +1.63325 q^{49} +(2.84169 - 2.84169i) q^{51} +(-8.63325 - 8.63325i) q^{52} +(3.31662 + 3.31662i) q^{53} -14.3166 q^{54} +(4.63325 - 4.63325i) q^{56} -0.683375i q^{57} +4.00000i q^{58} +(-1.31662 - 1.31662i) q^{59} +(9.63325 - 9.63325i) q^{61} +(2.31662 - 2.31662i) q^{62} -14.6332 q^{63} +8.00000i q^{64} +(13.6332 - 13.6332i) q^{66} +(-9.15831 + 9.15831i) q^{67} +2.63325i q^{68} +(0.683375 + 0.683375i) q^{69} -8.63325i q^{71} +(12.6332 - 12.6332i) q^{72} -6.68338i q^{73} +1.36675 q^{74} +(0.316625 + 0.316625i) q^{76} +(7.31662 - 7.31662i) q^{77} +(-18.6332 - 18.6332i) q^{78} +4.31662 q^{79} -11.9499 q^{81} +(-5.00000 - 5.00000i) q^{82} +(7.15831 - 7.15831i) q^{83} +(10.0000 - 10.0000i) q^{84} -15.2665 q^{86} +8.63325i q^{87} +12.6332i q^{88} +3.94987i q^{89} +(-10.0000 - 10.0000i) q^{91} -0.633250 q^{92} +(5.00000 - 5.00000i) q^{93} +(-8.00000 + 8.00000i) q^{94} +17.2665i q^{96} +6.63325 q^{97} +(-1.63325 + 1.63325i) q^{98} +(19.9499 - 19.9499i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 2 q^{3} + 8 q^{8} + 6 q^{11} + 4 q^{12} + 4 q^{13} - 4 q^{14} - 16 q^{16} + 8 q^{17} + 12 q^{18} + 6 q^{19} + 20 q^{21} - 12 q^{22} - 8 q^{24} + 22 q^{27} + 8 q^{28} + 8 q^{29} + 4 q^{31}+ \cdots + 40 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 2 * q^3 + 8 * q^8 + 6 * q^11 + 4 * q^12 + 4 * q^13 - 4 * q^14 - 16 * q^16 + 8 * q^17 + 12 * q^18 + 6 * q^19 + 20 * q^21 - 12 * q^22 - 8 * q^24 + 22 * q^27 + 8 * q^28 + 8 * q^29 + 4 * q^31 + 16 * q^32 - 28 * q^33 - 8 * q^34 - 24 * q^36 - 16 * q^37 - 40 * q^42 + 4 * q^43 + 12 * q^44 - 12 * q^46 + 32 * q^47 + 8 * q^48 - 20 * q^49 + 18 * q^51 - 8 * q^52 - 44 * q^54 - 8 * q^56 + 8 * q^59 + 12 * q^61 - 4 * q^62 - 32 * q^63 + 28 * q^66 - 30 * q^67 + 16 * q^69 + 24 * q^72 + 32 * q^74 - 12 * q^76 + 16 * q^77 - 48 * q^78 + 4 * q^79 - 8 * q^81 - 20 * q^82 + 22 * q^83 + 40 * q^84 - 8 * q^86 - 40 * q^91 + 24 * q^92 + 20 * q^93 - 32 * q^94 + 20 * q^98 + 40 * q^99

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