LMFDB - Embedded newform 400.2.q.c.149.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [400,2,Mod(149,400)] 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, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("400.149"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.q (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == 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			149.2
Root			$-1.65831 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	400.149
Dual form			400.2.q.c.349.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.00000i) q^{2} +(2.15831 + 2.15831i) q^{3} +2.00000i q^{4} -4.31662i q^{6} +2.31662 q^{7} +(2.00000 - 2.00000i) q^{8} +6.31662i q^{9} +(3.15831 + 3.15831i) q^{11} +(-4.31662 + 4.31662i) q^{12} +(-4.31662 - 4.31662i) q^{13} +(-2.31662 - 2.31662i) q^{14} -4.00000 q^{16} -1.31662i q^{17} +(6.31662 - 6.31662i) q^{18} +(0.158312 - 0.158312i) q^{19} +(5.00000 + 5.00000i) q^{21} -6.31662i q^{22} -0.316625 q^{23} +8.63325 q^{24} +8.63325i q^{26} +(-7.15831 + 7.15831i) q^{27} +4.63325i q^{28} +(-2.00000 + 2.00000i) q^{29} -2.31662 q^{31} +(4.00000 + 4.00000i) q^{32} +13.6332i q^{33} +(-1.31662 + 1.31662i) q^{34} -12.6332 q^{36} +(0.683375 - 0.683375i) q^{37} -0.316625 q^{38} -18.6332i q^{39} +5.00000i q^{41} -10.0000i q^{42} +(7.63325 - 7.63325i) q^{43} +(-6.31662 + 6.31662i) q^{44} +(0.316625 + 0.316625i) q^{46} +8.00000i q^{47} +(-8.63325 - 8.63325i) q^{48} -1.63325 q^{49} +(2.84169 - 2.84169i) q^{51} +(8.63325 - 8.63325i) q^{52} +(3.31662 - 3.31662i) q^{53} +14.3166 q^{54} +(4.63325 - 4.63325i) q^{56} +0.683375 q^{57} +4.00000 q^{58} +(1.31662 + 1.31662i) q^{59} +(9.63325 - 9.63325i) q^{61} +(2.31662 + 2.31662i) q^{62} +14.6332i q^{63} -8.00000i q^{64} +(13.6332 - 13.6332i) q^{66} +(-9.15831 - 9.15831i) q^{67} +2.63325 q^{68} +(-0.683375 - 0.683375i) q^{69} -8.63325i q^{71} +(12.6332 + 12.6332i) q^{72} -6.68338 q^{73} -1.36675 q^{74} +(0.316625 + 0.316625i) q^{76} +(7.31662 + 7.31662i) q^{77} +(-18.6332 + 18.6332i) q^{78} -4.31662 q^{79} -11.9499 q^{81} +(5.00000 - 5.00000i) q^{82} +(-7.15831 - 7.15831i) q^{83} +(-10.0000 + 10.0000i) q^{84} -15.2665 q^{86} -8.63325 q^{87} +12.6332 q^{88} -3.94987i q^{89} +(-10.0000 - 10.0000i) q^{91} -0.633250i q^{92} +(-5.00000 - 5.00000i) q^{93} +(8.00000 - 8.00000i) q^{94} +17.2665i q^{96} +6.63325i q^{97} +(1.63325 + 1.63325i) q^{98} +(-19.9499 + 19.9499i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 2 q^{3} - 4 q^{7} + 8 q^{8} + 6 q^{11} - 4 q^{12} - 4 q^{13} + 4 q^{14} - 16 q^{16} + 12 q^{18} - 6 q^{19} + 20 q^{21} + 12 q^{23} + 8 q^{24} - 22 q^{27} - 8 q^{29} + 4 q^{31} + 16 q^{32}+ \cdots - 40 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 2 * q^3 - 4 * q^7 + 8 * q^8 + 6 * q^11 - 4 * q^12 - 4 * q^13 + 4 * q^14 - 16 * q^16 + 12 * q^18 - 6 * q^19 + 20 * q^21 + 12 * q^23 + 8 * q^24 - 22 * q^27 - 8 * q^29 + 4 * q^31 + 16 * q^32 + 8 * q^34 - 24 * q^36 + 16 * q^37 + 12 * q^38 + 4 * q^43 - 12 * q^44 - 12 * q^46 - 8 * q^48 + 20 * q^49 + 18 * q^51 + 8 * q^52 + 44 * q^54 - 8 * q^56 + 16 * q^57 + 16 * q^58 - 8 * q^59 + 12 * q^61 - 4 * q^62 + 28 * q^66 - 30 * q^67 - 16 * q^68 - 16 * q^69 + 24 * q^72 - 40 * q^73 - 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 - 8 * q^87 + 24 * q^88 - 40 * q^91 - 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	0.957427	+	0.288675i	$0.0932147\pi$
$3$	2.15831	+	2.15831i	1.24610	+	1.24610i	0.288675	+	0.957427i	$0.406785\pi$
$4$			2.00000i			1.00000i
$5$		0			0
$5$		0			0
$6$		−	4.31662i		−	1.76225i
$7$	2.31662			0.875602			0.437801	−	0.899072i	$-0.355757\pi$
$7$	2.31662			0.875602			0.437801	+	0.899072i	$0.355757\pi$
$8$	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	−0.974997	−	0.222220i	$-0.928670\pi$
$13$	−4.31662	−	4.31662i	−1.19722	−	1.19722i	−0.222220	−	0.974997i	$-0.571330\pi$
$14$	−2.31662	−	2.31662i	−0.619144	−	0.619144i
$15$		0			0
$16$	−4.00000			−1.00000
$17$		−	1.31662i		−	0.319328i	−0.987171	−	0.159664i	$-0.948959\pi$
$17$		−	1.31662i		−	0.319328i	0.987171	−	0.159664i	$-0.0510411\pi$
$18$	6.31662	−	6.31662i	1.48884	−	1.48884i
$19$	0.158312	−	0.158312i	0.0363194	−	0.0363194i	−0.688714	−	0.725033i	$-0.741824\pi$
$19$	0.158312	−	0.158312i	0.0363194	−	0.0363194i	0.725033	+	0.688714i	$0.241824\pi$
$20$		0			0
$21$	5.00000	+	5.00000i	1.09109	+	1.09109i
$22$		−	6.31662i		−	1.34671i
$23$	−0.316625			−0.0660208			−0.0330104	−	0.999455i	$-0.510509\pi$
$23$	−0.316625			−0.0660208			−0.0330104	+	0.999455i	$0.510509\pi$
$24$	8.63325			1.76225
$25$		0			0
$26$			8.63325i			1.69312i
$27$	−7.15831	+	7.15831i	−1.37762	+	1.37762i
$28$			4.63325i			0.875602i
$29$	−2.00000	+	2.00000i	−0.371391	+	0.371391i	−0.867984	−	0.496593i	$-0.834584\pi$
$29$	−2.00000	+	2.00000i	−0.371391	+	0.371391i	0.496593	+	0.867984i	$0.334584\pi$
$30$		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
$33$			13.6332i			2.37324i
$34$	−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	$-0.724687\pi$
$37$	0.683375	−	0.683375i	0.112346	−	0.112346i	0.761045	+	0.648699i	$0.224687\pi$
$38$	−0.316625			−0.0513633
$39$		−	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	$0.872325\pi$
$42$		−	10.0000i		−	1.54303i
$43$	7.63325	−	7.63325i	1.16406	−	1.16406i	0.180481	−	0.983578i	$-0.442234\pi$
$43$	7.63325	−	7.63325i	1.16406	−	1.16406i	0.983578	−	0.180481i	$-0.0577655\pi$
$44$	−6.31662	+	6.31662i	−0.952267	+	0.952267i
$45$		0			0
$46$	0.316625	+	0.316625i	0.0466838	+	0.0466838i
$47$			8.00000i			1.16692i	0.812142	+	0.583460i	$0.198301\pi$
$47$			8.00000i			1.16692i	−0.812142	+	0.583460i	$0.801699\pi$
$48$	−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	−0.441626	−	0.897199i	$-0.645598\pi$
$53$	3.31662	−	3.31662i	0.455573	−	0.455573i	0.897199	+	0.441626i	$0.145598\pi$
$54$	14.3166			1.94825
$55$		0			0
$56$	4.63325	−	4.63325i	0.619144	−	0.619144i
$57$	0.683375			0.0905153
$58$	4.00000			0.525226
$59$	1.31662	+	1.31662i	0.171410	+	0.171410i	0.787599	−	0.616189i	$-0.211324\pi$
$59$	1.31662	+	1.31662i	0.171410	+	0.171410i	−0.616189	+	0.787599i	$0.711324\pi$
$60$		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
$63$			14.6332i			1.84362i
$64$		−	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	−0.991908	−	0.126958i	$-0.959479\pi$
$67$	−9.15831	−	9.15831i	−1.11887	−	1.11887i	−0.126958	−	0.991908i	$-0.540521\pi$
$68$	2.63325			0.319328
$69$	−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
$73$	−6.68338			−0.782230			−0.391115	−	0.920342i	$-0.627911\pi$
$73$	−6.68338			−0.782230			−0.391115	+	0.920342i	$0.627911\pi$
$74$	−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	$-0.578075\pi$
$79$	−4.31662			−0.485658			−0.242829	+	0.970069i	$0.578075\pi$
$80$		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	$-0.437509\pi$
$83$	−7.15831	−	7.15831i	−0.785727	−	0.785727i	−0.980791	+	0.195064i	$0.937509\pi$
$84$	−10.0000	+	10.0000i	−1.09109	+	1.09109i
$85$		0			0
$86$	−15.2665			−1.64623
$87$	−8.63325			−0.925582
$88$	12.6332			1.34671
$89$		−	3.94987i		−	0.418686i	−0.977842	−	0.209343i	$-0.932868\pi$
$89$		−	3.94987i		−	0.418686i	0.977842	−	0.209343i	$-0.0671325\pi$
$90$		0			0
$91$	−10.0000	−	10.0000i	−1.04828	−	1.04828i
$92$		−	0.633250i		−	0.0660208i
$93$	−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
$97$			6.63325i			0.673504i	0.941593	+	0.336752i	$0.109328\pi$
$97$			6.63325i			0.673504i	−0.941593	+	0.336752i	$0.890672\pi$
$98$	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	$0.627960\pi$
$102$	−5.68338			−0.562738
$103$	−4.63325			−0.456528			−0.228264	−	0.973599i	$-0.573305\pi$
$103$	−4.63325			−0.456528			−0.228264	+	0.973599i	$0.573305\pi$
$104$	−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	$-0.812229\pi$
$107$	−2.84169	+	2.84169i	−0.274716	+	0.274716i	0.556279	+	0.830995i	$0.312229\pi$
$108$	−14.3166	−	14.3166i	−1.37762	−	1.37762i
$109$	5.94987	−	5.94987i	0.569895	−	0.569895i	−0.362204	−	0.932099i	$-0.617976\pi$
$109$	5.94987	−	5.94987i	0.569895	−	0.569895i	0.932099	+	0.362204i	$0.117976\pi$
$110$		0			0
$111$	2.94987			0.279990
$112$	−9.26650			−0.875602
$113$			2.36675i			0.222645i	0.993784	+	0.111323i	$0.0355087\pi$
$113$			2.36675i			0.222645i	−0.993784	+	0.111323i	$0.964491\pi$
$114$	−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
$118$		−	2.63325i		−	0.242410i
$119$		−	3.05013i		−	0.279605i
$120$		0			0
$121$			8.94987i			0.813625i
$122$	−19.2665			−1.74431
$123$	−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
$127$		−	6.31662i		−	0.560510i	−0.959926	−	0.280255i	$-0.909581\pi$
$127$		−	6.31662i		−	0.560510i	0.959926	−	0.280255i	$-0.0904190\pi$
$128$	−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	$0.230322\pi$
$132$	−27.2665			−2.37324
$133$	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
$137$	11.6332			0.993896			0.496948	−	0.867780i	$-0.334454\pi$
$137$	11.6332			0.993896			0.496948	+	0.867780i	$0.334454\pi$
$138$			1.36675i			0.116346i
$139$	9.15831	+	9.15831i	0.776798	+	0.776798i	0.979285	−	0.202487i	$-0.0649024\pi$
$139$	9.15831	+	9.15831i	0.776798	+	0.776798i	−0.202487	+	0.979285i	$0.564902\pi$
$140$		0			0
$141$	−17.2665	+	17.2665i	−1.45410	+	1.45410i
$142$	−8.63325	+	8.63325i	−0.724486	+	0.724486i
$143$		−	27.2665i		−	2.28014i
$144$		−	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	$-0.836221\pi$
$149$	−16.6332	−	16.6332i	−1.36265	−	1.36265i	−0.492124	−	0.870525i	$-0.663779\pi$
$150$		0			0
$151$			4.31662i			0.351282i	0.984454	+	0.175641i	$0.0561998\pi$
$151$			4.31662i			0.351282i	−0.984454	+	0.175641i	$0.943800\pi$
$152$		−	0.633250i		−	0.0513633i
$153$	8.31662			0.672359
$154$		−	14.6332i		−	1.17918i
$155$		0			0
$156$	37.2665			2.98371
$157$	−11.3166	−	11.3166i	−0.903165	−	0.903165i	0.0925436	−	0.995709i	$-0.470500\pi$
$157$	−11.3166	−	11.3166i	−0.903165	−	0.903165i	−0.995709	+	0.0925436i	$0.970500\pi$
$158$	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	$-0.379762\pi$
$163$	−7.15831	−	7.15831i	−0.560682	−	0.560682i	−0.929501	+	0.368819i	$0.879762\pi$
$164$	−10.0000			−0.780869
$165$		0			0
$166$			14.3166i			1.11119i
$167$	18.0000			1.39288			0.696441	−	0.717614i	$-0.254766\pi$
$167$	18.0000			1.39288			0.696441	+	0.717614i	$0.254766\pi$
$168$	20.0000			1.54303
$169$			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	$-0.00487730\pi$
$173$	12.9499	+	12.9499i	0.984561	+	0.984561i	−0.0153219	+	0.999883i	$0.504877\pi$
$174$	8.63325	+	8.63325i	0.654485	+	0.654485i
$175$		0			0
$176$	−12.6332	−	12.6332i	−0.952267	−	0.952267i
$177$			5.68338i			0.427189i
$178$	−3.94987	+	3.94987i	−0.296056	+	0.296056i
$179$	8.79156	−	8.79156i	0.657112	−	0.657112i	−0.297584	−	0.954696i	$-0.596181\pi$
$179$	8.79156	−	8.79156i	0.657112	−	0.657112i	0.954696	+	0.297584i	$0.0961807\pi$
$180$		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	$0.805772\pi$
$182$			20.0000i			1.48250i
$183$	41.5831			3.07391
$184$	−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
$188$	−16.0000			−1.16692
$189$	−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
$193$		−	4.68338i		−	0.337117i	−0.985692	−	0.168558i	$-0.946089\pi$
$193$		−	4.68338i		−	0.337117i	0.985692	−	0.168558i	$-0.0539112\pi$
$194$	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	−0.202143	+	0.979356i	$0.564790\pi$
$197$	−16.5831	+	16.5831i	−1.18150	+	1.18150i	−0.979356	+	0.202143i	$0.935210\pi$
$198$	39.8997			2.83555
$199$			12.6332i			0.895547i	0.894147	+	0.447774i	$0.147783\pi$
$199$			12.6332i			0.895547i	−0.894147	+	0.447774i	$0.852217\pi$
$200$		0			0
$201$		−	39.5330i		−	2.78844i
$202$		−	10.6332i		−	0.748153i
$203$	−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
$207$		−	2.00000i		−	0.139010i
$208$	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
$217$	−5.36675			−0.364319
$218$	−11.8997			−0.805953
$219$	−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
$223$			6.00000i			0.401790i	0.979613	+	0.200895i	$0.0643850\pi$
$223$			6.00000i			0.401790i	−0.979613	+	0.200895i	$0.935615\pi$
$224$	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	0.837014	−	0.547182i	$-0.184300\pi$
$227$	4.36675	+	4.36675i	0.289831	+	0.289831i	−0.547182	+	0.837014i	$0.684300\pi$
$228$			1.36675i			0.0905153i
$229$	2.00000	+	2.00000i	0.132164	+	0.132164i	0.770094	−	0.637930i	$-0.220209\pi$
$229$	2.00000	+	2.00000i	0.132164	+	0.132164i	−0.637930	+	0.770094i	$0.720209\pi$
$230$		0			0
$231$			31.5831i			2.07802i
$232$			8.00000i			0.525226i
$233$	−11.8997			−0.779578			−0.389789	−	0.920904i	$-0.627452\pi$
$233$	−11.8997			−0.779578			−0.389789	+	0.920904i	$0.627452\pi$
$234$	−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	$-0.294115\pi$
$239$	18.6332			1.20528			0.602642	+	0.798011i	$0.294115\pi$
$240$		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
$247$	−1.36675			−0.0869642
$248$	−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	$0.883257\pi$
$252$	−29.2665			−1.84362
$253$	−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
$257$			16.6332i			1.03755i	0.854910	+	0.518777i	$0.173612\pi$
$257$			16.6332i			1.03755i	−0.854910	+	0.518777i	$0.826388\pi$
$258$	−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
$262$	−2.00000			−0.123560
$263$	15.5831			0.960897			0.480448	−	0.877023i	$-0.340474\pi$
$263$	15.5831			0.960897			0.480448	+	0.877023i	$0.340474\pi$
$264$	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	−0.872947	−	0.487815i	$-0.837794\pi$
$269$	−6.31662	+	6.31662i	−0.385131	+	0.385131i	0.487815	+	0.872947i	$0.337794\pi$
$270$		0			0
$271$	−0.949874			−0.0577008			−0.0288504	−	0.999584i	$-0.509185\pi$
$271$	−0.949874			−0.0577008			−0.0288504	+	0.999584i	$0.509185\pi$
$272$			5.26650i			0.319328i
$273$		−	43.1662i		−	2.61254i
$274$	−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	$-0.958130\pi$
$277$	−14.3166	+	14.3166i	−0.860203	+	0.860203i	0.131159	+	0.991361i	$0.458130\pi$
$278$		−	18.3166i		−	1.09856i
$279$		−	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	$0.930457\pi$
$282$	34.5330			2.05641
$283$	−3.84169	+	3.84169i	−0.228365	+	0.228365i	−0.812009	−	0.583645i	$-0.801626\pi$
$283$	−3.84169	+	3.84169i	−0.228365	+	0.228365i	0.583645	+	0.812009i	$0.301626\pi$
$284$	17.2665			1.02458
$285$		0			0
$286$	−27.2665	+	27.2665i	−1.61230	+	1.61230i
$287$			11.5831i			0.683730i
$288$	−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
$292$		−	13.3668i		−	0.782230i
$293$	−18.2665	+	18.2665i	−1.06714	+	1.06714i	−0.0695627	+	0.997578i	$0.522160\pi$
$293$	−18.2665	+	18.2665i	−1.06714	+	1.06714i	−0.997578	+	0.0695627i	$0.977840\pi$
$294$			7.05013i			0.411172i
$295$		0			0
$296$		−	2.73350i		−	0.158882i
$297$	−45.2164			−2.62372
$298$			33.2665i			1.92708i
$299$	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
$303$			22.9499i			1.31844i
$304$	−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	0.176282	−	0.984340i	$-0.443593\pi$
$307$	−14.1583	−	14.1583i	−0.808058	−	0.808058i	−0.984340	+	0.176282i	$0.943593\pi$
$308$	−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
$313$	−16.0000			−0.904373			−0.452187	−	0.891923i	$-0.649356\pi$
$313$	−16.0000			−0.904373			−0.452187	+	0.891923i	$0.649356\pi$
$314$			22.6332i			1.27727i
$315$		0			0
$316$		−	8.63325i		−	0.485658i
$317$	−14.9499	−	14.9499i	−0.839669	−	0.839669i	0.149147	−	0.988815i	$-0.452347\pi$
$317$	−14.9499	−	14.9499i	−0.839669	−	0.839669i	−0.988815	+	0.149147i	$0.952347\pi$
$318$	−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
$327$	25.6834			1.42029
$328$	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
$337$		−	22.8997i		−	1.24743i	−0.781652	−	0.623714i	$-0.785623\pi$
$337$		−	22.8997i		−	1.24743i	0.781652	−	0.623714i	$-0.214377\pi$
$338$	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
$342$		−	2.00000i		−	0.108148i
$343$	−20.0000			−1.07990
$344$		−	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	$-0.565557\pi$
$347$	14.4248	−	14.4248i	0.774364	−	0.774364i	0.978866	+	0.204502i	$0.0655574\pi$
$348$		−	17.2665i		−	0.925582i
$349$	−24.2665	+	24.2665i	−1.29896	+	1.29896i	−0.369874	+	0.929082i	$0.620599\pi$
$349$	−24.2665	+	24.2665i	−1.29896	+	1.29896i	−0.929082	+	0.369874i	$0.879401\pi$
$350$		0			0
$351$	61.7995			3.29861
$352$			25.2665i			1.34671i
$353$			33.2665i			1.77060i	0.465023	+	0.885299i	$0.346046\pi$
$353$			33.2665i			1.77060i	−0.465023	+	0.885299i	$0.653954\pi$
$354$	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
$358$	−17.5831			−0.929297
$359$			9.68338i			0.511069i	0.966800	+	0.255534i	$0.0822514\pi$
$359$			9.68338i			0.511069i	−0.966800	+	0.255534i	$0.917749\pi$
$360$		0			0
$361$			18.9499i			0.997362i
$362$			6.63325i			0.348636i
$363$	−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
$367$			26.6332i			1.39024i	0.718892	+	0.695122i	$0.244650\pi$
$367$			26.6332i			1.39024i	−0.718892	+	0.695122i	$0.755350\pi$
$368$	1.26650			0.0660208
$369$	−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	−0.765720	−	0.643174i	$-0.777617\pi$
$373$	−2.36675	+	2.36675i	−0.122546	+	0.122546i	0.643174	+	0.765720i	$0.277617\pi$
$374$	−8.31662			−0.430042
$375$		0			0
$376$	16.0000	+	16.0000i	0.825137	+	0.825137i
$377$	17.2665			0.889270
$378$	33.1662			1.70589
$379$	11.4248	+	11.4248i	0.586853	+	0.586853i	0.936778	−	0.349925i	$-0.113793\pi$
$379$	11.4248	+	11.4248i	0.586853	+	0.586853i	−0.349925	+	0.936778i	$0.613793\pi$
$380$		0			0
$381$	13.6332	−	13.6332i	0.698453	−	0.698453i
$382$	20.9499	+	20.9499i	1.07189	+	1.07189i
$383$		−	16.9499i		−	0.866098i	−0.901370	−	0.433049i	$-0.857438\pi$
$383$		−	16.9499i		−	0.866098i	0.901370	−	0.433049i	$-0.142562\pi$
$384$	−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
$388$	−13.2665			−0.673504
$389$	4.26650	+	4.26650i	0.216320	+	0.216320i	0.806946	−	0.590626i	$-0.201119\pi$
$389$	4.26650	+	4.26650i	0.216320	+	0.216320i	−0.590626	+	0.806946i	$0.701119\pi$
$390$		0			0
$391$			0.416876i			0.0210823i
$392$	−3.26650	+	3.26650i	−0.164983	+	0.164983i
$393$	4.31662			0.217745
$394$	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	0.947074	+	0.321015i	$0.104024\pi$
$397$	25.2665	+	25.2665i	1.26809	+	1.26809i	0.321015	+	0.947074i	$0.395976\pi$
$398$	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
$407$	4.31662			0.213967
$408$		−	11.3668i		−	0.562738i
$409$		−	19.6332i		−	0.970802i	−0.874292	−	0.485401i	$-0.838674\pi$
$409$		−	19.6332i		−	0.970802i	0.874292	−	0.485401i	$-0.161326\pi$
$410$		0			0
$411$	25.1082	+	25.1082i	1.23850	+	1.23850i
$412$		−	9.26650i		−	0.456528i
$413$	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
$417$			39.5330i			1.93594i
$418$	−1.00000	−	1.00000i	−0.0489116	−	0.0489116i
$419$	11.5251	−	11.5251i	0.563036	−	0.563036i	−0.367132	−	0.930169i	$-0.619660\pi$
$419$	11.5251	−	11.5251i	0.563036	−	0.563036i	0.930169	+	0.367132i	$0.119660\pi$
$420$		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	$0.698956\pi$
$422$	−23.5831			−1.14801
$423$	−50.5330			−2.45700
$424$		−	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
$433$			12.5831i			0.604706i	0.953196	+	0.302353i	$0.0977722\pi$
$433$			12.5831i			0.604706i	−0.953196	+	0.302353i	$0.902228\pi$
$434$	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
$438$			28.8496i			1.37849i
$439$			5.36675i			0.256141i	0.991765	+	0.128071i	$0.0408784\pi$
$439$			5.36675i			0.256141i	−0.991765	+	0.128071i	$0.959122\pi$
$440$		0			0
$441$		−	10.3166i		−	0.491268i
$442$	11.3668			0.540661
$443$	19.1082	−	19.1082i	0.907857	−	0.907857i	−0.0882417	−	0.996099i	$-0.528125\pi$
$443$	19.1082	−	19.1082i	0.907857	−	0.907857i	0.996099	+	0.0882417i	$0.0281248\pi$
$444$			5.89975i			0.279990i
$445$		0			0
$446$	6.00000	−	6.00000i	0.284108	−	0.284108i
$447$		−	71.7995i		−	3.39600i
$448$		−	18.5330i		−	0.875602i
$449$	−20.6834			−0.976109			−0.488054	−	0.872813i	$-0.662293\pi$
$449$	−20.6834			−0.976109			−0.488054	+	0.872813i	$0.662293\pi$
$450$		0			0
$451$	−15.7916	+	15.7916i	−0.743596	+	0.743596i
$452$	−4.73350			−0.222645
$453$	−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
$457$	−17.0000			−0.795226			−0.397613	−	0.917553i	$-0.630161\pi$
$457$	−17.0000			−0.795226			−0.397613	+	0.917553i	$0.630161\pi$
$458$		−	4.00000i		−	0.186908i
$459$	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
$463$			24.6332i			1.14480i	0.819973	+	0.572402i	$0.193988\pi$
$463$			24.6332i			1.14480i	−0.819973	+	0.572402i	$0.806012\pi$
$464$	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	0.295246	−	0.955421i	$-0.404598\pi$
$467$	−14.2665	−	14.2665i	−0.660175	−	0.660175i	−0.955421	+	0.295246i	$0.904598\pi$
$468$	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
$472$	5.26650			0.242410
$473$	48.2164			2.21699
$474$			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	$-0.574985\pi$
$479$	−10.2164			−0.466798			−0.233399	+	0.972381i	$0.574985\pi$
$480$		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
$487$	−32.2164			−1.45986			−0.729932	−	0.683520i	$-0.760448\pi$
$487$	−32.2164			−1.45986			−0.729932	+	0.683520i	$0.760448\pi$
$488$		−	38.5330i		−	1.74431i
$489$		−	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
$497$		−	20.0000i		−	0.897123i
$498$	−30.8997	+	30.8997i	−1.38465	+	1.38465i
$499$	−22.8997	+	22.8997i	−1.02513	+	1.02513i	−0.0254576	+	0.999676i	$0.508104\pi$
$499$	−22.8997	+	22.8997i	−1.02513	+	1.02513i	−0.999676	+	0.0254576i	$0.991896\pi$
$500$		0			0
$501$	38.8496	+	38.8496i	1.73567	+	1.73567i
$502$			18.2164i			0.813037i
$503$	−31.8997			−1.42234			−0.711170	−	0.703020i	$-0.751834\pi$
$503$	−31.8997			−1.42234			−0.711170	+	0.703020i	$0.751834\pi$
$504$	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
$508$	12.6332			0.560510
$509$	20.2665	−	20.2665i	0.898297	−	0.898297i	−0.0969887	−	0.995285i	$-0.530921\pi$
$509$	20.2665	−	20.2665i	0.898297	−	0.898297i	0.995285	+	0.0969887i	$0.0309211\pi$
$510$		0			0
$511$	−15.4829			−0.684922
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$			2.26650i			0.100068i
$514$	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
$518$	−3.16625			−0.139117
$519$			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	$-0.0965336\pi$
$522$			25.2665i			1.10588i
$523$	−7.47494	+	7.47494i	−0.326856	+	0.326856i	−0.851390	−	0.524534i	$-0.824240\pi$
$523$	−7.47494	+	7.47494i	−0.326856	+	0.326856i	0.524534	+	0.851390i	$0.324240\pi$
$524$	2.00000	+	2.00000i	0.0873704	+	0.0873704i
$525$		0			0
$526$	−15.5831	−	15.5831i	−0.679456	−	0.679456i
$527$			3.05013i			0.132866i
$528$		−	54.5330i		−	2.37324i
$529$	−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
$537$	37.9499			1.63766
$538$	12.6332			0.544658
$539$	−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
$543$		−	14.3166i		−	0.614385i
$544$	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	0.285364	−	0.958419i	$-0.407886\pi$
$547$	−15.7414	−	15.7414i	−0.673055	−	0.673055i	−0.958419	+	0.285364i	$0.907886\pi$
$548$			23.2665i			0.993896i
$549$	60.8496	+	60.8496i	2.59700	+	2.59700i
$550$		0			0
$551$			0.633250i			0.0269773i
$552$	−2.73350			−0.116346
$553$	−10.0000			−0.425243
$554$	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	−0.992454	−	0.122617i	$-0.960871\pi$
$557$	−26.3166	−	26.3166i	−1.11507	−	1.11507i	−0.122617	−	0.992454i	$-0.539129\pi$
$558$	−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	$-0.0703402\pi$
$563$	17.9499	+	17.9499i	0.756497	+	0.756497i	−0.219186	+	0.975683i	$0.570340\pi$
$564$	−34.5330	−	34.5330i	−1.45410	−	1.45410i
$565$		0			0
$566$	7.68338			0.322956
$567$	−27.6834			−1.16259
$568$	−17.2665	−	17.2665i	−0.724486	−	0.724486i
$569$			9.00000i			0.377300i	0.982044	+	0.188650i	$0.0604111\pi$
$569$			9.00000i			0.377300i	−0.982044	+	0.188650i	$0.939589\pi$
$570$		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	$0.766335\pi$
$572$	54.5330			2.28014
$573$	−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
$577$		−	15.6332i		−	0.650821i	−0.945573	−	0.325410i	$-0.894498\pi$
$577$		−	15.6332i		−	0.650821i	0.945573	−	0.325410i	$-0.105502\pi$
$578$	−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
$582$	28.6332			1.18689
$583$	20.9499			0.867655
$584$	−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	$-0.838700\pi$
$587$	−9.42481	+	9.42481i	−0.389004	+	0.389004i	0.485328	+	0.874332i	$0.338700\pi$
$588$	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
$593$			35.5330i			1.45917i	0.683893	+	0.729583i	$0.260286\pi$
$593$			35.5330i			1.45917i	−0.683893	+	0.729583i	$0.739714\pi$
$594$	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
$598$		−	2.73350i		−	0.111781i
$599$		−	36.2164i		−	1.47976i	−0.672738	−	0.739880i	$-0.734882\pi$
$599$		−	36.2164i		−	1.47976i	0.672738	−	0.739880i	$-0.265118\pi$
$600$		0			0
$601$			22.0501i			0.899443i	0.893169	+	0.449722i	$0.148477\pi$
$601$			22.0501i			0.899443i	−0.893169	+	0.449722i	$0.851523\pi$
$602$	−35.3668			−1.44144
$603$	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
$607$			21.1662i			0.859112i	0.903040	+	0.429556i	$0.141330\pi$
$607$			21.1662i			0.859112i	−0.903040	+	0.429556i	$0.858670\pi$
$608$	1.26650			0.0513633
$609$	−20.0000			−0.810441
$610$		0			0
$611$	34.5330	−	34.5330i	1.39706	−	1.39706i
$612$			16.6332i			0.672359i
$613$	16.2665	−	16.2665i	0.656998	−	0.656998i	−0.297671	−	0.954669i	$-0.596210\pi$
$613$	16.2665	−	16.2665i	0.656998	−	0.656998i	0.954669	+	0.297671i	$0.0962098\pi$
$614$			28.3166i			1.14277i
$615$		0			0
$616$	29.2665			1.17918
$617$	0.733501			0.0295296			0.0147648	−	0.999891i	$-0.495300\pi$
$617$	0.733501			0.0295296			0.0147648	+	0.999891i	$0.495300\pi$
$618$			20.0000i			0.804518i
$619$	8.36675	+	8.36675i	0.336288	+	0.336288i	0.854968	−	0.518680i	$-0.173576\pi$
$619$	8.36675	+	8.36675i	0.336288	+	0.336288i	−0.518680	+	0.854968i	$0.673576\pi$
$620$		0			0
$621$	2.26650	−	2.26650i	0.0909515	−	0.0909515i
$622$	12.9499	−	12.9499i	0.519243	−	0.519243i
$623$		−	9.15038i		−	0.366602i
$624$			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
$633$	50.8997			2.02308
$634$			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	$-0.229869\pi$
$643$	2.26650	+	2.26650i	0.0893820	+	0.0893820i	−0.661002	+	0.750384i	$0.729869\pi$
$644$		−	1.46700i		−	0.0578080i
$645$		0			0
$646$			0.416876i			0.0164018i
$647$	21.1662			0.832131			0.416066	−	0.909335i	$-0.363409\pi$
$647$	21.1662			0.832131			0.416066	+	0.909335i	$0.363409\pi$
$648$	−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	$-0.100394\pi$
$653$	16.3668	+	16.3668i	0.640480	+	0.640480i	−0.310193	+	0.950674i	$0.600394\pi$
$654$	−25.6834	−	25.6834i	−1.00430	−	1.00430i
$655$		0			0
$656$		−	20.0000i		−	0.780869i
$657$		−	42.2164i		−	1.64702i
$658$	18.5330	−	18.5330i	0.722491	−	0.722491i
$659$	25.1583	−	25.1583i	0.980029	−	0.980029i	−0.0197757	−	0.999804i	$-0.506295\pi$
$659$	25.1583	−	25.1583i	0.980029	−	0.980029i	0.999804	+	0.0197757i	$0.00629522\pi$
$660$		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	$-0.684110\pi$
$662$			2.31662i			0.0900382i
$663$	−24.5330			−0.952783
$664$	−28.6332			−1.11119
$665$		0			0
$666$		−	8.63325i		−	0.334532i
$667$	0.633250	−	0.633250i	0.0245195	−	0.0245195i
$668$			36.0000i			1.39288i
$669$	−12.9499	+	12.9499i	−0.500671	+	0.500671i
$670$		0			0
$671$	60.8496			2.34907
$672$			40.0000i			1.54303i
$673$		−	42.6332i		−	1.64339i	−0.569927	−	0.821696i	$-0.693028\pi$
$673$		−	42.6332i		−	1.64339i	0.569927	−	0.821696i	$-0.306972\pi$
$674$	−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	$-0.650037\pi$
$677$	11.3668	−	11.3668i	0.436860	−	0.436860i	0.890954	+	0.454094i	$0.150037\pi$
$678$	10.2164			0.392357
$679$			15.3668i			0.589722i
$680$		0			0
$681$			18.8496i			0.722319i
$682$			14.6332i			0.560336i
$683$	5.47494	−	5.47494i	0.209493	−	0.209493i	−0.594559	−	0.804052i	$-0.702673\pi$
$683$	5.47494	−	5.47494i	0.209493	−	0.209493i	0.804052	+	0.594559i	$0.202673\pi$
$684$	−2.00000	+	2.00000i	−0.0764719	+	0.0764719i
$685$		0			0
$686$	20.0000	+	20.0000i	0.763604	+	0.763604i
$687$			8.63325i			0.329379i
$688$	−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
$697$	6.58312			0.249354
$698$	48.5330			1.83700
$699$	−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
$703$		−	0.216374i		−	0.00816068i
$704$	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
$708$	−11.3668			−0.427189
$709$	22.0000	+	22.0000i	0.826227	+	0.826227i	0.986993	−	0.160765i	$-0.0513962\pi$
$709$	22.0000	+	22.0000i	0.826227	+	0.826227i	−0.160765	+	0.986993i	$0.551396\pi$
$710$		0			0
$711$		−	27.2665i		−	1.02257i
$712$	−7.89975	−	7.89975i	−0.296056	−	0.296056i
$713$	0.733501			0.0274698
$714$	−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	$-0.517518\pi$
$719$	−2.94987			−0.110012			−0.0550059	+	0.998486i	$0.517518\pi$
$720$		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
$727$	2.53300			0.0939437			0.0469719	−	0.998896i	$-0.485043\pi$
$727$	2.53300			0.0939437			0.0469719	+	0.998896i	$0.485043\pi$
$728$	−40.0000			−1.48250
$729$			17.2164i			0.637643i
$730$		0			0
$731$	−10.0501	−	10.0501i	−0.371717	−	0.371717i
$732$			83.1662i			3.07391i
$733$	5.68338	+	5.68338i	0.209920	+	0.209920i	0.804234	−	0.594313i	$-0.202576\pi$
$733$	5.68338	+	5.68338i	0.209920	+	0.209920i	−0.594313	+	0.804234i	$0.702576\pi$
$734$	26.6332	−	26.6332i	0.983051	−	0.983051i
$735$		0			0
$736$	−1.26650	−	1.26650i	−0.0466838	−	0.0466838i
$737$		−	57.8496i		−	2.13092i
$738$	31.5831	+	31.5831i	1.16259	+	1.16259i
$739$	14.3668	−	14.3668i	0.528489	−	0.528489i	−0.391632	−	0.920122i	$-0.628089\pi$
$739$	14.3668	−	14.3668i	0.528489	−	0.528489i	0.920122	+	0.391632i	$0.128089\pi$
$740$		0			0
$741$	−2.94987	−	2.94987i	−0.108366	−	0.108366i
$742$	−15.3668			−0.564131
$743$	−20.3166			−0.745345			−0.372672	−	0.927963i	$-0.621558\pi$
$743$	−20.3166			−0.745345			−0.372672	+	0.927963i	$0.621558\pi$
$744$	−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	$0.218154\pi$
$752$		−	32.0000i		−	1.16692i
$753$		−	39.3166i		−	1.43278i
$754$	−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	0.290333	−	0.956926i	$-0.406234\pi$
$757$	34.3166	−	34.3166i	1.24726	−	1.24726i	0.956926	−	0.290333i	$-0.0937662\pi$
$758$		−	22.8496i		−	0.829936i
$759$		−	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	$0.801161\pi$
$762$	−27.2665			−0.987761
$763$	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
$767$		−	11.3668i		−	0.410430i
$768$	34.5330	+	34.5330i	1.24610	+	1.24610i
$769$	32.4829			1.17136			0.585681	−	0.810542i	$-0.300827\pi$
$769$	32.4829			1.17136			0.585681	+	0.810542i	$0.300827\pi$
$770$		0			0
$771$	−35.8997	+	35.8997i	−1.29290	+	1.29290i
$772$	9.36675			0.337117
$773$	−17.3668	+	17.3668i	−0.624639	+	0.624639i	−0.946714	−	0.322075i	$-0.895620\pi$
$773$	−17.3668	+	17.3668i	−0.624639	+	0.624639i	0.322075	+	0.946714i	$0.395620\pi$
$774$		−	96.4327i		−	3.46620i
$775$		0			0
$776$	13.2665	+	13.2665i	0.476240	+	0.476240i
$777$	6.83375			0.245159
$778$		−	8.53300i		−	0.305923i
$779$	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
$783$		−	28.6332i		−	1.02327i
$784$	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	0.571252	−	0.820775i	$-0.306458\pi$
$787$	−7.00000	−	7.00000i	−0.249523	−	0.249523i	−0.820775	+	0.571252i	$0.806458\pi$
$788$	−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
$792$			79.7995i			2.83555i
$793$	−83.1662			−2.95332
$794$		−	50.5330i		−	1.79335i
$795$		0			0
$796$	−25.2665			−0.895547
$797$	−15.6332	−	15.6332i	−0.553758	−	0.553758i	0.373765	−	0.927523i	$-0.378067\pi$
$797$	−15.6332	−	15.6332i	−0.553758	−	0.553758i	−0.927523	+	0.373765i	$0.878067\pi$
$798$	−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
$807$	−27.2665			−0.959826
$808$	21.2665			0.748153
$809$			38.5330i			1.35475i	0.735639	+	0.677374i	$0.236882\pi$
$809$			38.5330i			1.35475i	−0.735639	+	0.677374i	$0.763118\pi$
$810$		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
$817$		−	2.41688i		−	0.0845558i
$818$	−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	$0.763621\pi$
$822$		−	50.2164i		−	1.75150i
$823$	9.89975			0.345084			0.172542	−	0.985002i	$-0.444802\pi$
$823$	9.89975			0.345084			0.172542	+	0.985002i	$0.444802\pi$
$824$	−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	$-0.811762\pi$
$827$	−7.84169	+	7.84169i	−0.272682	+	0.272682i	0.557497	+	0.830179i	$0.311762\pi$
$828$	4.00000			0.139010
$829$	0.733501	−	0.733501i	0.0254755	−	0.0254755i	−0.694254	−	0.719730i	$-0.744266\pi$
$829$	0.733501	−	0.733501i	0.0254755	−	0.0254755i	0.719730	+	0.694254i	$0.244266\pi$
$830$		0			0
$831$	−61.7995			−2.14380
$832$	−34.5330	+	34.5330i	−1.19722	+	1.19722i
$833$			2.15038i			0.0745061i
$834$	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
$838$	−23.0501			−0.796253
$839$			2.63325i			0.0909099i	0.998966	+	0.0454549i	$0.0144737\pi$
$839$			2.63325i			0.0909099i	−0.998966	+	0.0454549i	$0.985526\pi$
$840$		0			0
$841$			21.0000i			0.724138i
$842$		−	9.26650i		−	0.319345i
$843$	−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
$847$			20.7335i			0.712412i
$848$	−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	−0.266493	−	0.963837i	$-0.585865\pi$
$853$	20.3668	−	20.3668i	0.697344	−	0.697344i	0.963837	+	0.266493i	$0.0858648\pi$
$854$	−44.6332			−1.52732
$855$		0			0
$856$			11.3668i			0.388508i
$857$	21.6332			0.738978			0.369489	−	0.929235i	$-0.379533\pi$
$857$	21.6332			0.738978			0.369489	+	0.929235i	$0.379533\pi$
$858$	−117.699			−4.01819
$859$	−22.4248	−	22.4248i	−0.765125	−	0.765125i	0.212119	−	0.977244i	$-0.431964\pi$
$859$	−22.4248	−	22.4248i	−0.765125	−	0.765125i	−0.977244	+	0.212119i	$0.931964\pi$
$860$		0			0
$861$	−25.0000	+	25.0000i	−0.851998	+	0.851998i
$862$	10.9499	+	10.9499i	0.372954	+	0.372954i
$863$			20.5330i			0.698951i	0.936945	+	0.349476i	$0.113640\pi$
$863$			20.5330i			0.698951i	−0.936945	+	0.349476i	$0.886360\pi$
$864$	−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
$868$		−	10.7335i		−	0.364319i
$869$	−13.6332	−	13.6332i	−0.462476	−	0.462476i
$870$		0			0
$871$			79.0660i			2.67905i
$872$		−	23.7995i		−	0.805953i
$873$	−41.8997			−1.41809
$874$	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	0.807099	−	0.590416i	$-0.201036\pi$
$877$	6.41688	+	6.41688i	0.216683	+	0.216683i	−0.590416	+	0.807099i	$0.701036\pi$
$878$	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	$-0.0732119\pi$
$883$	22.1583	+	22.1583i	0.745687	+	0.745687i	−0.227979	+	0.973666i	$0.573212\pi$
$884$	−11.3668	−	11.3668i	−0.382305	−	0.382305i
$885$		0			0
$886$	−38.2164			−1.28390
$887$	−46.5330			−1.56243			−0.781213	−	0.624265i	$-0.785399\pi$
$887$	−46.5330			−1.56243			−0.781213	+	0.624265i	$0.785399\pi$
$888$	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
$892$	−12.0000			−0.401790
$893$	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
$897$			5.89975i			0.196987i
$898$	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
$902$	31.5831			1.05160
$903$	76.3325			2.54019
$904$	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	$-0.646285\pi$
$907$	13.6332	−	13.6332i	0.452685	−	0.452685i	0.896245	+	0.443560i	$0.146285\pi$
$908$	−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	$0.738868\pi$
$912$	−2.73350			−0.0905153
$913$		−	45.2164i		−	1.49644i
$914$	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
$918$		−	18.8496i		−	0.622130i
$919$		−	4.41688i		−	0.145699i	−0.997343	−	0.0728496i	$-0.976791\pi$
$919$		−	4.41688i		−	0.145699i	0.997343	−	0.0728496i	$-0.0232093\pi$
$920$		0			0
$921$		−	61.1161i		−	2.01384i
$922$	39.3668			1.29647
$923$	−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
$927$		−	29.2665i		−	0.961238i
$928$	−16.0000			−0.525226
$929$	20.0000			0.656179			0.328089	−	0.944647i	$-0.393595\pi$
$929$	20.0000			0.656179			0.328089	+	0.944647i	$0.393595\pi$
$930$		0			0
$931$	−0.258564	+	0.258564i	−0.00847408	+	0.00847408i
$932$		−	23.7995i		−	0.779578i
$933$	−27.9499	+	27.9499i	−0.915038	+	0.915038i
$934$			28.5330i			0.933628i
$935$		0			0
$936$		−	109.066i		−	3.56493i
$937$	35.9499			1.17443			0.587216	−	0.809431i	$-0.300224\pi$
$937$	35.9499			1.17443			0.587216	+	0.809431i	$0.300224\pi$
$938$			42.4327i			1.38548i
$939$	−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
$943$		−	1.58312i		−	0.0515536i
$944$	−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	0.613596	−	0.789620i	$-0.289723\pi$
$947$	−5.41688	−	5.41688i	−0.176025	−	0.176025i	−0.789620	+	0.613596i	$0.789723\pi$
$948$	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
$953$	−2.36675			−0.0766666			−0.0383333	−	0.999265i	$-0.512205\pi$
$953$	−2.36675			−0.0766666			−0.0383333	+	0.999265i	$0.512205\pi$
$954$		−	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
$967$	26.6332			0.856468			0.428234	−	0.903668i	$-0.359136\pi$
$967$	26.6332			0.856468			0.428234	+	0.903668i	$0.359136\pi$
$968$	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
$977$			56.3826i			1.80384i	0.431903	+	0.901920i	$0.357842\pi$
$977$			56.3826i			1.80384i	−0.431903	+	0.901920i	$0.642158\pi$
$978$	−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
$982$		−	59.2665i		−	1.89127i
$983$	28.3166			0.903160			0.451580	−	0.892231i	$-0.350861\pi$
$983$	28.3166			0.903160			0.451580	+	0.892231i	$0.350861\pi$
$984$			43.1662i			1.37609i
$985$		0			0
$986$		−	5.26650i		−	0.167720i
$987$	−40.0000	+	40.0000i	−1.27321	+	1.27321i
$988$		−	2.73350i		−	0.0869642i
$989$	−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
$993$		−	5.00000i		−	0.158670i
$994$	−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	$-0.728957\pi$
$997$	2.94987	−	2.94987i	0.0934235	−	0.0934235i	0.752274	+	0.658850i	$0.228957\pi$
$998$	45.7995			1.44976
$999$			9.78363i			0.309540i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.q (of order \(4\), degree \(2\), not minimal)

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

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