LMFDB - Embedded newform 420.2.bn.a.269.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [420,2,Mod(89,420)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(420, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("420.89"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.bn (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.12
Character	$\chi$	$=$	420.269
Dual form			420.2.bn.a.89.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.16448 - 1.28218i) q^{3} +(0.225553 + 2.22466i) q^{5} +(-2.08204 + 1.63251i) q^{7} +(-0.287951 - 2.98615i) q^{9} +(5.09034 + 2.93891i) q^{11} +3.54004 q^{13} +(3.11506 + 2.30139i) q^{15} +(2.69171 + 1.55406i) q^{17} +(3.58419 - 2.06933i) q^{19} +(-0.331334 + 4.57058i) q^{21} +(-3.57587 - 6.19358i) q^{23} +(-4.89825 + 1.00356i) q^{25} +(-4.16408 - 3.10812i) q^{27} +6.84761i q^{29} +(-3.90384 - 2.25388i) q^{31} +(9.69582 - 3.10439i) q^{33} +(-4.10141 - 4.26362i) q^{35} +(1.70926 - 0.986843i) q^{37} +(4.12233 - 4.53896i) q^{39} -6.33142 q^{41} -3.88979i q^{43} +(6.57823 - 1.31413i) q^{45} +(-1.58829 + 0.916997i) q^{47} +(1.66979 - 6.79793i) q^{49} +(5.12704 - 1.64157i) q^{51} +(-6.90391 + 11.9579i) q^{53} +(-5.38994 + 11.9872i) q^{55} +(1.52048 - 7.00526i) q^{57} +(2.32584 - 4.02848i) q^{59} +(0.702144 - 0.405383i) q^{61} +(5.47446 + 5.74720i) q^{63} +(0.798468 + 7.87540i) q^{65} +(8.84158 + 5.10469i) q^{67} +(-12.1053 - 2.62744i) q^{69} +1.18684i q^{71} +(-1.08522 + 1.87966i) q^{73} +(-4.41720 + 7.44905i) q^{75} +(-15.3961 + 2.19112i) q^{77} +(-5.05228 - 8.75081i) q^{79} +(-8.83417 + 1.71973i) q^{81} -5.31243i q^{83} +(-2.85014 + 6.33868i) q^{85} +(8.77984 + 7.97394i) q^{87} +(-6.28986 - 10.8944i) q^{89} +(-7.37052 + 5.77917i) q^{91} +(-7.43583 + 2.38080i) q^{93} +(5.41199 + 7.50686i) q^{95} +4.50686 q^{97} +(7.31025 - 16.0468i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{15} + 12 q^{19} - 8 q^{21} + 6 q^{25} - 12 q^{31} + 24 q^{39} + 33 q^{45} - 44 q^{49} - 10 q^{51} - 24 q^{61} + 21 q^{75} - 28 q^{79} - 20 q^{81} - 4 q^{85} + 16 q^{91} - 28 q^{99}+O(q^{100}) $ 32 * q + 2 * q^15 + 12 * q^19 - 8 * q^21 + 6 * q^25 - 12 * q^31 + 24 * q^39 + 33 * q^45 - 44 * q^49 - 10 * q^51 - 24 * q^61 + 21 * q^75 - 28 * q^79 - 20 * q^81 - 4 * q^85 + 16 * q^91 - 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	1.16448	−	1.28218i	0.672316	−	0.740265i
$3$	1.16448	−	1.28218i	0.672316	−	0.740265i
$4$		0			0
$5$	0.225553	+	2.22466i	0.100870	+	0.994900i
$5$	0.225553	+	2.22466i	0.100870	+	0.994900i
$6$		0			0
$7$	−2.08204	+	1.63251i	−0.786938	+	0.617033i
$7$	−2.08204	+	1.63251i	−0.786938	+	0.617033i
$8$		0			0
$9$	−0.287951	−	2.98615i	−0.0959835	−	0.995383i
$10$		0			0
$11$	5.09034	+	2.93891i	1.53479	+	0.886114i	0.999131	+	0.0416823i	$0.0132717\pi$
$11$	5.09034	+	2.93891i	1.53479	+	0.886114i	0.535663	+	0.844432i	$0.320062\pi$
$12$		0			0
$13$	3.54004			0.981831			0.490916	−	0.871207i	$-0.336662\pi$
$13$	3.54004			0.981831			0.490916	+	0.871207i	$0.336662\pi$
$14$		0			0
$15$	3.11506	+	2.30139i	0.804306	+	0.594216i
$16$		0			0
$17$	2.69171	+	1.55406i	0.652836	+	0.376915i	0.789542	−	0.613697i	$-0.210318\pi$
$17$	2.69171	+	1.55406i	0.652836	+	0.376915i	−0.136706	+	0.990612i	$0.543652\pi$
$18$		0			0
$19$	3.58419	−	2.06933i	0.822269	−	0.474737i	−0.0289296	−	0.999581i	$-0.509210\pi$
$19$	3.58419	−	2.06933i	0.822269	−	0.474737i	0.851198	+	0.524844i	$0.175877\pi$
$20$		0			0
$21$	−0.331334	+	4.57058i	−0.0723030	+	0.997383i
$22$		0			0
$23$	−3.57587	−	6.19358i	−0.745620	−	1.29145i	−0.949905	−	0.312539i	$-0.898820\pi$
$23$	−3.57587	−	6.19358i	−0.745620	−	1.29145i	0.204285	−	0.978911i	$-0.434513\pi$
$24$		0			0
$25$	−4.89825	+	1.00356i	−0.979650	+	0.200712i
$26$		0			0
$27$	−4.16408	−	3.10812i	−0.801378	−	0.598158i
$28$		0			0
$29$			6.84761i			1.27157i	0.771867	+	0.635785i	$0.219323\pi$
$29$			6.84761i			1.27157i	−0.771867	+	0.635785i	$0.780677\pi$
$30$		0			0
$31$	−3.90384	−	2.25388i	−0.701150	−	0.404809i	0.106626	−	0.994299i	$-0.465995\pi$
$31$	−3.90384	−	2.25388i	−0.701150	−	0.404809i	−0.807776	+	0.589490i	$0.799329\pi$
$32$		0			0
$33$	9.69582	−	3.10439i	1.68782	−	0.540406i
$34$		0			0
$35$	−4.10141	−	4.26362i	−0.693264	−	0.720684i
$36$		0			0
$37$	1.70926	−	0.986843i	0.281001	−	0.162236i	−0.352875	−	0.935670i	$-0.614796\pi$
$37$	1.70926	−	0.986843i	0.281001	−	0.162236i	0.633876	+	0.773434i	$0.281463\pi$
$38$		0			0
$39$	4.12233	−	4.53896i	0.660100	−	0.726815i
$40$		0			0
$41$	−6.33142			−0.988801			−0.494401	−	0.869234i	$-0.664612\pi$
$41$	−6.33142			−0.988801			−0.494401	+	0.869234i	$0.664612\pi$
$42$		0			0
$43$		−	3.88979i		−	0.593187i	−0.955004	−	0.296594i	$-0.904149\pi$
$43$		−	3.88979i		−	0.593187i	0.955004	−	0.296594i	$-0.0958507\pi$
$44$		0			0
$45$	6.57823	−	1.31413i	0.980624	−	0.195899i
$46$		0			0
$47$	−1.58829	+	0.916997i	−0.231675	+	0.133758i	−0.611345	−	0.791364i	$-0.709371\pi$
$47$	−1.58829	+	0.916997i	−0.231675	+	0.133758i	0.379669	+	0.925122i	$0.376038\pi$
$48$		0			0
$49$	1.66979	−	6.79793i	0.238541	−	0.971132i
$50$		0			0
$51$	5.12704	−	1.64157i	0.717929	−	0.229866i
$52$		0			0
$53$	−6.90391	+	11.9579i	−0.948325	+	1.64255i	−0.199371	+	0.979924i	$0.563890\pi$
$53$	−6.90391	+	11.9579i	−0.948325	+	1.64255i	−0.748954	+	0.662622i	$0.769443\pi$
$54$		0			0
$55$	−5.38994	+	11.9872i	−0.726779	+	1.61635i
$56$		0			0
$57$	1.52048	−	7.00526i	0.201393	−	0.927869i
$58$		0			0
$59$	2.32584	−	4.02848i	0.302799	−	0.524463i	−0.673970	−	0.738759i	$-0.735412\pi$
$59$	2.32584	−	4.02848i	0.302799	−	0.524463i	0.976769	+	0.214296i	$0.0687456\pi$
$60$		0			0
$61$	0.702144	−	0.405383i	0.0899003	−	0.0519040i	−0.454376	−	0.890810i	$-0.650138\pi$
$61$	0.702144	−	0.405383i	0.0899003	−	0.0519040i	0.544276	+	0.838906i	$0.316804\pi$
$62$		0			0
$63$	5.47446	+	5.74720i	0.689717	+	0.724079i
$64$		0			0
$65$	0.798468	+	7.87540i	0.0990377	+	0.976824i
$66$		0			0
$67$	8.84158	+	5.10469i	1.08017	+	0.623637i	0.930942	−	0.365166i	$-0.118988\pi$
$67$	8.84158	+	5.10469i	1.08017	+	0.623637i	0.149228	+	0.988803i	$0.452321\pi$
$68$		0			0
$69$	−12.1053	−	2.62744i	−1.45731	−	0.316307i
$70$		0			0
$71$			1.18684i			0.140852i	0.997517	+	0.0704262i	$0.0224359\pi$
$71$			1.18684i			0.140852i	−0.997517	+	0.0704262i	$0.977564\pi$
$72$		0			0
$73$	−1.08522	+	1.87966i	−0.127016	+	0.219998i	−0.922519	−	0.385951i	$-0.873873\pi$
$73$	−1.08522	+	1.87966i	−0.127016	+	0.219998i	0.795503	+	0.605949i	$0.207207\pi$
$74$		0			0
$75$	−4.41720	+	7.44905i	−0.510054	+	0.860142i
$76$		0			0
$77$	−15.3961	+	2.19112i	−1.75455	+	0.249702i
$78$		0			0
$79$	−5.05228	−	8.75081i	−0.568426	−	0.984543i	−0.996722	−	0.0809043i	$-0.974219\pi$
$79$	−5.05228	−	8.75081i	−0.568426	−	0.984543i	0.428296	−	0.903639i	$-0.359114\pi$
$80$		0			0
$81$	−8.83417	+	1.71973i	−0.981574	+	0.191081i
$82$		0			0
$83$		−	5.31243i		−	0.583115i	−0.956553	−	0.291558i	$-0.905826\pi$
$83$		−	5.31243i		−	0.583115i	0.956553	−	0.291558i	$-0.0941735\pi$
$84$		0			0
$85$	−2.85014	+	6.33868i	−0.309141	+	0.687526i
$86$		0			0
$87$	8.77984	+	7.97394i	0.941298	+	0.854896i
$88$		0			0
$89$	−6.28986	−	10.8944i	−0.666724	−	1.15480i	−0.978815	−	0.204747i	$-0.934363\pi$
$89$	−6.28986	−	10.8944i	−0.666724	−	1.15480i	0.312091	−	0.950052i	$-0.398971\pi$
$90$		0			0
$91$	−7.37052	+	5.77917i	−0.772640	+	0.605822i
$92$		0			0
$93$	−7.43583	+	2.38080i	−0.771060	+	0.246877i
$94$		0			0
$95$	5.41199	+	7.50686i	0.555258	+	0.770188i
$96$		0			0
$97$	4.50686			0.457602			0.228801	−	0.973473i	$-0.426519\pi$
$97$	4.50686			0.457602			0.228801	+	0.973473i	$0.426519\pi$
$98$		0			0
$99$	7.31025	−	16.0468i	0.734708	−	1.61276i
$100$		0			0
$101$	0.896791	−	1.55329i	0.0892340	−	0.154558i	−0.817954	−	0.575284i	$-0.804891\pi$
$101$	0.896791	−	1.55329i	0.0892340	−	0.154558i	0.907188	+	0.420726i	$0.138225\pi$
$102$		0			0
$103$	−6.30688	−	10.9238i	−0.621436	−	1.07636i	−0.989219	−	0.146446i	$-0.953216\pi$
$103$	−6.30688	−	10.9238i	−0.621436	−	1.07636i	0.367783	−	0.929912i	$-0.380117\pi$
$104$		0			0
$105$	−10.2427	+	0.293803i	−0.999589	+	0.0286722i
$106$		0			0
$107$	−1.73976	−	3.01335i	−0.168189	−	0.291311i	0.769594	−	0.638533i	$-0.220458\pi$
$107$	−1.73976	−	3.01335i	−0.168189	−	0.291311i	−0.937783	+	0.347222i	$0.887125\pi$
$108$		0			0
$109$	4.98802	−	8.63951i	0.477766	−	0.827515i	−0.521909	−	0.853001i	$-0.674780\pi$
$109$	4.98802	−	8.63951i	0.477766	−	0.827515i	0.999675	+	0.0254860i	$0.00811333\pi$
$110$		0			0
$111$	0.725103	−	3.34074i	0.0688238	−	0.317089i
$112$		0			0
$113$	−2.54532			−0.239444			−0.119722	−	0.992807i	$-0.538200\pi$
$113$	−2.54532			−0.239444			−0.119722	+	0.992807i	$0.538200\pi$
$114$		0			0
$115$	12.9721	−	9.35208i	1.20965	−	0.872086i
$116$		0			0
$117$	−1.01936	−	10.5711i	−0.0942396	−	0.977298i
$118$		0			0
$119$	−8.14128	+	1.15864i	−0.746310	+	0.106213i
$120$		0			0
$121$	11.7744	+	20.3938i	1.07040	+	1.85398i
$122$		0			0
$123$	−7.37284	+	8.11799i	−0.664787	+	0.731975i
$124$		0			0
$125$	−3.33740	−	10.6706i	−0.298506	−	0.954408i
$126$		0			0
$127$			12.6616i			1.12353i	0.827295	+	0.561767i	$0.189878\pi$
$127$			12.6616i			1.12353i	−0.827295	+	0.561767i	$0.810122\pi$
$128$		0			0
$129$	−4.98739	−	4.52960i	−0.439116	−	0.398809i
$130$		0			0
$131$	−6.34770	−	10.9945i	−0.554601	−	0.960597i	−0.997934	−	0.0642406i	$-0.979537\pi$
$131$	−6.34770	−	10.9945i	−0.554601	−	0.960597i	0.443333	−	0.896357i	$-0.353796\pi$
$132$		0			0
$133$	−4.08421	+	10.1597i	−0.354146	+	0.880955i
$134$		0			0
$135$	5.97530	−	9.96473i	0.514272	−	0.857627i
$136$		0			0
$137$	−2.62391	+	4.54475i	−0.224176	+	0.388284i	−0.956072	−	0.293132i	$-0.905302\pi$
$137$	−2.62391	+	4.54475i	−0.224176	+	0.388284i	0.731896	+	0.681416i	$0.238636\pi$
$138$		0			0
$139$		−	14.2842i		−	1.21157i	−0.795627	−	0.605787i	$-0.792858\pi$
$139$		−	14.2842i		−	1.21157i	0.795627	−	0.605787i	$-0.207142\pi$
$140$		0			0
$141$	−0.673782	+	3.10429i	−0.0567427	+	0.261428i
$142$		0			0
$143$	18.0200	+	10.4039i	1.50691	+	0.870014i
$144$		0			0
$145$	−15.2336	+	1.54450i	−1.26508	+	0.128264i
$146$		0			0
$147$	−6.77169	−	10.0570i	−0.558520	−	0.829491i
$148$		0			0
$149$	−13.0762	+	7.54956i	−1.07125	+	0.618484i	−0.928521	−	0.371279i	$-0.878919\pi$
$149$	−13.0762	+	7.54956i	−1.07125	+	0.618484i	−0.142724	+	0.989763i	$0.545586\pi$
$150$		0			0
$151$	4.16979	−	7.22229i	0.339333	−	0.587742i	−0.644975	−	0.764204i	$-0.723132\pi$
$151$	4.16979	−	7.22229i	0.339333	−	0.587742i	0.984307	+	0.176462i	$0.0564654\pi$
$152$		0			0
$153$	3.86558	−	8.48535i	0.312513	−	0.686000i
$154$		0			0
$155$	4.13361	−	9.19310i	0.332019	−	0.738407i
$156$		0			0
$157$	0.480298	−	0.831900i	0.0383319	−	0.0663929i	−0.846223	−	0.532829i	$-0.821129\pi$
$157$	0.480298	−	0.831900i	0.0383319	−	0.0663929i	0.884555	+	0.466436i	$0.154462\pi$
$158$		0			0
$159$	7.29266	+	22.7768i	0.578346	+	1.80632i
$160$		0			0
$161$	17.5562	+	7.05764i	1.38362	+	0.556220i
$162$		0			0
$163$	−16.1698	+	9.33565i	−1.26652	+	0.731224i	−0.974327	−	0.225136i	$-0.927717\pi$
$163$	−16.1698	+	9.33565i	−1.26652	+	0.731224i	−0.292190	+	0.956360i	$0.594384\pi$
$164$		0			0
$165$	9.09315	+	20.8697i	0.707901	+	1.62471i
$166$		0			0
$167$		−	14.2212i		−	1.10047i	−0.835011	−	0.550233i	$-0.814539\pi$
$167$		−	14.2212i		−	1.10047i	0.835011	−	0.550233i	$-0.185461\pi$
$168$		0			0
$169$	−0.468096			−0.0360074
$170$		0			0
$171$	−7.21140	−	10.1070i	−0.551469	−	0.772905i
$172$		0			0
$173$	0.618569	−	0.357131i	0.0470289	−	0.0271522i	−0.476301	−	0.879282i	$-0.658023\pi$
$173$	0.618569	−	0.357131i	0.0470289	−	0.0271522i	0.523330	+	0.852130i	$0.324689\pi$
$174$		0			0
$175$	8.56004	−	10.0859i	0.647078	−	0.762424i
$176$		0			0
$177$	−2.45681	−	7.67324i	−0.184665	−	0.576756i
$178$		0			0
$179$	9.68510	+	5.59169i	0.723898	+	0.417943i	0.816186	−	0.577790i	$-0.196085\pi$
$179$	9.68510	+	5.59169i	0.723898	+	0.417943i	−0.0922876	+	0.995732i	$0.529418\pi$
$180$		0			0
$181$			3.69700i			0.274796i	0.990516	+	0.137398i	$0.0438739\pi$
$181$			3.69700i			0.274796i	−0.990516	+	0.137398i	$0.956126\pi$
$182$		0			0
$183$	0.297864	−	1.37233i	0.0220187	−	0.101446i
$184$		0			0
$185$	2.58092	+	3.57995i	0.189753	+	0.263203i
$186$		0			0
$187$	9.13448	+	15.8214i	0.667979	+	1.15697i
$188$		0			0
$189$	13.7438	−	0.326689i	0.999718	−	0.0237632i
$190$		0			0
$191$	−8.99652	+	5.19414i	−0.650965	+	0.375835i	−0.788826	−	0.614617i	$-0.789311\pi$
$191$	−8.99652	+	5.19414i	−0.650965	+	0.375835i	0.137861	+	0.990452i	$0.455977\pi$
$192$		0			0
$193$	−5.12779	−	2.96053i	−0.369106	−	0.213104i	0.303962	−	0.952684i	$-0.401691\pi$
$193$	−5.12779	−	2.96053i	−0.369106	−	0.213104i	−0.673068	+	0.739581i	$0.735024\pi$
$194$		0			0
$195$	11.0275	+	8.14701i	0.789693	+	0.583420i
$196$		0			0
$197$	11.1053			0.791221			0.395610	−	0.918418i	$-0.370533\pi$
$197$	11.1053			0.791221			0.395610	+	0.918418i	$0.370533\pi$
$198$		0			0
$199$	11.4667	+	6.62029i	0.812851	+	0.469300i	0.847945	−	0.530084i	$-0.177840\pi$
$199$	11.4667	+	6.62029i	0.812851	+	0.469300i	−0.0350939	+	0.999384i	$0.511173\pi$
$200$		0			0
$201$	16.8410	−	5.39213i	1.18787	−	0.380331i
$202$		0			0
$203$	−11.1788	−	14.2570i	−0.784600	−	1.00065i
$204$		0			0
$205$	−1.42807	−	14.0853i	−0.0997408	−	0.983758i
$206$		0			0
$207$	−17.4653	+	12.4615i	−1.21392	+	0.866135i
$208$		0			0
$209$	24.3263			1.68268
$210$		0			0
$211$	−19.9122			−1.37082			−0.685408	−	0.728160i	$-0.740376\pi$
$211$	−19.9122			−1.37082			−0.685408	+	0.728160i	$0.740376\pi$
$212$		0			0
$213$	1.52174	+	1.38206i	0.104268	+	0.0946973i
$214$		0			0
$215$	8.65347	−	0.877354i	0.590162	−	0.0598350i
$216$		0			0
$217$	11.8074	−	1.68040i	0.801542	−	0.114073i
$218$		0			0
$219$	1.14633	+	3.58028i	0.0774619	+	0.241933i
$220$		0			0
$221$	9.52878	+	5.50144i	0.640975	+	0.370067i
$222$		0			0
$223$	10.4924			0.702623			0.351311	−	0.936259i	$-0.385736\pi$
$223$	10.4924			0.702623			0.351311	+	0.936259i	$0.385736\pi$
$224$		0			0
$225$	4.40723	+	14.3379i	0.293815	+	0.955862i
$226$		0			0
$227$	14.2249	+	8.21273i	0.944138	+	0.545098i	0.891255	−	0.453502i	$-0.149826\pi$
$227$	14.2249	+	8.21273i	0.944138	+	0.545098i	0.0528829	+	0.998601i	$0.483159\pi$
$228$		0			0
$229$	−0.903838	+	0.521831i	−0.0597273	+	0.0344836i	−0.529566	−	0.848269i	$-0.677645\pi$
$229$	−0.903838	+	0.521831i	−0.0597273	+	0.0344836i	0.469839	+	0.882752i	$0.344312\pi$
$230$		0			0
$231$	−15.1191	+	22.2920i	−0.994765	+	1.46671i
$232$		0			0
$233$	14.4619	+	25.0488i	0.947431	+	1.64100i	0.750809	+	0.660519i	$0.229664\pi$
$233$	14.4619	+	25.0488i	0.947431	+	1.64100i	0.196622	+	0.980479i	$0.437003\pi$
$234$		0			0
$235$	−2.39825	−	3.32657i	−0.156445	−	0.217001i
$236$		0			0
$237$	−17.1034	−	3.71227i	−1.11098	−	0.241138i
$238$		0			0
$239$			5.69731i			0.368528i	0.982877	+	0.184264i	$0.0589902\pi$
$239$			5.69731i			0.368528i	−0.982877	+	0.184264i	$0.941010\pi$
$240$		0			0
$241$	−6.10598	−	3.52529i	−0.393321	−	0.227084i	0.290277	−	0.956943i	$-0.406253\pi$
$241$	−6.10598	−	3.52529i	−0.393321	−	0.227084i	−0.683598	+	0.729859i	$0.739586\pi$
$242$		0			0
$243$	−8.08226	+	13.3296i	−0.518477	+	0.855091i
$244$		0			0
$245$	15.4997	+	2.18143i	0.990241	+	0.139366i
$246$		0			0
$247$	12.6882	−	7.32552i	0.807329	−	0.466112i
$248$		0			0
$249$	−6.81148	−	6.18625i	−0.431660	−	0.392038i
$250$		0			0
$251$	3.93237			0.248209			0.124105	−	0.992269i	$-0.460394\pi$
$251$	3.93237			0.248209			0.124105	+	0.992269i	$0.460394\pi$
$252$		0			0
$253$		−	42.0366i		−	2.64282i
$254$		0			0
$255$	4.80836	+	11.0357i	0.301111	+	0.691080i
$256$		0			0
$257$	13.2552	−	7.65287i	0.826834	−	0.477373i	−0.0259335	−	0.999664i	$-0.508256\pi$
$257$	13.2552	−	7.65287i	0.826834	−	0.477373i	0.852767	+	0.522291i	$0.174922\pi$
$258$		0			0
$259$	−1.94772	+	4.84504i	−0.121025	+	0.301056i
$260$		0			0
$261$	20.4480	−	1.97177i	1.26570	−	0.122050i
$262$		0			0
$263$	9.75977	−	16.9044i	0.601813	−	1.04237i	−0.390733	−	0.920504i	$-0.627778\pi$
$263$	9.75977	−	16.9044i	0.601813	−	1.04237i	0.992546	−	0.121867i	$-0.0388882\pi$
$264$		0			0
$265$	−28.1595	−	12.6617i	−1.72983	−	0.777803i
$266$		0			0
$267$	−21.2929	−	4.62161i	−1.30311	−	0.282838i
$268$		0			0
$269$	4.91865	−	8.51935i	0.299895	−	0.519434i	−0.676216	−	0.736703i	$-0.736382\pi$
$269$	4.91865	−	8.51935i	0.299895	−	0.519434i	0.976112	+	0.217269i	$0.0697149\pi$
$270$		0			0
$271$	18.0820	−	10.4397i	1.09841	−	0.634164i	0.162603	−	0.986691i	$-0.448011\pi$
$271$	18.0820	−	10.4397i	1.09841	−	0.634164i	0.935802	+	0.352527i	$0.114678\pi$
$272$		0			0
$273$	−1.17294	+	16.1801i	−0.0709893	+	0.979262i
$274$		0			0
$275$	−27.8831	−	9.28705i	−1.68142	−	0.560030i
$276$		0			0
$277$	7.36446	+	4.25187i	0.442487	+	0.255470i	0.704652	−	0.709553i	$-0.251103\pi$
$277$	7.36446	+	4.25187i	0.442487	+	0.255470i	−0.262165	+	0.965023i	$0.584436\pi$
$278$		0			0
$279$	−5.60632	+	12.3064i	−0.335641	+	0.736768i
$280$		0			0
$281$		−	7.63690i		−	0.455579i	−0.973710	−	0.227790i	$-0.926850\pi$
$281$		−	7.63690i		−	0.455579i	0.973710	−	0.227790i	$-0.0731499\pi$
$282$		0			0
$283$	−4.50375	+	7.80072i	−0.267720	+	0.463705i	−0.968273	−	0.249896i	$-0.919604\pi$
$283$	−4.50375	+	7.80072i	−0.267720	+	0.463705i	0.700553	+	0.713601i	$0.252937\pi$
$284$		0			0
$285$	15.9273	+	1.80251i	0.943451	+	0.106771i
$286$		0			0
$287$	13.1823	−	10.3361i	0.778125	−	0.610123i
$288$		0			0
$289$	−3.66979	−	6.35626i	−0.215870	−	0.373898i
$290$		0			0
$291$	5.24817	−	5.77858i	0.307653	−	0.338747i
$292$		0			0
$293$		−	27.6102i		−	1.61301i	−0.591231	−	0.806503i	$-0.701358\pi$
$293$		−	27.6102i		−	1.61301i	0.591231	−	0.806503i	$-0.298642\pi$
$294$		0			0
$295$	9.48660	+	4.26558i	0.552331	+	0.248352i
$296$		0			0
$297$	−12.0621	−	28.0592i	−0.699914	−	1.62816i
$298$		0			0
$299$	−12.6587	−	21.9255i	−0.732073	−	1.26799i
$300$		0			0
$301$	6.35014	+	8.09870i	0.366016	+	0.466801i
$302$		0			0
$303$	−0.947288	−	2.95862i	−0.0544203	−	0.169968i
$304$		0			0
$305$	1.06021	+	1.47060i	0.0607075	+	0.0842062i
$306$		0			0
$307$	−9.99609			−0.570507			−0.285253	−	0.958452i	$-0.592078\pi$
$307$	−9.99609			−0.570507			−0.285253	+	0.958452i	$0.592078\pi$
$308$		0			0
$309$	−21.3506	−	4.63411i	−1.21459	−	0.263625i
$310$		0			0
$311$	−11.9336	+	20.6696i	−0.676693	+	1.17207i	0.299278	+	0.954166i	$0.403254\pi$
$311$	−11.9336	+	20.6696i	−0.676693	+	1.17207i	−0.975971	+	0.217901i	$0.930079\pi$
$312$		0			0
$313$	2.79759	+	4.84558i	0.158129	+	0.273888i	0.934194	−	0.356765i	$-0.116120\pi$
$313$	2.79759	+	4.84558i	0.158129	+	0.273888i	−0.776065	+	0.630653i	$0.782787\pi$
$314$		0			0
$315$	−11.5508	+	13.4751i	−0.650814	+	0.759237i
$316$		0			0
$317$	5.86828	+	10.1642i	0.329596	+	0.570876i	0.982432	−	0.186623i	$-0.0597543\pi$
$317$	5.86828	+	10.1642i	0.329596	+	0.570876i	−0.652836	+	0.757499i	$0.726421\pi$
$318$		0			0
$319$	−20.1245	+	34.8566i	−1.12676	+	1.95160i
$320$		0			0
$321$	−5.88956	−	1.27832i	−0.328723	−	0.0713490i
$322$		0			0
$323$	12.8635			0.715742
$324$		0			0
$325$	−17.3400	+	3.55264i	−0.961851	+	0.197065i
$326$		0			0
$327$	−5.26890	−	16.4561i	−0.291371	−	0.910025i
$328$		0			0
$329$	1.80986	−	4.50212i	0.0997810	−	0.248210i
$330$		0			0
$331$	−1.26453	−	2.19023i	−0.0695050	−	0.120386i	0.829179	−	0.558984i	$-0.188809\pi$
$331$	−1.26453	−	2.19023i	−0.0695050	−	0.120386i	−0.898684	+	0.438598i	$0.855475\pi$
$332$		0			0
$333$	−3.43904	−	4.81995i	−0.188458	−	0.264132i
$334$		0			0
$335$	−9.36196	+	20.8209i	−0.511499	+	1.13757i
$336$		0			0
$337$			34.3299i			1.87007i	0.354560	+	0.935033i	$0.384631\pi$
$337$			34.3299i			1.87007i	−0.354560	+	0.935033i	$0.615369\pi$
$338$		0			0
$339$	−2.96399	+	3.26355i	−0.160982	+	0.177252i
$340$		0			0
$341$	−13.2479	−	22.9460i	−0.717414	−	1.24260i
$342$		0			0
$343$	7.62114	+	16.8795i	0.411503	+	0.911408i
$344$		0			0
$345$	3.11478	−	27.5228i	0.167694	−	1.48178i
$346$		0			0
$347$	−0.297864	+	0.515915i	−0.0159902	+	0.0276958i	−0.873910	−	0.486088i	$-0.838423\pi$
$347$	−0.297864	+	0.515915i	−0.0159902	+	0.0276958i	0.857920	+	0.513784i	$0.171757\pi$
$348$		0			0
$349$			23.0392i			1.23326i	0.787253	+	0.616630i	$0.211503\pi$
$349$			23.0392i			1.23326i	−0.787253	+	0.616630i	$0.788497\pi$
$350$		0			0
$351$	−14.7410	−	11.0029i	−0.786818	−	0.587290i
$352$		0			0
$353$	−9.43718	−	5.44856i	−0.502290	−	0.289997i	0.227369	−	0.973809i	$-0.426988\pi$
$353$	−9.43718	−	5.44856i	−0.502290	−	0.289997i	−0.729659	+	0.683811i	$0.760321\pi$
$354$		0			0
$355$	−2.64033	+	0.267696i	−0.140134	+	0.0142078i
$356$		0			0
$357$	−7.99482	+	11.7878i	−0.423131	+	0.623875i
$358$		0			0
$359$	−9.03320	+	5.21532i	−0.476754	+	0.275254i	−0.719063	−	0.694945i	$-0.755429\pi$
$359$	−9.03320	+	5.21532i	−0.476754	+	0.275254i	0.242309	+	0.970199i	$0.422095\pi$
$360$		0			0
$361$	−0.935743	+	1.62075i	−0.0492496	+	0.0853028i
$362$		0			0
$363$	39.8595	+	8.65145i	2.09208	+	0.454083i
$364$		0			0
$365$	−4.42639	−	1.99029i	−0.231688	−	0.104177i
$366$		0			0
$367$	4.27471	−	7.40402i	0.223138	−	0.386486i	−0.732621	−	0.680637i	$-0.761703\pi$
$367$	4.27471	−	7.40402i	0.223138	−	0.386486i	0.955759	+	0.294150i	$0.0950366\pi$
$368$		0			0
$369$	1.82314	+	18.9066i	0.0949086	+	0.984236i
$370$		0			0
$371$	−5.14726	−	36.1676i	−0.267232	−	1.87773i
$372$		0			0
$373$	5.74129	−	3.31473i	0.297273	−	0.171630i	−0.343944	−	0.938990i	$-0.611763\pi$
$373$	5.74129	−	3.31473i	0.297273	−	0.171630i	0.641217	+	0.767360i	$0.278430\pi$
$374$		0			0
$375$	−17.5679	−	8.14663i	−0.907204	−	0.420690i
$376$		0			0
$377$			24.2408i			1.24847i
$378$		0			0
$379$	22.3165			1.14632			0.573162	−	0.819442i	$-0.305717\pi$
$379$	22.3165			1.14632			0.573162	+	0.819442i	$0.305717\pi$
$380$		0			0
$381$	16.2344	+	14.7442i	0.831713	+	0.755370i
$382$		0			0
$383$	−24.4124	+	14.0945i	−1.24742	+	0.720196i	−0.970593	−	0.240725i	$-0.922615\pi$
$383$	−24.4124	+	14.0945i	−1.24742	+	0.720196i	−0.276822	+	0.960921i	$0.589281\pi$
$384$		0			0
$385$	−8.34715	−	33.7569i	−0.425410	−	1.72041i
$386$		0			0
$387$	−11.6155	+	1.12007i	−0.590448	+	0.0569362i
$388$		0			0
$389$	3.57909	+	2.06639i	0.181467	+	0.104770i	0.587982	−	0.808874i	$-0.299923\pi$
$389$	3.57909	+	2.06639i	0.181467	+	0.104770i	−0.406515	+	0.913644i	$0.633256\pi$
$390$		0			0
$391$		−	22.2284i		−	1.12414i
$392$		0			0
$393$	−21.4887	−	4.66411i	−1.08396	−	0.235273i
$394$		0			0
$395$	18.3280	−	13.2134i	0.922184	−	0.664838i
$396$		0			0
$397$	6.61890	+	11.4643i	0.332193	+	0.575375i	0.982942	−	0.183918i	$-0.0588781\pi$
$397$	6.61890	+	11.4643i	0.332193	+	0.575375i	−0.650748	+	0.759293i	$0.725545\pi$
$398$		0			0
$399$	8.27048	+	17.0675i	0.414042	+	0.854441i
$400$		0			0
$401$	0.671383	−	0.387623i	0.0335273	−	0.0193570i	−0.483143	−	0.875542i	$-0.660505\pi$
$401$	0.671383	−	0.387623i	0.0335273	−	0.0193570i	0.516670	+	0.856185i	$0.327171\pi$
$402$		0			0
$403$	−13.8198	−	7.97884i	−0.688411	−	0.397454i
$404$		0			0
$405$	−5.81839	−	19.2652i	−0.289118	−	0.957294i
$406$		0			0
$407$	11.6010			0.575038
$408$		0			0
$409$	3.97093	+	2.29262i	0.196350	+	0.113363i	0.594952	−	0.803761i	$-0.297171\pi$
$409$	3.97093	+	2.29262i	0.196350	+	0.113363i	−0.398602	+	0.917124i	$0.630504\pi$
$410$		0			0
$411$	2.77166	+	8.65660i	0.136716	+	0.426999i
$412$		0			0
$413$	1.73405	+	12.1844i	0.0853270	+	0.599556i
$414$		0			0
$415$	11.8184	−	1.19824i	0.580141	−	0.0588191i
$416$		0			0
$417$	−18.3149	−	16.6338i	−0.896885	−	0.814560i
$418$		0			0
$419$	−11.9761			−0.585070			−0.292535	−	0.956255i	$-0.594499\pi$
$419$	−11.9761			−0.585070			−0.292535	+	0.956255i	$0.594499\pi$
$420$		0			0
$421$	25.5487			1.24517			0.622584	−	0.782553i	$-0.286083\pi$
$421$	25.5487			1.24517			0.622584	+	0.782553i	$0.286083\pi$
$422$		0			0
$423$	3.19564	+	4.47881i	0.155377	+	0.217767i
$424$		0			0
$425$	−14.7443	−	4.91089i	−0.715202	−	0.238213i
$426$		0			0
$427$	−0.800099	+	1.99028i	−0.0387195	+	0.0963166i
$428$		0			0
$429$	34.3236	−	10.9897i	1.65716	−	0.530587i
$430$		0			0
$431$	−12.5634	−	7.25351i	−0.605160	−	0.349389i	0.165909	−	0.986141i	$-0.446944\pi$
$431$	−12.5634	−	7.25351i	−0.605160	−	0.349389i	−0.771069	+	0.636752i	$0.780278\pi$
$432$		0			0
$433$	40.0655			1.92543			0.962713	−	0.270524i	$-0.0871969\pi$
$433$	40.0655			1.92543			0.962713	+	0.270524i	$0.0871969\pi$
$434$		0			0
$435$	−15.7590	+	21.3307i	−0.755586	+	1.02273i
$436$		0			0
$437$	−25.6331	−	14.7993i	−1.22620	−	0.707946i
$438$		0			0
$439$	−27.1838	+	15.6945i	−1.29741	+	0.749060i	−0.979956	−	0.199214i	$-0.936161\pi$
$439$	−27.1838	+	15.6945i	−1.29741	+	0.749060i	−0.317454	+	0.948274i	$0.602828\pi$
$440$		0			0
$441$	−20.7804	−	3.02878i	−0.989545	−	0.144227i
$442$		0			0
$443$	5.01776	+	8.69101i	0.238401	+	0.412923i	0.960256	−	0.279122i	$-0.0900434\pi$
$443$	5.01776	+	8.69101i	0.238401	+	0.412923i	−0.721855	+	0.692045i	$0.756710\pi$
$444$		0			0
$445$	22.8176	−	16.4501i	1.08166	−	0.779808i
$446$		0			0
$447$	−5.54719	+	25.5574i	−0.262373	+	1.20882i
$448$		0			0
$449$			16.7060i			0.788405i	0.919024	+	0.394203i	$0.128979\pi$
$449$			16.7060i			0.788405i	−0.919024	+	0.394203i	$0.871021\pi$
$450$		0			0
$451$	−32.2291	−	18.6075i	−1.51761	−	0.876191i
$452$		0			0
$453$	−4.40459	−	13.7567i	−0.206946	−	0.646344i
$454$		0			0
$455$	−14.5192	−	15.0934i	−0.680668	−	0.707590i
$456$		0			0
$457$	−12.2526	+	7.07406i	−0.573154	+	0.330910i	−0.758408	−	0.651780i	$-0.774022\pi$
$457$	−12.2526	+	7.07406i	−0.573154	+	0.330910i	0.185254	+	0.982691i	$0.440689\pi$
$458$		0			0
$459$	−6.37830	−	14.8374i	−0.297714	−	0.692551i
$460$		0			0
$461$	4.22519			0.196787			0.0983935	−	0.995148i	$-0.468630\pi$
$461$	4.22519			0.196787			0.0983935	+	0.995148i	$0.468630\pi$
$462$		0			0
$463$		−	33.2490i		−	1.54521i	−0.634886	−	0.772606i	$-0.718953\pi$
$463$		−	33.2490i		−	1.54521i	0.634886	−	0.772606i	$-0.281047\pi$
$464$		0			0
$465$	−6.97365	−	16.0052i	−0.323395	−	0.742225i
$466$		0			0
$467$	−31.9242	+	18.4314i	−1.47727	+	0.852905i	−0.999670	−	0.0256700i	$-0.991828\pi$
$467$	−31.9242	+	18.4314i	−1.47727	+	0.852905i	−0.477604	+	0.878575i	$0.658495\pi$
$468$		0			0
$469$	−26.7420	+	3.80584i	−1.23483	+	0.175737i
$470$		0			0
$471$	−0.507343	−	1.58456i	−0.0233771	−	0.0730128i
$472$		0			0
$473$	11.4317	−	19.8003i	0.525631	−	0.910420i
$474$		0			0
$475$	−15.4795	+	13.7330i	−0.710250	+	0.630115i
$476$		0			0
$477$	37.6961	+	17.1728i	1.72599	+	0.786289i
$478$		0			0
$479$	−4.66797	+	8.08516i	−0.213285	+	0.369420i	−0.952741	−	0.303785i	$-0.901750\pi$
$479$	−4.66797	+	8.08516i	−0.213285	+	0.369420i	0.739456	+	0.673205i	$0.235083\pi$
$480$		0			0
$481$	6.05086	−	3.49347i	0.275896	−	0.159288i
$482$		0			0
$483$	29.4931	−	14.2916i	1.34198	−	0.650292i
$484$		0			0
$485$	1.01654	+	10.0262i	0.0461585	+	0.455268i
$486$		0			0
$487$	21.9442	+	12.6695i	0.994385	+	0.574109i	0.906582	−	0.422029i	$-0.138682\pi$
$487$	21.9442	+	12.6695i	0.994385	+	0.574109i	0.0878031	+	0.996138i	$0.472015\pi$
$488$		0			0
$489$	−6.85956	+	31.6038i	−0.310200	+	1.42917i
$490$		0			0
$491$			35.4614i			1.60035i	0.599765	+	0.800176i	$0.295261\pi$
$491$			35.4614i			1.60035i	−0.599765	+	0.800176i	$0.704739\pi$
$492$		0			0
$493$	−10.6416	+	18.4318i	−0.479274	+	0.830126i
$494$		0			0
$495$	37.3475	+	12.6434i	1.67864	+	0.568281i
$496$		0			0
$497$	−1.93754	−	2.47106i	−0.0869106	−	0.110842i
$498$		0			0
$499$	14.7087	+	25.4762i	0.658451	+	1.14047i	0.981017	+	0.193923i	$0.0621213\pi$
$499$	14.7087	+	25.4762i	0.658451	+	1.14047i	−0.322566	+	0.946547i	$0.604545\pi$
$500$		0			0
$501$	−18.2340	−	16.5603i	−0.814636	−	0.739860i
$502$		0			0
$503$			20.9709i			0.935046i	0.883981	+	0.467523i	$0.154853\pi$
$503$			20.9709i			0.935046i	−0.883981	+	0.467523i	$0.845147\pi$
$504$		0			0
$505$	3.65781	+	1.64471i	0.162771	+	0.0731886i
$506$		0			0
$507$	−0.545091	+	0.600181i	−0.0242083	+	0.0266550i
$508$		0			0
$509$	3.71821	+	6.44013i	0.164807	+	0.285454i	0.936587	−	0.350436i	$-0.113967\pi$
$509$	3.71821	+	6.44013i	0.164807	+	0.285454i	−0.771780	+	0.635890i	$0.780633\pi$
$510$		0			0
$511$	−0.809096	−	5.68518i	−0.0357923	−	0.251497i
$512$		0			0
$513$	−21.3566	−	2.52322i	−0.942916	−	0.111403i
$514$		0			0
$515$	22.8793	−	16.4946i	1.00818	−	0.726839i
$516$		0			0
$517$	−10.7799			−0.474098
$518$		0			0
$519$	0.262409	−	1.20899i	0.0115185	−	0.0530687i
$520$		0			0
$521$	2.55125	−	4.41889i	0.111772	−	0.193595i	−0.804713	−	0.593665i	$-0.797681\pi$
$521$	2.55125	−	4.41889i	0.111772	−	0.193595i	0.916485	+	0.400069i	$0.131014\pi$
$522$		0			0
$523$	−8.24829	−	14.2865i	−0.360673	−	0.624703i	0.627399	−	0.778698i	$-0.284119\pi$
$523$	−8.24829	−	14.2865i	−0.360673	−	0.624703i	−0.988072	+	0.153995i	$0.950786\pi$
$524$		0			0
$525$	−2.96389	−	22.7204i	−0.129355	−	0.991598i
$526$		0			0
$527$	−7.00534	−	12.1336i	−0.305157	−	0.528548i
$528$		0			0
$529$	−14.0736	+	24.3762i	−0.611897	+	1.05984i
$530$		0			0
$531$	−12.6994	−	5.78531i	−0.551105	−	0.251061i
$532$		0			0
$533$	−22.4135			−0.970836
$534$		0			0
$535$	6.31128	−	4.55004i	0.272860	−	0.196716i
$536$		0			0
$537$	18.4477	−	5.90656i	0.796076	−	0.254887i
$538$		0			0
$539$	28.4783	−	29.6964i	1.22665	−	1.27911i
$540$		0			0
$541$	−10.3077	−	17.8534i	−0.443162	−	0.767578i	0.554760	−	0.832010i	$-0.312810\pi$
$541$	−10.3077	−	17.8534i	−0.443162	−	0.767578i	−0.997922	+	0.0644316i	$0.979477\pi$
$542$		0			0
$543$	4.74020	+	4.30510i	0.203422	+	0.184749i
$544$		0			0
$545$	20.3451	+	9.14800i	0.871487	+	0.391857i
$546$		0			0
$547$		−	25.6070i		−	1.09488i	−0.836846	−	0.547438i	$-0.815603\pi$
$547$		−	25.6070i		−	1.09488i	0.836846	−	0.547438i	$-0.184397\pi$
$548$		0			0
$549$	−1.41272	−	1.97998i	−0.0602933	−	0.0845033i
$550$		0			0
$551$	14.1700	+	24.5431i	0.603661	+	1.04557i
$552$		0			0
$553$	24.8049	+	9.97162i	1.05481	+	0.424036i
$554$		0			0
$555$	7.59557	+	0.859597i	0.322414	+	0.0364879i
$556$		0			0
$557$	18.0986	−	31.3477i	0.766862	−	1.32824i	−0.172394	−	0.985028i	$-0.555150\pi$
$557$	18.0986	−	31.3477i	0.766862	−	1.32824i	0.939256	−	0.343216i	$-0.111516\pi$
$558$		0			0
$559$		−	13.7700i		−	0.582410i
$560$		0			0
$561$	30.9228	+	6.71175i	1.30556	+	0.283370i
$562$		0			0
$563$	−26.5408	−	15.3233i	−1.11856	−	0.645801i	−0.177527	−	0.984116i	$-0.556810\pi$
$563$	−26.5408	−	15.3233i	−1.11856	−	0.645801i	−0.941033	+	0.338315i	$0.890143\pi$
$564$		0			0
$565$	−0.574105	−	5.66248i	−0.0241528	−	0.238222i
$566$		0			0
$567$	15.5856	−	18.0025i	0.654535	−	0.756032i
$568$		0			0
$569$	13.2153	−	7.62988i	0.554016	−	0.319861i	−0.196724	−	0.980459i	$-0.563030\pi$
$569$	13.2153	−	7.62988i	0.554016	−	0.319861i	0.750740	+	0.660598i	$0.229697\pi$
$570$		0			0
$571$	9.05228	−	15.6790i	0.378826	−	0.656146i	−0.612066	−	0.790807i	$-0.709661\pi$
$571$	9.05228	−	15.6790i	0.378826	−	0.656146i	0.990892	+	0.134661i	$0.0429945\pi$
$572$		0			0
$573$	−3.81650	+	17.5836i	−0.159437	+	0.734566i
$574$		0			0
$575$	23.7311	+	26.7491i	0.989656	+	1.11552i
$576$		0			0
$577$	−3.28336	+	5.68695i	−0.136688	+	0.236751i	−0.926241	−	0.376932i	$-0.876979\pi$
$577$	−3.28336	+	5.68695i	−0.136688	+	0.236751i	0.789553	+	0.613682i	$0.210312\pi$
$578$		0			0
$579$	−9.76715	+	3.12723i	−0.405909	+	0.129963i
$580$		0			0
$581$	8.67263	+	11.0607i	0.359801	+	0.458875i
$582$		0			0
$583$	−70.2864	+	40.5799i	−2.91097	+	1.68065i
$584$		0			0
$585$	23.2872	−	4.65207i	0.962807	−	0.192339i
$586$		0			0
$587$			9.35074i			0.385946i	0.981204	+	0.192973i	$0.0618130\pi$
$587$			9.35074i			0.385946i	−0.981204	+	0.192973i	$0.938187\pi$
$588$		0			0
$589$	−18.6561			−0.768712
$590$		0			0
$591$	12.9320	−	14.2390i	0.531950	−	0.585713i
$592$		0			0
$593$	23.3806	−	13.4988i	0.960126	−	0.554329i	0.0639141	−	0.997955i	$-0.479642\pi$
$593$	23.3806	−	13.4988i	0.960126	−	0.554329i	0.896212	+	0.443626i	$0.146308\pi$
$594$		0			0
$595$	−4.41388	−	17.8503i	−0.180951	−	0.731790i
$596$		0			0
$597$	21.8411	−	6.99307i	0.893899	−	0.286207i
$598$		0			0
$599$	19.7216	+	11.3863i	0.805803	+	0.465231i	0.845496	−	0.533981i	$-0.179305\pi$
$599$	19.7216	+	11.3863i	0.805803	+	0.465231i	−0.0396931	+	0.999212i	$0.512638\pi$
$600$		0			0
$601$			5.26871i			0.214915i	0.994210	+	0.107458i	$0.0342710\pi$
$601$			5.26871i			0.214915i	−0.994210	+	0.107458i	$0.965729\pi$
$602$		0			0
$603$	12.6974	−	27.8722i	0.517079	−	1.13504i
$604$		0			0
$605$	−42.7135	+	30.7938i	−1.73655	+	1.25195i
$606$		0			0
$607$	4.67749	+	8.10166i	0.189854	+	0.328836i	0.945201	−	0.326488i	$-0.105865\pi$
$607$	4.67749	+	8.10166i	0.189854	+	0.328836i	−0.755348	+	0.655324i	$0.772532\pi$
$608$		0			0
$609$	−31.2976	−	2.26884i	−1.26824	−	0.0919382i
$610$		0			0
$611$	−5.62260	+	3.24621i	−0.227466	+	0.131328i
$612$		0			0
$613$	−27.3310	−	15.7796i	−1.10389	−	0.637330i	−0.166649	−	0.986016i	$-0.553295\pi$
$613$	−27.3310	−	15.7796i	−1.10389	−	0.637330i	−0.937240	+	0.348686i	$0.886628\pi$
$614$		0			0
$615$	−19.7228	−	14.5710i	−0.795299	−	0.587561i
$616$		0			0
$617$	−39.6450			−1.59605			−0.798023	−	0.602626i	$-0.794121\pi$
$617$	−39.6450			−1.59605			−0.798023	+	0.602626i	$0.794121\pi$
$618$		0			0
$619$	33.2406	+	19.1915i	1.33605	+	0.771370i	0.986219	−	0.165443i	$-0.0529052\pi$
$619$	33.2406	+	19.1915i	1.33605	+	0.771370i	0.349832	+	0.936812i	$0.386239\pi$
$620$		0			0
$621$	−4.36020	+	36.9048i	−0.174969	+	1.48094i
$622$		0			0
$623$	30.8810	+	12.4142i	1.23722	+	0.497365i
$624$		0			0
$625$	22.9857	−	9.83137i	0.919430	−	0.393255i
$626$		0			0
$627$	28.3276	−	31.1906i	1.13129	−	1.24563i
$628$		0			0
$629$	6.13446			0.244597
$630$		0			0
$631$	1.06381			0.0423495			0.0211748	−	0.999776i	$-0.493259\pi$
$631$	1.06381			0.0423495			0.0211748	+	0.999776i	$0.493259\pi$
$632$		0			0
$633$	−23.1875	+	25.5310i	−0.921620	+	1.01477i
$634$		0			0
$635$	−28.1678	+	2.85586i	−1.11780	+	0.113331i
$636$		0			0
$637$	5.91113	−	24.0650i	0.234207	−	0.953488i
$638$		0			0
$639$	3.54409	−	0.341752i	0.140202	−	0.0135195i
$640$		0			0
$641$	25.9645	+	14.9906i	1.02553	+	0.592093i	0.915702	−	0.401858i	$-0.131635\pi$
$641$	25.9645	+	14.9906i	1.02553	+	0.592093i	0.109832	+	0.993950i	$0.464969\pi$
$642$		0			0
$643$	16.0861			0.634373			0.317187	−	0.948363i	$-0.397262\pi$
$643$	16.0861			0.634373			0.317187	+	0.948363i	$0.397262\pi$
$644$		0			0
$645$	8.95191	−	12.1169i	0.352481	−	0.477104i
$646$		0			0
$647$	−21.6193	−	12.4819i	−0.849944	−	0.490716i	0.0106878	−	0.999943i	$-0.496598\pi$
$647$	−21.6193	−	12.4819i	−0.849944	−	0.490716i	−0.860632	+	0.509227i	$0.829931\pi$
$648$		0			0
$649$	23.6786	−	13.6709i	0.929468	−	0.536629i
$650$		0			0
$651$	11.5950	−	17.0960i	0.454445	−	0.670046i
$652$		0			0
$653$	2.19607	+	3.80370i	0.0859387	+	0.148850i	0.905791	−	0.423725i	$-0.139278\pi$
$653$	2.19607	+	3.80370i	0.0859387	+	0.148850i	−0.819852	+	0.572575i	$0.805944\pi$
$654$		0			0
$655$	23.0274	−	16.6013i	0.899755	−	0.648668i
$656$		0			0
$657$	5.92544	+	2.69939i	0.231173	+	0.105313i
$658$		0			0
$659$			1.93959i			0.0755557i	0.999286	+	0.0377778i	$0.0120279\pi$
$659$			1.93959i			0.0755557i	−0.999286	+	0.0377778i	$0.987972\pi$
$660$		0			0
$661$	21.6034	+	12.4727i	0.840274	+	0.485132i	0.857357	−	0.514722i	$-0.172105\pi$
$661$	21.6034	+	12.4727i	0.840274	+	0.485132i	−0.0170833	+	0.999854i	$0.505438\pi$
$662$		0			0
$663$	18.1499	−	5.81122i	0.704885	−	0.225689i
$664$		0			0
$665$	−23.5230	−	6.79444i	−0.912184	−	0.263477i
$666$		0			0
$667$	42.4112	−	24.4861i	1.64217	−	0.948107i
$668$		0			0
$669$	12.2182	−	13.4531i	0.472384	−	0.520127i
$670$		0			0
$671$	4.76553			0.183971
$672$		0			0
$673$			6.21519i			0.239578i	0.992799	+	0.119789i	$0.0382218\pi$
$673$			6.21519i			0.239578i	−0.992799	+	0.119789i	$0.961778\pi$
$674$		0			0
$675$	23.5159	+	11.0455i	0.905128	+	0.425140i
$676$		0			0
$677$	−14.4283	+	8.33017i	−0.554524	+	0.320154i	−0.750945	−	0.660365i	$-0.770401\pi$
$677$	−14.4283	+	8.33017i	−0.554524	+	0.320154i	0.196421	+	0.980520i	$0.437068\pi$
$678$		0			0
$679$	−9.38346	+	7.35751i	−0.360104	+	0.282355i
$680$		0			0
$681$	27.0948	−	8.67519i	1.03828	−	0.332434i
$682$		0			0
$683$	−11.1339	+	19.2844i	−0.426025	+	0.737898i	−0.996516	−	0.0834067i	$-0.973420\pi$
$683$	−11.1339	+	19.2844i	−0.426025	+	0.737898i	0.570490	+	0.821304i	$0.306753\pi$
$684$		0			0
$685$	−10.7024	−	4.81224i	−0.408916	−	0.183866i
$686$		0			0
$687$	−0.383426	+	1.76654i	−0.0146286	+	0.0673979i
$688$		0			0
$689$	−24.4401	+	42.3315i	−0.931095	+	1.61270i
$690$		0			0
$691$	−24.0492	+	13.8848i	−0.914873	+	0.528202i	−0.881996	−	0.471257i	$-0.843800\pi$
$691$	−24.0492	+	13.8848i	−0.914873	+	0.528202i	−0.0328772	+	0.999459i	$0.510467\pi$
$692$		0			0
$693$	10.9763	+	45.3441i	0.416957	+	1.72248i
$694$		0			0
$695$	31.7776	−	3.22185i	1.20539	−	0.122212i
$696$		0			0
$697$	−17.0424	−	9.83941i	−0.645525	−	0.372694i
$698$		0			0
$699$	48.9576	+	10.6262i	1.85175	+	0.401919i
$700$		0			0
$701$			0.789291i			0.0298111i	0.999889	+	0.0149056i	$0.00474476\pi$
$701$			0.789291i			0.0298111i	−0.999889	+	0.0149056i	$0.995255\pi$
$702$		0			0
$703$	4.08421	−	7.07406i	0.154039	−	0.266803i
$704$		0			0
$705$	−7.05797	−	0.798757i	−0.265819	−	0.0300829i
$706$		0			0
$707$	0.668609	+	4.69803i	0.0251456	+	0.176688i
$708$		0			0
$709$	−7.93432	−	13.7427i	−0.297980	−	0.516116i	0.677694	−	0.735344i	$-0.262979\pi$
$709$	−7.93432	−	13.7427i	−0.297980	−	0.516116i	−0.975674	+	0.219228i	$0.929646\pi$
$710$		0			0
$711$	−24.6764	+	17.6067i	−0.925438	+	0.660301i
$712$		0			0
$713$			32.2383i			1.20733i
$714$		0			0
$715$	−19.0806	+	42.4351i	−0.713574	+	1.58698i
$716$		0			0
$717$	7.30496	+	6.63443i	0.272809	+	0.247767i
$718$		0			0
$719$	22.6303	+	39.1968i	0.843967	+	1.46179i	0.886516	+	0.462699i	$0.153119\pi$
$719$	22.6303	+	39.1968i	0.843967	+	1.46179i	−0.0425492	+	0.999094i	$0.513548\pi$
$720$		0			0
$721$	30.9645	+	12.4478i	1.15318	+	0.463581i
$722$		0			0
$723$	−11.6304	+	3.72380i	−0.432538	+	0.138489i
$724$		0			0
$725$	−6.87198	−	33.5413i	−0.255219	−	1.24569i
$726$		0			0
$727$	21.4724			0.796369			0.398185	−	0.917305i	$-0.369640\pi$
$727$	21.4724			0.796369			0.398185	+	0.917305i	$0.369640\pi$
$728$		0			0
$729$	7.67916	+	25.8849i	0.284413	+	0.958702i
$730$		0			0
$731$	6.04497	−	10.4702i	0.223581	−	0.387254i
$732$		0			0
$733$	−7.38122	−	12.7846i	−0.272631	−	0.472211i	0.696903	−	0.717165i	$-0.254561\pi$
$733$	−7.38122	−	12.7846i	−0.272631	−	0.472211i	−0.969535	+	0.244954i	$0.921227\pi$
$734$		0			0
$735$	20.8462	−	17.3331i	0.768922	−	0.639342i
$736$		0			0
$737$	30.0044	+	51.9691i	1.10523	+	1.91431i
$738$		0			0
$739$	1.22065	−	2.11423i	0.0449024	−	0.0777733i	−0.842701	−	0.538382i	$-0.819036\pi$
$739$	1.22065	−	2.11423i	0.0449024	−	0.0777733i	0.887603	+	0.460609i	$0.152369\pi$
$740$		0			0
$741$	5.38258	−	24.7989i	0.197734	−	0.911011i
$742$		0			0
$743$	−32.2677			−1.18379			−0.591894	−	0.806016i	$-0.701620\pi$
$743$	−32.2677			−1.18379			−0.591894	+	0.806016i	$0.701620\pi$
$744$		0			0
$745$	−19.7446	−	27.3873i	−0.723386	−	1.00339i
$746$		0			0
$747$	−15.8637	+	1.52972i	−0.580423	+	0.0559695i
$748$		0			0
$749$	8.54158	+	3.43373i	0.312103	+	0.125466i
$750$		0			0
$751$	−7.00840	−	12.1389i	−0.255740	−	0.442955i	0.709356	−	0.704850i	$-0.248986\pi$
$751$	−7.00840	−	12.1389i	−0.255740	−	0.442955i	−0.965096	+	0.261895i	$0.915652\pi$
$752$		0			0
$753$	4.57919	−	5.04199i	0.166875	−	0.183740i
$754$		0			0
$755$	17.0077	+	7.64737i	0.618972	+	0.278316i
$756$		0			0
$757$			41.4500i			1.50653i	0.657720	+	0.753263i	$0.271521\pi$
$757$			41.4500i			1.50653i	−0.657720	+	0.753263i	$0.728479\pi$
$758$		0			0
$759$	−53.8983	−	48.9509i	−1.95638	−	1.77681i
$760$		0			0
$761$	−20.0586	−	34.7425i	−0.727124	−	1.25942i	−0.958094	−	0.286455i	$-0.907523\pi$
$761$	−20.0586	−	34.7425i	−0.727124	−	1.25942i	0.230969	−	0.972961i	$-0.425810\pi$
$762$		0			0
$763$	3.71886	+	26.1308i	0.134632	+	0.946000i
$764$		0			0
$765$	19.7489	+	6.68571i	0.714024	+	0.241722i
$766$		0			0
$767$	8.23358	−	14.2610i	0.297297	−	0.514934i
$768$		0			0
$769$		−	22.4441i		−	0.809355i	−0.914459	−	0.404677i	$-0.867384\pi$
$769$		−	22.4441i		−	0.809355i	0.914459	−	0.404677i	$-0.132616\pi$
$770$		0			0
$771$	5.62310	−	25.9071i	0.202511	−	0.933021i
$772$		0			0
$773$	−25.1951	−	14.5464i	−0.906206	−	0.523198i	−0.0269973	−	0.999636i	$-0.508595\pi$
$773$	−25.1951	−	14.5464i	−0.906206	−	0.523198i	−0.879208	+	0.476437i	$0.841928\pi$
$774$		0			0
$775$	21.3839	+	7.12235i	0.768132	+	0.255842i
$776$		0			0
$777$	3.94411	+	8.13930i	0.141494	+	0.291996i
$778$		0			0
$779$	−22.6930	+	13.1018i	−0.813060	+	0.469421i
$780$		0			0
$781$	−3.48802	+	6.04143i	−0.124811	+	0.216180i
$782$		0			0
$783$	21.2832	−	28.5140i	0.760600	−	1.01901i
$784$		0			0
$785$	1.95903	+	0.880863i	0.0699208	+	0.0314394i
$786$		0			0
$787$	−16.9461	+	29.3516i	−0.604064	+	1.04627i	0.388134	+	0.921603i	$0.373120\pi$
$787$	−16.9461	+	29.3516i	−0.604064	+	1.04627i	−0.992199	+	0.124667i	$0.960214\pi$
$788$		0			0
$789$	−10.3093	−	32.1987i	−0.367022	−	1.14630i
$790$		0			0
$791$	5.29946	−	4.15527i	0.188427	−	0.147745i
$792$		0			0
$793$	2.48562	−	1.43507i	0.0882669	−	0.0509609i
$794$		0			0
$795$	−49.0259	+	21.3611i	−1.73877	+	0.757600i
$796$		0			0
$797$		−	30.8362i		−	1.09227i	−0.837696	−	0.546137i	$-0.816098\pi$
$797$		−	30.8362i		−	1.09227i	0.837696	−	0.546137i	$-0.183902\pi$
$798$		0			0
$799$	−5.70028			−0.201661
$800$		0			0
$801$	−30.7210	+	21.9195i	−1.08547	+	0.774487i
$802$		0			0
$803$	−11.0483	+	6.37874i	−0.389886	+	0.225101i
$804$		0			0
$805$	−11.7410	+	40.6485i	−0.413816	+	1.43267i
$806$		0			0
$807$	−5.19561	−	16.2272i	−0.182894	−	0.571226i
$808$		0			0
$809$	−32.1338	−	18.5524i	−1.12976	−	0.652269i	−0.185888	−	0.982571i	$-0.559516\pi$
$809$	−32.1338	−	18.5524i	−1.12976	−	0.652269i	−0.943875	+	0.330302i	$0.892849\pi$
$810$		0			0
$811$			33.9956i			1.19375i	0.802336	+	0.596873i	$0.203590\pi$
$811$			33.9956i			1.19375i	−0.802336	+	0.596873i	$0.796410\pi$
$812$		0			0
$813$	7.67076	−	35.3412i	0.269025	−	1.23947i
$814$		0			0
$815$	−24.4158	−	33.8667i	−0.855249	−	1.18630i
$816$		0			0
$817$	−8.04926	−	13.9417i	−0.281608	−	0.487759i
$818$		0			0
$819$	19.3798	+	20.3453i	0.677185	+	0.710924i
$820$		0			0
$821$	−40.0563	+	23.1265i	−1.39798	+	0.807122i	−0.994180	−	0.107727i	$-0.965643\pi$
$821$	−40.0563	+	23.1265i	−1.39798	+	0.807122i	−0.403796	+	0.914849i	$0.632309\pi$
$822$		0			0
$823$	−40.7593	−	23.5324i	−1.42078	−	0.820288i	−0.424414	−	0.905468i	$-0.639520\pi$
$823$	−40.7593	−	23.5324i	−1.42078	−	0.820288i	−0.996366	+	0.0851803i	$0.972853\pi$
$824$		0			0
$825$	−44.3771	+	24.9364i	−1.54501	+	0.868175i
$826$		0			0
$827$	14.6102			0.508046			0.254023	−	0.967198i	$-0.418246\pi$
$827$	14.6102			0.508046			0.254023	+	0.967198i	$0.418246\pi$
$828$		0			0
$829$	27.9876	+	16.1586i	0.972049	+	0.561213i	0.899860	−	0.436178i	$-0.143668\pi$
$829$	27.9876	+	16.1586i	0.972049	+	0.561213i	0.0721885	+	0.997391i	$0.477002\pi$
$830$		0			0
$831$	14.0275	−	4.49129i	0.486607	−	0.155801i
$832$		0			0
$833$	15.0590	−	15.7031i	0.521763	−	0.544080i
$834$		0			0
$835$	31.6373	−	3.20763i	1.09485	−	0.111004i
$836$		0			0
$837$	9.25056	+	21.5190i	0.319746	+	0.743804i
$838$		0			0
$839$	−15.0113			−0.518249			−0.259124	−	0.965844i	$-0.583434\pi$
$839$	−15.0113			−0.518249			−0.259124	+	0.965844i	$0.583434\pi$
$840$		0			0
$841$	−17.8898			−0.616888
$842$		0			0
$843$	−9.79185	−	8.89305i	−0.337249	−	0.306293i
$844$		0			0
$845$	−0.105580	−	1.04136i	−0.00363208	−	0.0358237i
$846$		0			0
$847$	−57.8078	−	23.2389i	−1.98630	−	0.798497i
$848$		0			0
$849$	4.75735	+	14.8584i	0.163272	+	0.509940i
$850$		0			0
$851$	−12.2242	−	7.05764i	−0.419040	−	0.241933i
$852$		0			0
$853$	43.2807			1.48190			0.740952	−	0.671558i	$-0.234374\pi$
$853$	43.2807			1.48190			0.740952	+	0.671558i	$0.234374\pi$
$854$		0			0
$855$	20.8582	−	18.3226i	0.713336	−	0.626620i
$856$		0			0
$857$	18.3255	+	10.5802i	0.625986	+	0.361413i	0.779196	−	0.626780i	$-0.215628\pi$
$857$	18.3255	+	10.5802i	0.625986	+	0.361413i	−0.153210	+	0.988194i	$0.548961\pi$
$858$		0			0
$859$	36.5871	−	21.1236i	1.24834	−	0.720728i	0.277560	−	0.960708i	$-0.410474\pi$
$859$	36.5871	−	21.1236i	1.24834	−	0.720728i	0.970778	+	0.239981i	$0.0771411\pi$
$860$		0			0
$861$	2.09781	−	28.9383i	0.0714933	−	0.986213i
$862$		0			0
$863$	−17.8457	−	30.9097i	−0.607475	−	1.05218i	−0.991655	−	0.128919i	$-0.958849\pi$
$863$	−17.8457	−	30.9097i	−0.607475	−	1.05218i	0.384181	−	0.923258i	$-0.374484\pi$
$864$		0			0
$865$	0.934016	+	1.29556i	0.0317575	+	0.0440502i
$866$		0			0
$867$	−12.4233	−	2.69645i	−0.421916	−	0.0915764i
$868$		0			0
$869$		−	59.3927i		−	2.01476i
$870$		0			0
$871$	31.2996	+	18.0708i	1.06055	+	0.612306i
$872$		0			0
$873$	−1.29775	−	13.4581i	−0.0439222	−	0.455489i
$874$		0			0
$875$	24.3685	+	16.7683i	0.823806	+	0.566872i
$876$		0			0
$877$	−1.90519	+	1.09996i	−0.0643336	+	0.0371430i	−0.531822	−	0.846856i	$-0.678492\pi$
$877$	−1.90519	+	1.09996i	−0.0643336	+	0.0371430i	0.467488	+	0.883999i	$0.345159\pi$
$878$		0			0
$879$	−35.4011	−	32.1517i	−1.19405	−	1.08445i
$880$		0			0
$881$	29.2075			0.984025			0.492013	−	0.870588i	$-0.336261\pi$
$881$	29.2075			0.984025			0.492013	+	0.870588i	$0.336261\pi$
$882$		0			0
$883$			2.21069i			0.0743956i	0.999308	+	0.0371978i	$0.0118432\pi$
$883$			2.21069i			0.0743956i	−0.999308	+	0.0371978i	$0.988157\pi$
$884$		0			0
$885$	16.5162	−	7.19629i	0.555187	−	0.241901i
$886$		0			0
$887$	−11.5724	+	6.68134i	−0.388564	+	0.224337i	−0.681538	−	0.731783i	$-0.738688\pi$
$887$	−11.5724	+	6.68134i	−0.388564	+	0.224337i	0.292974	+	0.956120i	$0.405355\pi$
$888$		0			0
$889$	−20.6702	−	26.3620i	−0.693258	−	0.884152i
$890$		0			0
$891$	−50.0230	−	17.2088i	−1.67583	−	0.576517i
$892$		0			0
$893$	−3.79514	+	6.57337i	−0.126999	+	0.219970i
$894$		0			0
$895$	−10.2551	+	22.8073i	−0.342791	+	0.762364i
$896$		0			0
$897$	−42.8533	−	9.30126i	−1.43083	−	0.310560i
$898$		0			0
$899$	15.4337	−	26.7320i	0.514743	−	0.891561i
$900$		0			0
$901$	−37.1667	+	21.4582i	−1.23820	+	0.714876i
$902$		0			0
$903$	17.7786	+	1.28882i	0.591635	+	0.0428892i
$904$		0			0
$905$	−8.22458	+	0.833869i	−0.273394	+	0.0277188i
$906$		0			0
$907$	3.62770	+	2.09445i	0.120456	+	0.0695451i	0.559017	−	0.829156i	$-0.311179\pi$
$907$	3.62770	+	2.09445i	0.120456	+	0.0695451i	−0.438562	+	0.898701i	$0.644512\pi$
$908$		0			0
$909$	−4.89658	−	2.23068i	−0.162409	−	0.0739870i
$910$		0			0
$911$		−	22.5190i		−	0.746087i	−0.927814	−	0.373043i	$-0.878314\pi$
$911$		−	22.5190i		−	0.746087i	0.927814	−	0.373043i	$-0.121686\pi$
$912$		0			0
$913$	15.6128	−	27.0421i	0.516707	−	0.894962i
$914$		0			0
$915$	3.12017	+	0.353112i	0.103149	+	0.0116735i
$916$		0			0
$917$	31.1649	+	12.5284i	1.02916	+	0.413723i
$918$		0			0
$919$	−7.26453	−	12.5825i	−0.239635	−	0.415060i	0.720975	−	0.692961i	$-0.243694\pi$
$919$	−7.26453	−	12.5825i	−0.239635	−	0.415060i	−0.960610	+	0.277902i	$0.910361\pi$
$920$		0			0
$921$	−11.6403	+	12.8167i	−0.383561	+	0.422326i
$922$		0			0
$923$			4.20148i			0.138293i
$924$		0			0
$925$	−7.38204	+	6.54915i	−0.242720	+	0.215335i
$926$		0			0
$927$	−30.8041	+	21.9788i	−1.01174	+	0.721879i
$928$		0			0
$929$	−20.7788	−	35.9900i	−0.681732	−	1.18079i	−0.974452	−	0.224596i	$-0.927894\pi$
$929$	−20.7788	−	35.9900i	−0.681732	−	1.18079i	0.292720	−	0.956198i	$-0.405440\pi$
$930$		0			0
$931$	−8.08232	−	27.8204i	−0.264887	−	0.911776i
$932$		0			0
$933$	12.6056	+	39.3705i	0.412688	+	1.28893i
$934$		0			0
$935$	−33.1369	+	23.8897i	−1.08369	+	0.781277i
$936$		0			0
$937$	−45.5010			−1.48645			−0.743226	−	0.669040i	$-0.766705\pi$
$937$	−45.5010			−1.48645			−0.743226	+	0.669040i	$0.766705\pi$
$938$		0			0
$939$	9.47064	+	2.05559i	0.309063	+	0.0670817i
$940$		0			0
$941$	−10.0244	+	17.3627i	−0.326785	+	0.566007i	−0.981872	−	0.189546i	$-0.939298\pi$
$941$	−10.0244	+	17.3627i	−0.326785	+	0.566007i	0.655087	+	0.755553i	$0.272632\pi$
$942$		0			0
$943$	22.6403	+	39.2142i	0.737270	+	1.27699i
$944$		0			0
$945$	3.82674	+	30.5017i	0.124484	+	0.992222i
$946$		0			0
$947$	−14.7490	−	25.5460i	−0.479278	−	0.830133i	0.520440	−	0.853898i	$-0.325768\pi$
$947$	−14.7490	−	25.5460i	−0.479278	−	0.830133i	−0.999718	+	0.0237652i	$0.992435\pi$
$948$		0			0
$949$	−3.84174	+	6.65408i	−0.124708	+	0.216001i
$950$		0			0
$951$	19.8658	+	4.31184i	0.644192	+	0.139821i
$952$		0			0
$953$	1.26250			0.0408964			0.0204482	−	0.999791i	$-0.493491\pi$
$953$	1.26250			0.0408964			0.0204482	+	0.999791i	$0.493491\pi$
$954$		0			0
$955$	−13.5844	−	18.8427i	−0.439581	−	0.609734i
$956$		0			0
$957$	21.2577	+	66.3932i	0.687163	+	2.14619i
$958$		0			0
$959$	−1.95628	−	13.7459i	−0.0631715	−	0.443879i
$960$		0			0
$961$	−5.34003	−	9.24920i	−0.172259	−	0.298361i
$962$		0			0
$963$	−8.49734	+	6.06287i	−0.273823	+	0.195373i
$964$		0			0
$965$	5.42959	−	12.0754i	0.174785	−	0.388719i
$966$		0			0
$967$		−	26.0942i		−	0.839132i	−0.907725	−	0.419566i	$-0.862182\pi$
$967$		−	26.0942i		−	0.839132i	0.907725	−	0.419566i	$-0.137818\pi$
$968$		0			0
$969$	14.9793	−	16.4932i	0.481205	−	0.529839i
$970$		0			0
$971$	6.95317	+	12.0432i	0.223138	+	0.386486i	0.955759	−	0.294150i	$-0.0950367\pi$
$971$	6.95317	+	12.0432i	0.223138	+	0.386486i	−0.732621	+	0.680636i	$0.761703\pi$
$972$		0			0
$973$	23.3192	+	29.7404i	0.747580	+	0.953433i
$974$		0			0
$975$	−15.6371	+	26.3700i	−0.500787	+	0.844514i
$976$		0			0
$977$	1.41905	−	2.45787i	0.0453995	−	0.0786342i	−0.842433	−	0.538802i	$-0.818877\pi$
$977$	1.41905	−	2.45787i	0.0453995	−	0.0786342i	0.887832	+	0.460167i	$0.152211\pi$
$978$		0			0
$979$		−	73.9413i		−	2.36317i
$980$		0			0
$981$	−27.2352	−	12.4072i	−0.869552	−	0.396132i
$982$		0			0
$983$	42.5573	+	24.5705i	1.35737	+	0.783677i	0.989268	−	0.146110i	$-0.0466753\pi$
$983$	42.5573	+	24.5705i	1.35737	+	0.783677i	0.368099	+	0.929787i	$0.380009\pi$
$984$		0			0
$985$	2.50484	+	24.7056i	0.0798108	+	0.787185i
$986$		0			0
$987$	−3.66496	−	7.56322i	−0.116657	−	0.240740i
$988$		0			0
$989$	−24.0917	+	13.9094i	−0.766072	+	0.442292i
$990$		0			0
$991$	−10.3281	+	17.8887i	−0.328081	+	0.568254i	−0.982131	−	0.188198i	$-0.939735\pi$
$991$	−10.3281	+	17.8887i	−0.328081	+	0.568254i	0.654050	+	0.756452i	$0.273069\pi$
$992$		0			0
$993$	−4.28080	−	0.929142i	−0.135847	−	0.0294854i
$994$		0			0
$995$	−12.1416	+	27.0027i	−0.384914	+	0.856044i
$996$		0			0
$997$	20.8453	−	36.1051i	0.660177	−	1.14346i	−0.320392	−	0.947285i	$-0.603814\pi$
$997$	20.8453	−	36.1051i	0.660177	−	1.14346i	0.980569	−	0.196175i	$-0.0628522\pi$
$998$		0			0
$999$	−10.1847	−	1.20330i	−0.322231	−	0.0380707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.bn.a.269.12	yes	32
3.2	odd	2	inner	420.2.bn.a.269.10	yes	32
5.2	odd	4		2100.2.bi.n.101.4		32
5.3	odd	4		2100.2.bi.n.101.13		32
5.4	even	2	inner	420.2.bn.a.269.5	yes	32
7.3	odd	6		2940.2.f.a.1469.32		32
7.4	even	3		2940.2.f.a.1469.1		32
7.5	odd	6	inner	420.2.bn.a.89.7	yes	32
15.2	even	4		2100.2.bi.n.101.2		32
15.8	even	4		2100.2.bi.n.101.15		32
15.14	odd	2	inner	420.2.bn.a.269.7	yes	32
21.5	even	6	inner	420.2.bn.a.89.5	✓	32
21.11	odd	6		2940.2.f.a.1469.4		32
21.17	even	6		2940.2.f.a.1469.29		32
35.4	even	6		2940.2.f.a.1469.31		32
35.12	even	12		2100.2.bi.n.1601.2		32
35.19	odd	6	inner	420.2.bn.a.89.10	yes	32
35.24	odd	6		2940.2.f.a.1469.2		32
35.33	even	12		2100.2.bi.n.1601.15		32
105.47	odd	12		2100.2.bi.n.1601.4		32
105.59	even	6		2940.2.f.a.1469.3		32
105.68	odd	12		2100.2.bi.n.1601.13		32
105.74	odd	6		2940.2.f.a.1469.30		32
105.89	even	6	inner	420.2.bn.a.89.12	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bn.a.89.5	✓	32	21.5	even	6	inner
420.2.bn.a.89.7	yes	32	7.5	odd	6	inner
420.2.bn.a.89.10	yes	32	35.19	odd	6	inner
420.2.bn.a.89.12	yes	32	105.89	even	6	inner
420.2.bn.a.269.5	yes	32	5.4	even	2	inner
420.2.bn.a.269.7	yes	32	15.14	odd	2	inner
420.2.bn.a.269.10	yes	32	3.2	odd	2	inner
420.2.bn.a.269.12	yes	32	1.1	even	1	trivial
2100.2.bi.n.101.2		32	15.2	even	4
2100.2.bi.n.101.4		32	5.2	odd	4
2100.2.bi.n.101.13		32	5.3	odd	4
2100.2.bi.n.101.15		32	15.8	even	4
2100.2.bi.n.1601.2		32	35.12	even	12
2100.2.bi.n.1601.4		32	105.47	odd	12
2100.2.bi.n.1601.13		32	105.68	odd	12
2100.2.bi.n.1601.15		32	35.33	even	12
2940.2.f.a.1469.1		32	7.4	even	3
2940.2.f.a.1469.2		32	35.24	odd	6
2940.2.f.a.1469.3		32	105.59	even	6
2940.2.f.a.1469.4		32	21.11	odd	6
2940.2.f.a.1469.29		32	21.17	even	6
2940.2.f.a.1469.30		32	105.74	odd	6
2940.2.f.a.1469.31		32	35.4	even	6
2940.2.f.a.1469.32		32	7.3	odd	6

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:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.bn (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16448 - 1.28218i) q^{3} +(0.225553 + 2.22466i) q^{5} +(-2.08204 + 1.63251i) q^{7} +(-0.287951 - 2.98615i) q^{9} +(5.09034 + 2.93891i) q^{11} +3.54004 q^{13} +(3.11506 + 2.30139i) q^{15} +(2.69171 + 1.55406i) q^{17} +(3.58419 - 2.06933i) q^{19} +(-0.331334 + 4.57058i) q^{21} +(-3.57587 - 6.19358i) q^{23} +(-4.89825 + 1.00356i) q^{25} +(-4.16408 - 3.10812i) q^{27} +6.84761i q^{29} +(-3.90384 - 2.25388i) q^{31} +(9.69582 - 3.10439i) q^{33} +(-4.10141 - 4.26362i) q^{35} +(1.70926 - 0.986843i) q^{37} +(4.12233 - 4.53896i) q^{39} -6.33142 q^{41} -3.88979i q^{43} +(6.57823 - 1.31413i) q^{45} +(-1.58829 + 0.916997i) q^{47} +(1.66979 - 6.79793i) q^{49} +(5.12704 - 1.64157i) q^{51} +(-6.90391 + 11.9579i) q^{53} +(-5.38994 + 11.9872i) q^{55} +(1.52048 - 7.00526i) q^{57} +(2.32584 - 4.02848i) q^{59} +(0.702144 - 0.405383i) q^{61} +(5.47446 + 5.74720i) q^{63} +(0.798468 + 7.87540i) q^{65} +(8.84158 + 5.10469i) q^{67} +(-12.1053 - 2.62744i) q^{69} +1.18684i q^{71} +(-1.08522 + 1.87966i) q^{73} +(-4.41720 + 7.44905i) q^{75} +(-15.3961 + 2.19112i) q^{77} +(-5.05228 - 8.75081i) q^{79} +(-8.83417 + 1.71973i) q^{81} -5.31243i q^{83} +(-2.85014 + 6.33868i) q^{85} +(8.77984 + 7.97394i) q^{87} +(-6.28986 - 10.8944i) q^{89} +(-7.37052 + 5.77917i) q^{91} +(-7.43583 + 2.38080i) q^{93} +(5.41199 + 7.50686i) q^{95} +4.50686 q^{97} +(7.31025 - 16.0468i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{15} + 12 q^{19} - 8 q^{21} + 6 q^{25} - 12 q^{31} + 24 q^{39} + 33 q^{45} - 44 q^{49} - 10 q^{51} - 24 q^{61} + 21 q^{75} - 28 q^{79} - 20 q^{81} - 4 q^{85} + 16 q^{91} - 28 q^{99}+O(q^{100}) \) 32 * q + 2 * q^15 + 12 * q^19 - 8 * q^21 + 6 * q^25 - 12 * q^31 + 24 * q^39 + 33 * q^45 - 44 * q^49 - 10 * q^51 - 24 * q^61 + 21 * q^75 - 28 * q^79 - 20 * q^81 - 4 * q^85 + 16 * q^91 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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