LMFDB - Embedded newform 1218.2.m.a.307.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1218,2,Mod(307,1218)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1218.307"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1218, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1218 = 2 \cdot 3 \cdot 7 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1218.m (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0,0,0,-40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$9.72577896619$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.1
Character	$\chi$	$=$	1218.307
Dual form			1218.2.m.a.853.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} -3.66176 q^{5} -1.00000 q^{6} +(-1.87946 - 1.86216i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(2.58925 - 2.58925i) q^{10} +(3.90483 - 3.90483i) q^{11} +(0.707107 - 0.707107i) q^{12} -6.46283 q^{13} +(2.64572 - 0.0122313i) q^{14} +(-2.58925 - 2.58925i) q^{15} -1.00000 q^{16} +(3.63679 + 3.63679i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(1.96925 + 1.96925i) q^{19} +3.66176i q^{20} +(-0.0122313 - 2.64572i) q^{21} +5.52226i q^{22} -1.88723 q^{23} +1.00000i q^{24} +8.40845 q^{25} +(4.56991 - 4.56991i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.86216 + 1.87946i) q^{28} +(4.00171 + 3.60365i) q^{29} +3.66176 q^{30} +(1.04212 + 1.04212i) q^{31} +(0.707107 - 0.707107i) q^{32} +5.52226 q^{33} -5.14319 q^{34} +(6.88211 + 6.81877i) q^{35} +1.00000 q^{36} +(1.02071 + 1.02071i) q^{37} -2.78495 q^{38} +(-4.56991 - 4.56991i) q^{39} +(-2.58925 - 2.58925i) q^{40} +(7.51360 - 7.51360i) q^{41} +(1.87946 + 1.86216i) q^{42} +(-6.36372 + 6.36372i) q^{43} +(-3.90483 - 3.90483i) q^{44} -3.66176i q^{45} +(1.33447 - 1.33447i) q^{46} +(-6.78006 + 6.78006i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(0.0647212 + 6.99970i) q^{49} +(-5.94568 + 5.94568i) q^{50} +5.14319i q^{51} +6.46283i q^{52} +13.5738 q^{53} -1.00000i q^{54} +(-14.2985 + 14.2985i) q^{55} +(-0.0122313 - 2.64572i) q^{56} +2.78495i q^{57} +(-5.37780 + 0.281472i) q^{58} +2.64616i q^{59} +(-2.58925 + 2.58925i) q^{60} +(8.08912 + 8.08912i) q^{61} -1.47379 q^{62} +(1.86216 - 1.87946i) q^{63} +1.00000i q^{64} +23.6653 q^{65} +(-3.90483 + 3.90483i) q^{66} -0.980797i q^{67} +(3.63679 - 3.63679i) q^{68} +(-1.33447 - 1.33447i) q^{69} +(-9.68799 + 0.0447880i) q^{70} -1.68936i q^{71} +(-0.707107 + 0.707107i) q^{72} +(-8.58204 + 8.58204i) q^{73} -1.44351 q^{74} +(5.94568 + 5.94568i) q^{75} +(1.96925 - 1.96925i) q^{76} +(-14.6104 + 0.0675444i) q^{77} +6.46283 q^{78} +(5.39398 - 5.39398i) q^{79} +3.66176 q^{80} -1.00000 q^{81} +10.6258i q^{82} -4.30382i q^{83} +(-2.64572 + 0.0122313i) q^{84} +(-13.3170 - 13.3170i) q^{85} -8.99966i q^{86} +(0.281472 + 5.37780i) q^{87} +5.52226 q^{88} +(-4.97318 - 4.97318i) q^{89} +(2.58925 + 2.58925i) q^{90} +(12.1466 + 12.0348i) q^{91} +1.88723i q^{92} +1.47379i q^{93} -9.58845i q^{94} +(-7.21093 - 7.21093i) q^{95} +1.00000 q^{96} +(-2.61488 + 2.61488i) q^{97} +(-4.99530 - 4.90377i) q^{98} +(3.90483 + 3.90483i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{6} + 4 q^{10} + 4 q^{14} - 4 q^{15} - 40 q^{16} + 8 q^{19} - 4 q^{21} + 24 q^{25} - 12 q^{28} + 8 q^{29} - 24 q^{31} - 12 q^{35} + 40 q^{36} - 16 q^{37} - 4 q^{40} + 16 q^{41} - 20 q^{43} + 4 q^{46}+ \cdots - 8 q^{98}+O(q^{100}) $ 40 * q - 40 * q^6 + 4 * q^10 + 4 * q^14 - 4 * q^15 - 40 * q^16 + 8 * q^19 - 4 * q^21 + 24 * q^25 - 12 * q^28 + 8 * q^29 - 24 * q^31 - 12 * q^35 + 40 * q^36 - 16 * q^37 - 4 * q^40 + 16 * q^41 - 20 * q^43 + 4 * q^46 - 16 * q^47 + 28 * q^49 + 32 * q^50 + 16 * q^53 - 24 * q^55 - 4 * q^56 - 20 * q^58 - 4 * q^60 - 44 * q^61 + 12 * q^63 - 4 * q^69 - 28 * q^70 - 52 * q^73 - 32 * q^75 + 8 * q^76 + 44 * q^77 + 4 * q^79 - 40 * q^81 - 4 * q^84 - 24 * q^85 - 12 * q^87 + 24 * q^89 + 4 * q^90 - 16 * q^95 + 40 * q^96 - 68 * q^97 - 8 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1218\mathbb{Z}\right)^\times$.

$n$	$379$	$407$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	−3.66176			−1.63759			−0.818793	−	0.574088i	$-0.805357\pi$
$5$	−3.66176			−1.63759			−0.818793	+	0.574088i	$0.805357\pi$
$6$	−1.00000			−0.408248
$7$	−1.87946	−	1.86216i	−0.710368	−	0.703830i
$7$	−1.87946	−	1.86216i	−0.710368	−	0.703830i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$			1.00000i			0.333333i
$10$	2.58925	−	2.58925i	0.818793	−	0.818793i
$11$	3.90483	−	3.90483i	1.17735	−	1.17735i	0.196934	−	0.980417i	$-0.436901\pi$
$11$	3.90483	−	3.90483i	1.17735	−	1.17735i	0.980417	−	0.196934i	$-0.0630985\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	−6.46283			−1.79247			−0.896234	−	0.443582i	$-0.853707\pi$
$13$	−6.46283			−1.79247			−0.896234	+	0.443582i	$0.853707\pi$
$14$	2.64572	−	0.0122313i	0.707099	−	0.00326895i
$15$	−2.58925	−	2.58925i	−0.668542	−	0.668542i
$16$	−1.00000			−0.250000
$17$	3.63679	+	3.63679i	0.882050	+	0.882050i	0.993743	−	0.111693i	$-0.0356272\pi$
$17$	3.63679	+	3.63679i	0.882050	+	0.882050i	−0.111693	+	0.993743i	$0.535627\pi$
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	1.96925	+	1.96925i	0.451778	+	0.451778i	0.895944	−	0.444167i	$-0.146500\pi$
$19$	1.96925	+	1.96925i	0.451778	+	0.451778i	−0.444167	+	0.895944i	$0.646500\pi$
$20$			3.66176i			0.818793i
$21$	−0.0122313	−	2.64572i	−0.00266909	−	0.577344i
$22$			5.52226i			1.17735i
$23$	−1.88723			−0.393515			−0.196757	−	0.980452i	$-0.563041\pi$
$23$	−1.88723			−0.393515			−0.196757	+	0.980452i	$0.563041\pi$
$24$			1.00000i			0.204124i
$25$	8.40845			1.68169
$26$	4.56991	−	4.56991i	0.896234	−	0.896234i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−1.86216	+	1.87946i	−0.351915	+	0.355184i
$29$	4.00171	+	3.60365i	0.743099	+	0.669181i
$29$	4.00171	+	3.60365i	0.743099	+	0.669181i
$30$	3.66176			0.668542
$31$	1.04212	+	1.04212i	0.187171	+	0.187171i	0.794472	−	0.607301i	$-0.207748\pi$
$31$	1.04212	+	1.04212i	0.187171	+	0.187171i	−0.607301	+	0.794472i	$0.707748\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	5.52226			0.961303
$34$	−5.14319			−0.882050
$35$	6.88211	+	6.81877i	1.16329	+	1.15258i
$36$	1.00000			0.166667
$37$	1.02071	+	1.02071i	0.167804	+	0.167804i	0.786014	−	0.618209i	$-0.212142\pi$
$37$	1.02071	+	1.02071i	0.167804	+	0.167804i	−0.618209	+	0.786014i	$0.712142\pi$
$38$	−2.78495			−0.451778
$39$	−4.56991	−	4.56991i	−0.731772	−	0.731772i
$40$	−2.58925	−	2.58925i	−0.409397	−	0.409397i
$41$	7.51360	−	7.51360i	1.17343	−	1.17343i	0.192040	−	0.981387i	$-0.438490\pi$
$41$	7.51360	−	7.51360i	1.17343	−	1.17343i	0.981387	−	0.192040i	$-0.0615104\pi$
$42$	1.87946	+	1.86216i	0.290007	+	0.287338i
$43$	−6.36372	+	6.36372i	−0.970459	+	0.970459i	−0.999576	−	0.0291172i	$-0.990730\pi$
$43$	−6.36372	+	6.36372i	−0.970459	+	0.970459i	0.0291172	+	0.999576i	$0.490730\pi$
$44$	−3.90483	−	3.90483i	−0.588675	−	0.588675i
$45$		−	3.66176i		−	0.545862i
$46$	1.33447	−	1.33447i	0.196757	−	0.196757i
$47$	−6.78006	+	6.78006i	−0.988973	+	0.988973i	−0.999940	−	0.0109665i	$-0.996509\pi$
$47$	−6.78006	+	6.78006i	−0.988973	+	0.988973i	0.0109665	+	0.999940i	$0.496509\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$	0.0647212	+	6.99970i	0.00924588	+	0.999957i
$50$	−5.94568	+	5.94568i	−0.840845	+	0.840845i
$51$			5.14319i			0.720191i
$52$			6.46283i			0.896234i
$53$	13.5738			1.86451			0.932254	−	0.361805i	$-0.117839\pi$
$53$	13.5738			1.86451			0.932254	+	0.361805i	$0.117839\pi$
$54$		−	1.00000i		−	0.136083i
$55$	−14.2985	+	14.2985i	−1.92801	+	1.92801i
$56$	−0.0122313	−	2.64572i	−0.00163447	−	0.353550i
$57$			2.78495i			0.368875i
$58$	−5.37780	+	0.281472i	−0.706140	+	0.0369591i
$59$			2.64616i			0.344500i	0.985053	+	0.172250i	$0.0551037\pi$
$59$			2.64616i			0.344500i	−0.985053	+	0.172250i	$0.944896\pi$
$60$	−2.58925	+	2.58925i	−0.334271	+	0.334271i
$61$	8.08912	+	8.08912i	1.03571	+	1.03571i	0.999338	+	0.0363672i	$0.0115786\pi$
$61$	8.08912	+	8.08912i	1.03571	+	1.03571i	0.0363672	+	0.999338i	$0.488421\pi$
$62$	−1.47379			−0.187171
$63$	1.86216	−	1.87946i	0.234610	−	0.236789i
$64$			1.00000i			0.125000i
$65$	23.6653			2.93532
$66$	−3.90483	+	3.90483i	−0.480651	+	0.480651i
$67$		−	0.980797i		−	0.119823i	−0.998204	−	0.0599117i	$-0.980918\pi$
$67$		−	0.980797i		−	0.119823i	0.998204	−	0.0599117i	$-0.0190819\pi$
$68$	3.63679	−	3.63679i	0.441025	−	0.441025i
$69$	−1.33447	−	1.33447i	−0.160652	−	0.160652i
$70$	−9.68799	+	0.0447880i	−1.15794	+	0.00535319i
$71$		−	1.68936i		−	0.200491i	−0.994963	−	0.100245i	$-0.968037\pi$
$71$		−	1.68936i		−	0.200491i	0.994963	−	0.100245i	$-0.0319628\pi$
$72$	−0.707107	+	0.707107i	−0.0833333	+	0.0833333i
$73$	−8.58204	+	8.58204i	−1.00445	+	1.00445i	−0.00446173	+	0.999990i	$0.501420\pi$
$73$	−8.58204	+	8.58204i	−1.00445	+	1.00445i	−0.999990	+	0.00446173i	$0.998580\pi$
$74$	−1.44351			−0.167804
$75$	5.94568	+	5.94568i	0.686547	+	0.686547i
$76$	1.96925	−	1.96925i	0.225889	−	0.225889i
$77$	−14.6104	+	0.0675444i	−1.66501	+	0.00769740i
$78$	6.46283			0.731772
$79$	5.39398	−	5.39398i	0.606870	−	0.606870i	−0.335257	−	0.942127i	$-0.608823\pi$
$79$	5.39398	−	5.39398i	0.606870	−	0.606870i	0.942127	+	0.335257i	$0.108823\pi$
$80$	3.66176			0.409397
$81$	−1.00000			−0.111111
$82$			10.6258i			1.17343i
$83$		−	4.30382i		−	0.472405i	−0.971704	−	0.236203i	$-0.924097\pi$
$83$		−	4.30382i		−	0.472405i	0.971704	−	0.236203i	$-0.0759029\pi$
$84$	−2.64572	+	0.0122313i	−0.288672	+	0.00133454i
$85$	−13.3170	−	13.3170i	−1.44443	−	1.44443i
$86$		−	8.99966i		−	0.970459i
$87$	0.281472	+	5.37780i	0.0301770	+	0.576561i
$88$	5.52226			0.588675
$89$	−4.97318	−	4.97318i	−0.527156	−	0.527156i	0.392567	−	0.919723i	$-0.371587\pi$
$89$	−4.97318	−	4.97318i	−0.527156	−	0.527156i	−0.919723	+	0.392567i	$0.871587\pi$
$90$	2.58925	+	2.58925i	0.272931	+	0.272931i
$91$	12.1466	+	12.0348i	1.27331	+	1.26159i
$92$			1.88723i			0.196757i
$93$			1.47379i			0.152825i
$94$		−	9.58845i		−	0.988973i
$95$	−7.21093	−	7.21093i	−0.739825	−	0.739825i
$96$	1.00000			0.102062
$97$	−2.61488	+	2.61488i	−0.265501	+	0.265501i	−0.827284	−	0.561784i	$-0.810115\pi$
$97$	−2.61488	+	2.61488i	−0.265501	+	0.265501i	0.561784	+	0.827284i	$0.310115\pi$
$98$	−4.99530	−	4.90377i	−0.504602	−	0.495356i
$99$	3.90483	+	3.90483i	0.392450	+	0.392450i
$100$		−	8.40845i		−	0.840845i
$101$	6.54466	+	6.54466i	0.651218	+	0.651218i	0.953286	−	0.302068i	$-0.0976770\pi$
$101$	6.54466	+	6.54466i	0.651218	+	0.651218i	−0.302068	+	0.953286i	$0.597677\pi$
$102$	−3.63679	−	3.63679i	−0.360095	−	0.360095i
$103$		−	12.8805i		−	1.26916i	−0.772858	−	0.634579i	$-0.781174\pi$
$103$		−	12.8805i		−	1.26916i	0.772858	−	0.634579i	$-0.218826\pi$
$104$	−4.56991	−	4.56991i	−0.448117	−	0.448117i
$105$	0.0447880	+	9.68799i	0.00437086	+	0.945451i
$106$	−9.59814	+	9.59814i	−0.932254	+	0.932254i
$107$	11.5173			1.11342			0.556708	−	0.830708i	$-0.312064\pi$
$107$	11.5173			1.11342			0.556708	+	0.830708i	$0.312064\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$			0.398380i			0.0381579i	0.999818	+	0.0190789i	$0.00607339\pi$
$109$			0.398380i			0.0381579i	−0.999818	+	0.0190789i	$0.993927\pi$
$110$		−	20.2212i		−	1.92801i
$111$			1.44351i			0.137012i
$112$	1.87946	+	1.86216i	0.177592	+	0.175958i
$113$	12.8169	+	12.8169i	1.20571	+	1.20571i	0.972402	+	0.233313i	$0.0749568\pi$
$113$	12.8169	+	12.8169i	1.20571	+	1.20571i	0.233313	+	0.972402i	$0.425043\pi$
$114$	−1.96925	−	1.96925i	−0.184437	−	0.184437i
$115$	6.91058			0.644415
$116$	3.60365	−	4.00171i	0.334591	−	0.371550i
$117$		−	6.46283i		−	0.597489i
$118$	−1.87111	−	1.87111i	−0.172250	−	0.172250i
$119$	−0.0629078	−	13.6075i	−0.00576675	−	1.24739i
$120$		−	3.66176i		−	0.334271i
$121$		−	19.4954i		−	1.77231i
$122$	−11.4397			−1.03571
$123$	10.6258			0.958099
$124$	1.04212	−	1.04212i	0.0935856	−	0.0935856i
$125$	−12.4809			−1.11633
$126$	0.0122313	+	2.64572i	0.00108965	+	0.235700i
$127$	1.37247	−	1.37247i	0.121787	−	0.121787i	−0.643587	−	0.765373i	$-0.722554\pi$
$127$	1.37247	−	1.37247i	0.121787	−	0.121787i	0.765373	+	0.643587i	$0.222554\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−8.99966			−0.792376
$130$	−16.7339	+	16.7339i	−1.46766	+	1.46766i
$131$	0.645117	−	0.645117i	0.0563642	−	0.0563642i	−0.678363	−	0.734727i	$-0.737310\pi$
$131$	0.645117	−	0.645117i	0.0563642	−	0.0563642i	0.734727	+	0.678363i	$0.237310\pi$
$132$		−	5.52226i		−	0.480651i
$133$	−0.0340635	−	7.36819i	−0.00295368	−	0.638903i
$134$	0.693528	+	0.693528i	0.0599117	+	0.0599117i
$135$	2.58925	−	2.58925i	0.222847	−	0.222847i
$136$			5.14319i			0.441025i
$137$	−7.67530	+	7.67530i	−0.655745	+	0.655745i	−0.954371	−	0.298625i	$-0.903472\pi$
$137$	−7.67530	+	7.67530i	−0.655745	+	0.655745i	0.298625	+	0.954371i	$0.403472\pi$
$138$	1.88723			0.160652
$139$			5.20671i			0.441627i	0.975316	+	0.220814i	$0.0708712\pi$
$139$			5.20671i			0.441627i	−0.975316	+	0.220814i	$0.929129\pi$
$140$	6.81877	−	6.88211i	0.576292	−	0.581645i
$141$	−9.58845			−0.807493
$142$	1.19456	+	1.19456i	0.100245	+	0.100245i
$143$	−25.2363	+	25.2363i	−2.11036	+	2.11036i
$144$		−	1.00000i		−	0.0833333i
$145$	−14.6533	−	13.1957i	−1.21689	−	1.09584i
$146$		−	12.1368i		−	1.00445i
$147$	−4.90377	+	4.99530i	−0.404456	+	0.412005i
$148$	1.02071	−	1.02071i	0.0839021	−	0.0839021i
$149$			13.6021i			1.11432i	0.830404	+	0.557162i	$0.188110\pi$
$149$			13.6021i			1.11432i	−0.830404	+	0.557162i	$0.811890\pi$
$150$	−8.40845			−0.686547
$151$		−	13.6357i		−	1.10965i	−0.831965	−	0.554827i	$-0.812784\pi$
$151$		−	13.6357i		−	1.10965i	0.831965	−	0.554827i	$-0.187216\pi$
$152$			2.78495i			0.225889i
$153$	−3.63679	+	3.63679i	−0.294017	+	0.294017i
$154$	10.2833	−	10.3789i	0.828655	−	0.836353i
$155$	−3.81601	−	3.81601i	−0.306509	−	0.306509i
$156$	−4.56991	+	4.56991i	−0.365886	+	0.365886i
$157$	5.42216	−	5.42216i	0.432735	−	0.432735i	−0.456823	−	0.889558i	$-0.651013\pi$
$157$	5.42216	−	5.42216i	0.432735	−	0.432735i	0.889558	+	0.456823i	$0.151013\pi$
$158$			7.62824i			0.606870i
$159$	9.59814	+	9.59814i	0.761182	+	0.761182i
$160$	−2.58925	+	2.58925i	−0.204698	+	0.204698i
$161$	3.54697	+	3.51433i	0.279540	+	0.276968i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	3.51944	+	3.51944i	0.275664	+	0.275664i	0.831375	−	0.555712i	$-0.187554\pi$
$163$	3.51944	+	3.51944i	0.275664	+	0.275664i	−0.555712	+	0.831375i	$0.687554\pi$
$164$	−7.51360	−	7.51360i	−0.586714	−	0.586714i
$165$	−20.2212			−1.57422
$166$	3.04326	+	3.04326i	0.236203	+	0.236203i
$167$	11.0268			0.853280			0.426640	−	0.904422i	$-0.359697\pi$
$167$	11.0268			0.853280			0.426640	+	0.904422i	$0.359697\pi$
$168$	1.86216	−	1.87946i	0.143669	−	0.145003i
$169$	28.7682			2.21294
$170$	18.8331			1.44443
$171$	−1.96925	+	1.96925i	−0.150593	+	0.150593i
$172$	6.36372	+	6.36372i	0.485229	+	0.485229i
$173$	4.86418			0.369817			0.184908	−	0.982756i	$-0.440801\pi$
$173$	4.86418			0.369817			0.184908	+	0.982756i	$0.440801\pi$
$174$	−4.00171	−	3.60365i	−0.303369	−	0.273192i
$175$	−15.8033	−	15.6579i	−1.19462	−	1.18362i
$176$	−3.90483	+	3.90483i	−0.294338	+	0.294338i
$177$	−1.87111	+	1.87111i	−0.140642	+	0.140642i
$178$	7.03314			0.527156
$179$			12.4043i			0.927143i	0.886060	+	0.463571i	$0.153432\pi$
$179$			12.4043i			0.927143i	−0.886060	+	0.463571i	$0.846568\pi$
$180$	−3.66176			−0.272931
$181$			1.40839i			0.104685i	0.998629	+	0.0523424i	$0.0166687\pi$
$181$			1.40839i			0.104685i	−0.998629	+	0.0523424i	$0.983331\pi$
$182$	−17.0989	+	0.0790487i	−1.26745	+	0.00585948i
$183$			11.4397i			0.845650i
$184$	−1.33447	−	1.33447i	−0.0983787	−	0.0983787i
$185$	−3.73760	−	3.73760i	−0.274794	−	0.274794i
$186$	−1.04212	−	1.04212i	−0.0764123	−	0.0764123i
$187$	28.4021			2.07696
$188$	6.78006	+	6.78006i	0.494487	+	0.494487i
$189$	2.64572	−	0.0122313i	0.192448	−	0.000889695i
$190$	10.1978			0.739825
$191$	−9.13815	+	9.13815i	−0.661213	+	0.661213i	−0.955666	−	0.294453i	$-0.904863\pi$
$191$	−9.13815	+	9.13815i	−0.661213	+	0.661213i	0.294453	+	0.955666i	$0.404863\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	−8.81474	+	8.81474i	−0.634499	+	0.634499i	−0.949193	−	0.314694i	$-0.898098\pi$
$193$	−8.81474	+	8.81474i	−0.634499	+	0.634499i	0.314694	+	0.949193i	$0.398098\pi$
$194$		−	3.69799i		−	0.265501i
$195$	16.7339	+	16.7339i	1.19834	+	1.19834i
$196$	6.99970	−	0.0647212i	0.499979	−	0.00462294i
$197$	7.54058			0.537244			0.268622	−	0.963246i	$-0.413432\pi$
$197$	7.54058			0.537244			0.268622	+	0.963246i	$0.413432\pi$
$198$	−5.52226			−0.392450
$199$			12.9406i			0.917333i	0.888608	+	0.458667i	$0.151673\pi$
$199$			12.9406i			0.917333i	−0.888608	+	0.458667i	$0.848327\pi$
$200$	5.94568	+	5.94568i	0.420423	+	0.420423i
$201$	0.693528	−	0.693528i	0.0489177	−	0.0489177i
$202$	−9.25555			−0.651218
$203$	−0.810475	−	14.2247i	−0.0568842	−	0.998381i
$204$	5.14319			0.360095
$205$	−27.5130	+	27.5130i	−1.92159	+	1.92159i
$206$	9.10792	+	9.10792i	0.634579	+	0.634579i
$207$		−	1.88723i		−	0.131172i
$208$	6.46283			0.448117
$209$	15.3792			1.06380
$210$	−6.88211	−	6.81877i	−0.474911	−	0.470540i
$211$	−3.76259	−	3.76259i	−0.259027	−	0.259027i	0.565631	−	0.824658i	$-0.308633\pi$
$211$	−3.76259	−	3.76259i	−0.259027	−	0.259027i	−0.824658	+	0.565631i	$0.808633\pi$
$212$		−	13.5738i		−	0.932254i
$213$	1.19456	−	1.19456i	0.0818500	−	0.0818500i
$214$	−8.14394	+	8.14394i	−0.556708	+	0.556708i
$215$	23.3024	−	23.3024i	1.58921	−	1.58921i
$216$	−1.00000			−0.0680414
$217$	−0.0180263	−	3.89923i	−0.00122371	−	0.264697i
$218$	−0.281697	−	0.281697i	−0.0190789	−	0.0190789i
$219$	−12.1368			−0.820131
$220$	14.2985	+	14.2985i	0.964007	+	0.964007i
$221$	−23.5039	−	23.5039i	−1.58105	−	1.58105i
$222$	−1.02071	−	1.02071i	−0.0685058	−	0.0685058i
$223$			6.40263i			0.428752i	0.976751	+	0.214376i	$0.0687718\pi$
$223$			6.40263i			0.428752i	−0.976751	+	0.214376i	$0.931228\pi$
$224$	−2.64572	+	0.0122313i	−0.176775	+	0.000817237i
$225$			8.40845i			0.560564i
$226$	−18.1259			−1.20571
$227$		−	20.2626i		−	1.34487i	−0.740154	−	0.672437i	$-0.765247\pi$
$227$		−	20.2626i		−	1.34487i	0.740154	−	0.672437i	$-0.234753\pi$
$228$	2.78495			0.184437
$229$	−8.12556	+	8.12556i	−0.536952	+	0.536952i	−0.922632	−	0.385680i	$-0.873967\pi$
$229$	−8.12556	+	8.12556i	−0.536952	+	0.536952i	0.385680	+	0.922632i	$0.373967\pi$
$230$	−4.88652	+	4.88652i	−0.322207	+	0.322207i
$231$	−10.3789	−	10.2833i	−0.682879	−	0.676594i
$232$	0.281472	+	5.37780i	0.0184796	+	0.353070i
$233$	10.5637			0.692051			0.346026	−	0.938225i	$-0.387531\pi$
$233$	10.5637			0.692051			0.346026	+	0.938225i	$0.387531\pi$
$234$	4.56991	+	4.56991i	0.298745	+	0.298745i
$235$	24.8269	−	24.8269i	1.61953	−	1.61953i
$236$	2.64616			0.172250
$237$	7.62824			0.495507
$238$	9.66641	+	9.57745i	0.626580	+	0.620814i
$239$	−12.8622			−0.831987			−0.415994	−	0.909367i	$-0.636566\pi$
$239$	−12.8622			−0.831987			−0.415994	+	0.909367i	$0.636566\pi$
$240$	2.58925	+	2.58925i	0.167136	+	0.167136i
$241$	7.99052			0.514715			0.257357	−	0.966316i	$-0.417148\pi$
$241$	7.99052			0.514715			0.257357	+	0.966316i	$0.417148\pi$
$242$	13.7853	+	13.7853i	0.886155	+	0.886155i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	8.08912	−	8.08912i	0.517853	−	0.517853i
$245$	−0.236993	−	25.6312i	−0.0151409	−	1.63752i
$246$	−7.51360	+	7.51360i	−0.479050	+	0.479050i
$247$	−12.7270	−	12.7270i	−0.809797	−	0.809797i
$248$			1.47379i			0.0935856i
$249$	3.04326	−	3.04326i	0.192859	−	0.192859i
$250$	8.82535	−	8.82535i	0.558164	−	0.558164i
$251$	15.5773	+	15.5773i	0.983233	+	0.983233i	0.999862	−	0.0166288i	$-0.00529336\pi$
$251$	15.5773	+	15.5773i	0.983233	+	0.983233i	−0.0166288	+	0.999862i	$0.505293\pi$
$252$	−1.87946	−	1.86216i	−0.118395	−	0.117305i
$253$	−7.36932	+	7.36932i	−0.463305	+	0.463305i
$254$			1.94096i			0.121787i
$255$		−	18.8331i		−	1.17938i
$256$	1.00000			0.0625000
$257$			2.42032i			0.150976i	0.997147	+	0.0754878i	$0.0240514\pi$
$257$			2.42032i			0.150976i	−0.997147	+	0.0754878i	$0.975949\pi$
$258$	6.36372	−	6.36372i	0.396188	−	0.396188i
$259$	−0.0176559	−	3.81912i	−0.00109709	−	0.237308i
$260$		−	23.6653i		−	1.46766i
$261$	−3.60365	+	4.00171i	−0.223060	+	0.247700i
$262$			0.912334i			0.0563642i
$263$	5.73007	−	5.73007i	0.353331	−	0.353331i	−0.508016	−	0.861347i	$-0.669621\pi$
$263$	5.73007	−	5.73007i	0.353331	−	0.353331i	0.861347	+	0.508016i	$0.169621\pi$
$264$	3.90483	+	3.90483i	0.240326	+	0.240326i
$265$	−49.7040			−3.05329
$266$	5.23419	+	5.18601i	0.320929	+	0.317975i
$267$		−	7.03314i		−	0.430421i
$268$	−0.980797			−0.0599117
$269$	11.0738	−	11.0738i	0.675179	−	0.675179i	−0.283726	−	0.958905i	$-0.591571\pi$
$269$	11.0738	−	11.0738i	0.675179	−	0.675179i	0.958905	+	0.283726i	$0.0915708\pi$
$270$			3.66176i			0.222847i
$271$	18.4815	−	18.4815i	1.12267	−	1.12267i	0.131333	−	0.991338i	$-0.458074\pi$
$271$	18.4815	−	18.4815i	1.12267	−	1.12267i	0.991338	−	0.131333i	$-0.0419258\pi$
$272$	−3.63679	−	3.63679i	−0.220513	−	0.220513i
$273$	0.0790487	+	17.0989i	0.00478425	+	1.03487i
$274$		−	10.8545i		−	0.655745i
$275$	32.8336	−	32.8336i	1.97994	−	1.97994i
$276$	−1.33447	+	1.33447i	−0.0803259	+	0.0803259i
$277$	−12.3020			−0.739158			−0.369579	−	0.929199i	$-0.620498\pi$
$277$	−12.3020			−0.739158			−0.369579	+	0.929199i	$0.620498\pi$
$278$	−3.68170	−	3.68170i	−0.220814	−	0.220814i
$279$	−1.04212	+	1.04212i	−0.0623904	+	0.0623904i
$280$	0.0447880	+	9.68799i	0.00267659	+	0.578968i
$281$	−16.8666			−1.00618			−0.503088	−	0.864235i	$-0.667803\pi$
$281$	−16.8666			−1.00618			−0.503088	+	0.864235i	$0.667803\pi$
$282$	6.78006	−	6.78006i	0.403747	−	0.403747i
$283$	0.823083			0.0489272			0.0244636	−	0.999701i	$-0.492212\pi$
$283$	0.823083			0.0489272			0.0244636	+	0.999701i	$0.492212\pi$
$284$	−1.68936			−0.100245
$285$		−	10.1978i		−	0.604065i
$286$		−	35.6895i		−	2.11036i
$287$	−28.1130	+	0.129968i	−1.65946	+	0.00767175i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$			9.45242i			0.556025i
$290$	19.6922	−	1.03068i	1.15637	−	0.0605238i
$291$	−3.69799			−0.216780
$292$	8.58204	+	8.58204i	0.502226	+	0.502226i
$293$	1.91754	+	1.91754i	0.112024	+	0.112024i	0.760897	−	0.648873i	$-0.224759\pi$
$293$	1.91754	+	1.91754i	0.112024	+	0.112024i	−0.648873	+	0.760897i	$0.724759\pi$
$294$	−0.0647212	−	6.99970i	−0.00377462	−	0.408231i
$295$		−	9.68958i		−	0.564149i
$296$			1.44351i			0.0839021i
$297$			5.52226i			0.320434i
$298$	−9.61811	−	9.61811i	−0.557162	−	0.557162i
$299$	12.1969			0.705363
$300$	5.94568	−	5.94568i	0.343274	−	0.343274i
$301$	23.8106	−	0.110077i	1.37242	−	0.00634476i
$302$	9.64187	+	9.64187i	0.554827	+	0.554827i
$303$			9.25555i			0.531718i
$304$	−1.96925	−	1.96925i	−0.112944	−	0.112944i
$305$	−29.6204	−	29.6204i	−1.69606	−	1.69606i
$306$		−	5.14319i		−	0.294017i
$307$	−12.6975	−	12.6975i	−0.724687	−	0.724687i	0.244869	−	0.969556i	$-0.421255\pi$
$307$	−12.6975	−	12.6975i	−0.724687	−	0.724687i	−0.969556	+	0.244869i	$0.921255\pi$
$308$	0.0675444	+	14.6104i	0.00384870	+	0.832504i
$309$	9.10792	−	9.10792i	0.518131	−	0.518131i
$310$	5.39665			0.306509
$311$	−24.6439	−	24.6439i	−1.39743	−	1.39743i	−0.807336	−	0.590092i	$-0.799092\pi$
$311$	−24.6439	−	24.6439i	−1.39743	−	1.39743i	−0.590092	−	0.807336i	$-0.700908\pi$
$312$		−	6.46283i		−	0.365886i
$313$		−	9.32874i		−	0.527291i	−0.964620	−	0.263646i	$-0.915075\pi$
$313$		−	9.32874i		−	0.527291i	0.964620	−	0.263646i	$-0.0849250\pi$
$314$			7.66809i			0.432735i
$315$	−6.81877	+	6.88211i	−0.384194	+	0.387763i
$316$	−5.39398	−	5.39398i	−0.303435	−	0.303435i
$317$	0.738414	+	0.738414i	0.0414735	+	0.0414735i	0.727539	−	0.686066i	$-0.240664\pi$
$317$	0.738414	+	0.738414i	0.0414735	+	0.0414735i	−0.686066	+	0.727539i	$0.740664\pi$
$318$	−13.5738			−0.761182
$319$	29.6977	−	1.55436i	1.66275	−	0.0870277i
$320$		−	3.66176i		−	0.204698i
$321$	8.14394	+	8.14394i	0.454550	+	0.454550i
$322$	−4.99309	+	0.0230833i	−0.278254	+	0.00128638i
$323$			14.3235i			0.796981i
$324$			1.00000i			0.0555556i
$325$	−54.3424			−3.01438
$326$	−4.97724			−0.275664
$327$	−0.281697	+	0.281697i	−0.0155779	+	0.0155779i
$328$	10.6258			0.586714
$329$	25.3684	−	0.117279i	1.39860	−	0.00646581i
$330$	14.2985	−	14.2985i	0.787109	−	0.787109i
$331$	11.5342	+	11.5342i	0.633976	+	0.633976i	0.949063	−	0.315087i	$-0.102034\pi$
$331$	11.5342	+	11.5342i	0.633976	+	0.633976i	−0.315087	+	0.949063i	$0.602034\pi$
$332$	−4.30382			−0.236203
$333$	−1.02071	+	1.02071i	−0.0559347	+	0.0559347i
$334$	−7.79713	+	7.79713i	−0.426640	+	0.426640i
$335$			3.59144i			0.196221i
$336$	0.0122313	+	2.64572i	0.000667271	+	0.144336i
$337$	−19.6526	−	19.6526i	−1.07055	−	1.07055i	−0.997315	−	0.0732328i	$-0.976668\pi$
$337$	−19.6526	−	19.6526i	−1.07055	−	1.07055i	−0.0732328	−	0.997315i	$-0.523332\pi$
$338$	−20.3422	+	20.3422i	−1.10647	+	1.10647i
$339$			18.1259i			0.984462i
$340$	−13.3170	+	13.3170i	−0.722217	+	0.722217i
$341$	8.13864			0.440732
$342$		−	2.78495i		−	0.150593i
$343$	12.9129	−	13.2762i	0.697232	−	0.716845i
$344$	−8.99966			−0.485229
$345$	4.88652	+	4.88652i	0.263081	+	0.263081i
$346$	−3.43950	+	3.43950i	−0.184908	+	0.184908i
$347$			29.5102i			1.58419i	0.610398	+	0.792095i	$0.291009\pi$
$347$			29.5102i			1.58419i	−0.610398	+	0.792095i	$0.708991\pi$
$348$	5.37780	−	0.281472i	0.288281	−	0.0150885i
$349$			19.8941i			1.06491i	0.846459	+	0.532453i	$0.178730\pi$
$349$			19.8941i			1.06491i	−0.846459	+	0.532453i	$0.821270\pi$
$350$	22.2464	−	0.102846i	1.18912	−	0.00549736i
$351$	4.56991	−	4.56991i	0.243924	−	0.243924i
$352$		−	5.52226i		−	0.294338i
$353$	18.1648			0.966814			0.483407	−	0.875396i	$-0.339399\pi$
$353$	18.1648			0.966814			0.483407	+	0.875396i	$0.339399\pi$
$354$		−	2.64616i		−	0.140642i
$355$			6.18604i			0.328321i
$356$	−4.97318	+	4.97318i	−0.263578	+	0.263578i
$357$	9.57745	−	9.66641i	0.506892	−	0.511601i
$358$	−8.77118	−	8.77118i	−0.463571	−	0.463571i
$359$	−18.3421	+	18.3421i	−0.968061	+	0.968061i	−0.999506	−	0.0314440i	$-0.989989\pi$
$359$	−18.3421	+	18.3421i	−0.968061	+	0.968061i	0.0314440	+	0.999506i	$0.489989\pi$
$360$	2.58925	−	2.58925i	0.136466	−	0.136466i
$361$		−	11.2441i		−	0.591794i
$362$	−0.995883	−	0.995883i	−0.0523424	−	0.0523424i
$363$	13.7853	−	13.7853i	0.723543	−	0.723543i
$364$	12.0348	−	12.1466i	0.630796	−	0.636656i
$365$	31.4253	−	31.4253i	1.64488	−	1.64488i
$366$	−8.08912	−	8.08912i	−0.422825	−	0.422825i
$367$	17.4424	+	17.4424i	0.910485	+	0.910485i	0.996310	−	0.0858248i	$-0.0273525\pi$
$367$	17.4424	+	17.4424i	0.910485	+	0.910485i	−0.0858248	+	0.996310i	$0.527353\pi$
$368$	1.88723			0.0983787
$369$	7.51360	+	7.51360i	0.391142	+	0.391142i
$370$	5.28577			0.274794
$371$	−25.5114	−	25.2766i	−1.32449	−	1.31230i
$372$	1.47379			0.0764123
$373$	−13.5522			−0.701706			−0.350853	−	0.936431i	$-0.614108\pi$
$373$	−13.5522			−0.701706			−0.350853	+	0.936431i	$0.614108\pi$
$374$	−20.0833	+	20.0833i	−1.03848	+	1.03848i
$375$	−8.82535	−	8.82535i	−0.455739	−	0.455739i
$376$	−9.58845			−0.494487
$377$	−25.8624	−	23.2898i	−1.33198	−	1.19949i
$378$	−1.86216	+	1.87946i	−0.0957792	+	0.0966689i
$379$	−10.7796	+	10.7796i	−0.553713	+	0.553713i	−0.927510	−	0.373797i	$-0.878056\pi$
$379$	−10.7796	+	10.7796i	−0.553713	+	0.553713i	0.373797	+	0.927510i	$0.378056\pi$
$380$	−7.21093	+	7.21093i	−0.369913	+	0.369913i
$381$	1.94096			0.0994383
$382$		−	12.9233i		−	0.661213i
$383$	12.0093			0.613646			0.306823	−	0.951767i	$-0.400734\pi$
$383$	12.0093			0.613646			0.306823	+	0.951767i	$0.400734\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	53.4997	−	0.247331i	2.72659	−	0.0126052i
$386$		−	12.4659i		−	0.634499i
$387$	−6.36372	−	6.36372i	−0.323486	−	0.323486i
$388$	2.61488	+	2.61488i	0.132750	+	0.132750i
$389$	15.9811	+	15.9811i	0.810276	+	0.810276i	0.984675	−	0.174399i	$-0.0557982\pi$
$389$	15.9811	+	15.9811i	0.810276	+	0.810276i	−0.174399	+	0.984675i	$0.555798\pi$
$390$	−23.6653			−1.19834
$391$	−6.86346	−	6.86346i	−0.347100	−	0.347100i
$392$	−4.90377	+	4.99530i	−0.247678	+	0.252301i
$393$	0.912334			0.0460212
$394$	−5.33199	+	5.33199i	−0.268622	+	0.268622i
$395$	−19.7514	+	19.7514i	−0.993802	+	0.993802i
$396$	3.90483	−	3.90483i	0.196225	−	0.196225i
$397$		−	26.9841i		−	1.35430i	−0.735847	−	0.677148i	$-0.763216\pi$
$397$		−	26.9841i		−	1.35430i	0.735847	−	0.677148i	$-0.236784\pi$
$398$	−9.15037	−	9.15037i	−0.458667	−	0.458667i
$399$	5.18601	−	5.23419i	0.259625	−	0.262037i
$400$	−8.40845			−0.420423
$401$	−21.0602			−1.05169			−0.525847	−	0.850579i	$-0.676252\pi$
$401$	−21.0602			−1.05169			−0.525847	+	0.850579i	$0.676252\pi$
$402$			0.980797i			0.0489177i
$403$	−6.73508	−	6.73508i	−0.335498	−	0.335498i
$404$	6.54466	−	6.54466i	0.325609	−	0.325609i
$405$	3.66176			0.181954
$406$	10.6315	+	9.48532i	0.527632	+	0.470748i
$407$	7.97143			0.395129
$408$	−3.63679	+	3.63679i	−0.180048	+	0.180048i
$409$	10.6984	+	10.6984i	0.529004	+	0.529004i	0.920275	−	0.391271i	$-0.127965\pi$
$409$	10.6984	+	10.6984i	0.529004	+	0.529004i	−0.391271	+	0.920275i	$0.627965\pi$
$410$		−	38.9092i		−	1.92159i
$411$	−10.8545			−0.535414
$412$	−12.8805			−0.634579
$413$	4.92757	−	4.97334i	0.242470	−	0.244722i
$414$	1.33447	+	1.33447i	0.0655858	+	0.0655858i
$415$			15.7595i			0.773605i
$416$	−4.56991	+	4.56991i	−0.224058	+	0.224058i
$417$	−3.68170	+	3.68170i	−0.180294	+	0.180294i
$418$	−10.8747	+	10.8747i	−0.531901	+	0.531901i
$419$	12.9812			0.634174			0.317087	−	0.948397i	$-0.397295\pi$
$419$	12.9812			0.634174			0.317087	+	0.948397i	$0.397295\pi$
$420$	9.68799	−	0.0447880i	0.472726	−	0.00218543i
$421$	13.6916	+	13.6916i	0.667289	+	0.667289i	0.957088	−	0.289798i	$-0.0935883\pi$
$421$	13.6916	+	13.6916i	0.667289	+	0.667289i	−0.289798	+	0.957088i	$0.593588\pi$
$422$	5.32111			0.259027
$423$	−6.78006	−	6.78006i	−0.329658	−	0.329658i
$424$	9.59814	+	9.59814i	0.466127	+	0.466127i
$425$	30.5797	+	30.5797i	1.48334	+	1.48334i
$426$			1.68936i			0.0818500i
$427$	−0.139923	−	30.2664i	−0.00677134	−	1.46469i
$428$		−	11.5173i		−	0.556708i
$429$	−35.6895			−1.72310
$430$			32.9546i			1.58921i
$431$	30.1597			1.45274			0.726371	−	0.687303i	$-0.241205\pi$
$431$	30.1597			1.45274			0.726371	+	0.687303i	$0.241205\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	−13.1359	+	13.1359i	−0.631272	+	0.631272i	−0.948387	−	0.317115i	$-0.897286\pi$
$433$	−13.1359	+	13.1359i	−0.631272	+	0.631272i	0.317115	+	0.948387i	$0.397286\pi$
$434$	2.76992	+	2.74443i	0.132960	+	0.131737i
$435$	−1.03068	−	19.6922i	−0.0494174	−	0.944169i
$436$	0.398380			0.0190789
$437$	−3.71644	−	3.71644i	−0.177781	−	0.177781i
$438$	8.58204	−	8.58204i	0.410066	−	0.410066i
$439$	28.2963			1.35051			0.675254	−	0.737585i	$-0.264034\pi$
$439$	28.2963			1.35051			0.675254	+	0.737585i	$0.264034\pi$
$440$	−20.2212			−0.964007
$441$	−6.99970	+	0.0647212i	−0.333319	+	0.00308196i
$442$	33.2396			1.58105
$443$	−4.43660	−	4.43660i	−0.210789	−	0.210789i	0.593814	−	0.804603i	$-0.297622\pi$
$443$	−4.43660	−	4.43660i	−0.210789	−	0.210789i	−0.804603	+	0.593814i	$0.797622\pi$
$444$	1.44351			0.0685058
$445$	18.2106	+	18.2106i	0.863264	+	0.863264i
$446$	−4.52734	−	4.52734i	−0.214376	−	0.214376i
$447$	−9.61811	+	9.61811i	−0.454921	+	0.454921i
$448$	1.86216	−	1.87946i	0.0879788	−	0.0887960i
$449$	11.9891	−	11.9891i	0.565801	−	0.565801i	−0.365149	−	0.930949i	$-0.618982\pi$
$449$	11.9891	−	11.9891i	0.565801	−	0.565801i	0.930949	+	0.365149i	$0.118982\pi$
$450$	−5.94568	−	5.94568i	−0.280282	−	0.280282i
$451$		−	58.6787i		−	2.76307i
$452$	12.8169	−	12.8169i	0.602857	−	0.602857i
$453$	9.64187	−	9.64187i	0.453015	−	0.453015i
$454$	14.3278	+	14.3278i	0.672437	+	0.672437i
$455$	−44.4779	−	44.0686i	−2.08516	−	2.06597i
$456$	−1.96925	+	1.96925i	−0.0922187	+	0.0922187i
$457$			13.8990i			0.650168i	0.945685	+	0.325084i	$0.105393\pi$
$457$			13.8990i			0.650168i	−0.945685	+	0.325084i	$0.894607\pi$
$458$		−	11.4913i		−	0.536952i
$459$	−5.14319			−0.240064
$460$		−	6.91058i		−	0.322207i
$461$	−17.3861	+	17.3861i	−0.809751	+	0.809751i	−0.984596	−	0.174845i	$-0.944058\pi$
$461$	−17.3861	+	17.3861i	−0.809751	+	0.809751i	0.174845	+	0.984596i	$0.444058\pi$
$462$	14.6104	−	0.0675444i	0.679737	−	0.00314245i
$463$		−	27.2623i		−	1.26699i	−0.773747	−	0.633494i	$-0.781620\pi$
$463$		−	27.2623i		−	1.26699i	0.773747	−	0.633494i	$-0.218380\pi$
$464$	−4.00171	−	3.60365i	−0.185775	−	0.167295i
$465$		−	5.39665i		−	0.250264i
$466$	−7.46967	+	7.46967i	−0.346026	+	0.346026i
$467$	−14.2999	−	14.2999i	−0.661721	−	0.661721i	0.294065	−	0.955785i	$-0.404992\pi$
$467$	−14.2999	−	14.2999i	−0.661721	−	0.661721i	−0.955785	+	0.294065i	$0.904992\pi$
$468$	−6.46283			−0.298745
$469$	−1.82640	+	1.84337i	−0.0843354	+	0.0851188i
$470$			35.1106i			1.61953i
$471$	7.66809			0.353327
$472$	−1.87111	+	1.87111i	−0.0861250	+	0.0861250i
$473$			49.6985i			2.28514i
$474$	−5.39398	+	5.39398i	−0.247754	+	0.247754i
$475$	16.5584	+	16.5584i	0.759751	+	0.759751i
$476$	−13.6075	+	0.0629078i	−0.623697	+	0.00288338i
$477$			13.5738i			0.621503i
$478$	9.09496	−	9.09496i	0.415994	−	0.415994i
$479$	1.70045	−	1.70045i	0.0776955	−	0.0776955i	−0.667191	−	0.744887i	$-0.732504\pi$
$479$	1.70045	−	1.70045i	0.0776955	−	0.0776955i	0.744887	+	0.667191i	$0.232504\pi$
$480$	−3.66176			−0.167136
$481$	−6.59670	−	6.59670i	−0.300784	−	0.300784i
$482$	−5.65015	+	5.65015i	−0.257357	+	0.257357i
$483$	0.0230833	+	4.99309i	0.00105032	+	0.227194i
$484$	−19.4954			−0.886155
$485$	9.57504	−	9.57504i	0.434780	−	0.434780i
$486$	1.00000			0.0453609
$487$	−4.57867			−0.207479			−0.103740	−	0.994604i	$-0.533081\pi$
$487$	−4.57867			−0.207479			−0.103740	+	0.994604i	$0.533081\pi$
$488$			11.4397i			0.517853i
$489$			4.97724i			0.225078i
$490$	18.2916	+	17.9564i	0.826329	+	0.811188i
$491$	−16.4436	−	16.4436i	−0.742088	−	0.742088i	0.230892	−	0.972979i	$-0.425836\pi$
$491$	−16.4436	−	16.4436i	−0.742088	−	0.742088i	−0.972979	+	0.230892i	$0.925836\pi$
$492$		−	10.6258i		−	0.479050i
$493$	1.44767	+	27.6591i	0.0651996	+	1.24570i
$494$	17.9986			0.809797
$495$	−14.2985	−	14.2985i	−0.642671	−	0.642671i
$496$	−1.04212	−	1.04212i	−0.0467928	−	0.0467928i
$497$	−3.14587	+	3.17509i	−0.141111	+	0.142422i
$498$			4.30382i			0.192859i
$499$			38.2226i			1.71108i	0.517739	+	0.855538i	$0.326774\pi$
$499$			38.2226i			1.71108i	−0.517739	+	0.855538i	$0.673226\pi$
$500$			12.4809i			0.558164i
$501$	7.79713	+	7.79713i	0.348350	+	0.348350i
$502$	−22.0297			−0.983233
$503$	−27.9861	+	27.9861i	−1.24784	+	1.24784i	−0.291164	+	0.956673i	$0.594042\pi$
$503$	−27.9861	+	27.9861i	−1.24784	+	1.24784i	−0.956673	+	0.291164i	$0.905958\pi$
$504$	2.64572	−	0.0122313i	0.117850	−	0.000544825i
$505$	−23.9650	−	23.9650i	−1.06643	−	1.06643i
$506$		−	10.4218i		−	0.463305i
$507$	20.3422	+	20.3422i	0.903428	+	0.903428i
$508$	−1.37247	−	1.37247i	−0.0608933	−	0.0608933i
$509$			4.21311i			0.186743i	0.995631	+	0.0933715i	$0.0297644\pi$
$509$			4.21311i			0.186743i	−0.995631	+	0.0933715i	$0.970236\pi$
$510$	13.3170	+	13.3170i	0.589688	+	0.589688i
$511$	32.1107	−	0.148449i	1.42049	−	0.00656700i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−2.78495			−0.122958
$514$	−1.71143	−	1.71143i	−0.0754878	−	0.0754878i
$515$			47.1654i			2.07836i
$516$			8.99966i			0.396188i
$517$			52.9500i			2.32874i
$518$	2.71301	+	2.68804i	0.119203	+	0.118106i
$519$	3.43950	+	3.43950i	0.150977	+	0.150977i
$520$	16.7339	+	16.7339i	0.733830	+	0.733830i
$521$	19.7679			0.866049			0.433025	−	0.901382i	$-0.357446\pi$
$521$	19.7679			0.866049			0.433025	+	0.901382i	$0.357446\pi$
$522$	−0.281472	−	5.37780i	−0.0123197	−	0.235380i
$523$			4.36118i			0.190701i	0.995444	+	0.0953506i	$0.0303972\pi$
$523$			4.36118i			0.190701i	−0.995444	+	0.0953506i	$0.969603\pi$
$524$	−0.645117	−	0.645117i	−0.0281821	−	0.0281821i
$525$	−0.102846	−	22.2464i	−0.00448858	−	0.970914i
$526$			8.10354i			0.353331i
$527$			7.57997i			0.330189i
$528$	−5.52226			−0.240326
$529$	−19.4384			−0.845146
$530$	35.1460	−	35.1460i	1.52665	−	1.52665i
$531$	−2.64616			−0.114833
$532$	−7.36819	+	0.0340635i	−0.319452	+	0.00147684i
$533$	−48.5591	+	48.5591i	−2.10333	+	2.10333i
$534$	4.97318	+	4.97318i	0.215211	+	0.215211i
$535$	−42.1734			−1.82332
$536$	0.693528	−	0.693528i	0.0299559	−	0.0299559i
$537$	−8.77118	+	8.77118i	−0.378504	+	0.378504i
$538$			15.6607i			0.675179i
$539$	27.5854	+	27.0799i	1.18819	+	1.16641i
$540$	−2.58925	−	2.58925i	−0.111424	−	0.111424i
$541$	−25.1909	+	25.1909i	−1.08304	+	1.08304i	−0.0868149	+	0.996224i	$0.527669\pi$
$541$	−25.1909	+	25.1909i	−1.08304	+	1.08304i	−0.996224	+	0.0868149i	$0.972331\pi$
$542$			26.1368i			1.12267i
$543$	−0.995883	+	0.995883i	−0.0427374	+	0.0427374i
$544$	5.14319			0.220513
$545$		−	1.45877i		−	0.0624869i
$546$	−12.1466	−	12.0348i	−0.519827	−	0.515043i
$547$	−6.31604			−0.270054			−0.135027	−	0.990842i	$-0.543112\pi$
$547$	−6.31604			−0.270054			−0.135027	+	0.990842i	$0.543112\pi$
$548$	7.67530	+	7.67530i	0.327873	+	0.327873i
$549$	−8.08912	+	8.08912i	−0.345235	+	0.345235i
$550$			46.4337i			1.97994i
$551$	0.783885	+	14.9769i	0.0333946	+	0.638037i
$552$		−	1.88723i		−	0.0803259i
$553$	−20.1822	+	0.0933032i	−0.858235	+	0.00396765i
$554$	8.69885	−	8.69885i	0.369579	−	0.369579i
$555$		−	5.28577i		−	0.224368i
$556$	5.20671			0.220814
$557$		−	25.8087i		−	1.09355i	−0.837280	−	0.546775i	$-0.815855\pi$
$557$		−	25.8087i		−	1.09355i	0.837280	−	0.546775i	$-0.184145\pi$
$558$		−	1.47379i		−	0.0623904i
$559$	41.1277	−	41.1277i	1.73952	−	1.73952i
$560$	−6.88211	−	6.81877i	−0.290822	−	0.288146i
$561$	20.0833	+	20.0833i	0.847917	+	0.847917i
$562$	11.9265	−	11.9265i	0.503088	−	0.503088i
$563$	8.88429	−	8.88429i	0.374428	−	0.374428i	−0.494659	−	0.869087i	$-0.664707\pi$
$563$	8.88429	−	8.88429i	0.374428	−	0.374428i	0.869087	+	0.494659i	$0.164707\pi$
$564$			9.58845i			0.403747i
$565$	−46.9324	−	46.9324i	−1.97446	−	1.97446i
$566$	−0.582008	+	0.582008i	−0.0244636	+	0.0244636i
$567$	1.87946	+	1.86216i	0.0789298	+	0.0782034i
$568$	1.19456	−	1.19456i	0.0501227	−	0.0501227i
$569$	−15.1220	−	15.1220i	−0.633945	−	0.633945i	0.315110	−	0.949055i	$-0.397959\pi$
$569$	−15.1220	−	15.1220i	−0.633945	−	0.633945i	−0.949055	+	0.315110i	$0.897959\pi$
$570$	7.21093	+	7.21093i	0.302032	+	0.302032i
$571$	−36.1399			−1.51241			−0.756203	−	0.654337i	$-0.772948\pi$
$571$	−36.1399			−1.51241			−0.756203	+	0.654337i	$0.772948\pi$
$572$	25.2363	+	25.2363i	1.05518	+	1.05518i
$573$	−12.9233			−0.539878
$574$	19.7870	−	19.9708i	0.825894	−	0.833565i
$575$	−15.8687			−0.661770
$576$	−1.00000			−0.0416667
$577$	19.1725	−	19.1725i	0.798163	−	0.798163i	−0.184643	−	0.982806i	$-0.559113\pi$
$577$	19.1725	−	19.1725i	0.798163	−	0.798163i	0.982806	+	0.184643i	$0.0591129\pi$
$578$	−6.68387	−	6.68387i	−0.278012	−	0.278012i
$579$	−12.4659			−0.518066
$580$	−13.1957	+	14.6533i	−0.547921	+	0.608445i
$581$	−8.01440	+	8.08884i	−0.332493	+	0.335582i
$582$	2.61488	−	2.61488i	0.108390	−	0.108390i
$583$	53.0035	−	53.0035i	2.19518	−	2.19518i
$584$	−12.1368			−0.502226
$585$			23.6653i			0.978440i
$586$	−2.71180			−0.112024
$587$		−	9.48610i		−	0.391533i	−0.980651	−	0.195767i	$-0.937281\pi$
$587$		−	9.48610i		−	0.391533i	0.980651	−	0.195767i	$-0.0627195\pi$
$588$	4.99530	+	4.90377i	0.206003	+	0.202228i
$589$			4.10442i			0.169120i
$590$	6.85157	+	6.85157i	0.282074	+	0.282074i
$591$	5.33199	+	5.33199i	0.219329	+	0.219329i
$592$	−1.02071	−	1.02071i	−0.0419511	−	0.0419511i
$593$	−4.85245			−0.199266			−0.0996331	−	0.995024i	$-0.531767\pi$
$593$	−4.85245			−0.199266			−0.0996331	+	0.995024i	$0.531767\pi$
$594$	−3.90483	−	3.90483i	−0.160217	−	0.160217i
$595$	0.230353	+	49.8272i	0.00944356	+	2.04272i
$596$	13.6021			0.557162
$597$	−9.15037	+	9.15037i	−0.374500	+	0.374500i
$598$	−8.62448	+	8.62448i	−0.352681	+	0.352681i
$599$	−25.4689	+	25.4689i	−1.04063	+	1.04063i	−0.0414918	+	0.999139i	$0.513211\pi$
$599$	−25.4689	+	25.4689i	−1.04063	+	1.04063i	−0.999139	+	0.0414918i	$0.986789\pi$
$600$			8.40845i			0.343274i
$601$	8.62472	+	8.62472i	0.351810	+	0.351810i	0.860783	−	0.508973i	$-0.169975\pi$
$601$	8.62472	+	8.62472i	0.351810	+	0.351810i	−0.508973	+	0.860783i	$0.669975\pi$
$602$	−16.7588	+	16.9145i	−0.683038	+	0.689383i
$603$	0.980797			0.0399411
$604$	−13.6357			−0.554827
$605$			71.3874i			2.90231i
$606$	−6.54466	−	6.54466i	−0.265859	−	0.265859i
$607$	−3.29419	+	3.29419i	−0.133707	+	0.133707i	−0.770793	−	0.637086i	$-0.780140\pi$
$607$	−3.29419	+	3.29419i	−0.133707	+	0.133707i	0.637086	+	0.770793i	$0.280140\pi$
$608$	2.78495			0.112944
$609$	9.48532	−	10.6315i	0.384364	−	0.430810i
$610$	41.8895			1.69606
$611$	43.8184	−	43.8184i	1.77270	−	1.77270i
$612$	3.63679	+	3.63679i	0.147008	+	0.147008i
$613$			37.9508i			1.53282i	0.642352	+	0.766410i	$0.277959\pi$
$613$			37.9508i			1.53282i	−0.642352	+	0.766410i	$0.722041\pi$
$614$	17.9570			0.724687
$615$	−38.9092			−1.56897
$616$	−10.3789	−	10.2833i	−0.418176	−	0.414328i
$617$	−14.5528	−	14.5528i	−0.585873	−	0.585873i	0.350638	−	0.936511i	$-0.385965\pi$
$617$	−14.5528	−	14.5528i	−0.585873	−	0.585873i	−0.936511	+	0.350638i	$0.885965\pi$
$618$			12.8805i			0.518131i
$619$	−17.3732	+	17.3732i	−0.698287	+	0.698287i	−0.964041	−	0.265754i	$-0.914379\pi$
$619$	−17.3732	+	17.3732i	−0.698287	+	0.698287i	0.265754	+	0.964041i	$0.414379\pi$
$620$	−3.81601	+	3.81601i	−0.153255	+	0.153255i
$621$	1.33447	−	1.33447i	0.0535506	−	0.0535506i
$622$	34.8518			1.39743
$623$	0.0860244	+	18.6077i	0.00344649	+	0.745504i
$624$	4.56991	+	4.56991i	0.182943	+	0.182943i
$625$	3.65983			0.146393
$626$	6.59641	+	6.59641i	0.263646	+	0.263646i
$627$	10.8747	+	10.8747i	0.434295	+	0.434295i
$628$	−5.42216	−	5.42216i	−0.216368	−	0.216368i
$629$			7.42423i			0.296023i
$630$	−0.0447880	−	9.68799i	−0.00178440	−	0.385979i
$631$		−	5.64254i		−	0.224626i	−0.993673	−	0.112313i	$-0.964174\pi$
$631$		−	5.64254i		−	0.224626i	0.993673	−	0.112313i	$-0.0358259\pi$
$632$	7.62824			0.303435
$633$		−	5.32111i		−	0.211495i
$634$	−1.04428			−0.0414735
$635$	−5.02563	+	5.02563i	−0.199436	+	0.199436i
$636$	9.59814	−	9.59814i	0.380591	−	0.380591i
$637$	−0.418282	−	45.2379i	−0.0165729	−	1.79239i
$638$	−19.9003	+	22.0985i	−0.787861	+	0.874889i
$639$	1.68936			0.0668302
$640$	2.58925	+	2.58925i	0.102349	+	0.102349i
$641$	11.4231	−	11.4231i	0.451185	−	0.451185i	−0.444563	−	0.895748i	$-0.646641\pi$
$641$	11.4231	−	11.4231i	0.451185	−	0.451185i	0.895748	+	0.444563i	$0.146641\pi$
$642$	−11.5173			−0.454550
$643$	10.3887			0.409690			0.204845	−	0.978794i	$-0.434331\pi$
$643$	10.3887			0.409690			0.204845	+	0.978794i	$0.434331\pi$
$644$	3.51433	−	3.54697i	0.138484	−	0.139770i
$645$	32.9546			1.29759
$646$	−10.1282	−	10.1282i	−0.398491	−	0.398491i
$647$	−22.4869			−0.884050			−0.442025	−	0.897003i	$-0.645740\pi$
$647$	−22.4869			−0.884050			−0.442025	+	0.897003i	$0.645740\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	10.3328	+	10.3328i	0.405598	+	0.405598i
$650$	38.4259	−	38.4259i	1.50719	−	1.50719i
$651$	2.74443	−	2.76992i	0.107563	−	0.108562i
$652$	3.51944	−	3.51944i	0.137832	−	0.137832i
$653$	29.7535	+	29.7535i	1.16434	+	1.16434i	0.983515	+	0.180828i	$0.0578777\pi$
$653$	29.7535	+	29.7535i	1.16434	+	1.16434i	0.180828	+	0.983515i	$0.442122\pi$
$654$		−	0.398380i		−	0.0155779i
$655$	−2.36226	+	2.36226i	−0.0923012	+	0.0923012i
$656$	−7.51360	+	7.51360i	−0.293357	+	0.293357i
$657$	−8.58204	−	8.58204i	−0.334817	−	0.334817i
$658$	−17.8552	+	18.0211i	−0.696069	+	0.702535i
$659$	−19.3051	+	19.3051i	−0.752018	+	0.752018i	−0.974856	−	0.222837i	$-0.928468\pi$
$659$	−19.3051	+	19.3051i	−0.752018	+	0.752018i	0.222837	+	0.974856i	$0.428468\pi$
$660$			20.2212i			0.787109i
$661$			6.28568i			0.244485i	0.992500	+	0.122242i	$0.0390085\pi$
$661$			6.28568i			0.244485i	−0.992500	+	0.122242i	$0.960991\pi$
$662$	−16.3118			−0.633976
$663$		−	33.2396i		−	1.29092i
$664$	3.04326	−	3.04326i	0.118101	−	0.118101i
$665$	0.124732	+	26.9805i	0.00483690	+	1.04626i
$666$		−	1.44351i		−	0.0559347i
$667$	−7.55216	−	6.80092i	−0.292421	−	0.263333i
$668$		−	11.0268i		−	0.426640i
$669$	−4.52734	+	4.52734i	−0.175037	+	0.175037i
$670$	−2.53953	−	2.53953i	−0.0981106	−	0.0981106i
$671$	63.1733			2.43878
$672$	−1.87946	−	1.86216i	−0.0725016	−	0.0718344i
$673$			15.4680i			0.596247i	0.954527	+	0.298123i	$0.0963607\pi$
$673$			15.4680i			0.596247i	−0.954527	+	0.298123i	$0.903639\pi$
$674$	27.7930			1.07055
$675$	−5.94568	+	5.94568i	−0.228849	+	0.228849i
$676$		−	28.7682i		−	1.10647i
$677$	−33.9281	+	33.9281i	−1.30396	+	1.30396i	−0.378265	+	0.925697i	$0.623479\pi$
$677$	−33.9281	+	33.9281i	−1.30396	+	1.30396i	−0.925697	+	0.378265i	$0.876521\pi$
$678$	−12.8169	−	12.8169i	−0.492231	−	0.492231i
$679$	9.78387	−	0.0452312i	0.375470	−	0.00173582i
$680$		−	18.8331i		−	0.722217i
$681$	14.3278	−	14.3278i	0.549043	−	0.549043i
$682$	−5.75489	+	5.75489i	−0.220366	+	0.220366i
$683$	25.5112			0.976159			0.488080	−	0.872799i	$-0.337698\pi$
$683$	25.5112			0.976159			0.488080	+	0.872799i	$0.337698\pi$
$684$	1.96925	+	1.96925i	0.0752963	+	0.0752963i
$685$	28.1051	−	28.1051i	1.07384	−	1.07384i
$686$	0.256850	+	18.5185i	0.00980657	+	0.707039i
$687$	−11.4913			−0.438420
$688$	6.36372	−	6.36372i	0.242615	−	0.242615i
$689$	−87.7253			−3.34207
$690$	−6.91058			−0.263081
$691$		−	1.09496i		−	0.0416543i	−0.999783	−	0.0208272i	$-0.993370\pi$
$691$		−	1.09496i		−	0.0416543i	0.999783	−	0.0208272i	$-0.00662997\pi$
$692$		−	4.86418i		−	0.184908i
$693$	−0.0675444	−	14.6104i	−0.00256580	−	0.555003i
$694$	−20.8668	−	20.8668i	−0.792095	−	0.792095i
$695$		−	19.0657i		−	0.723203i
$696$	−3.60365	+	4.00171i	−0.136596	+	0.151685i
$697$	54.6507			2.07004
$698$	−14.0673	−	14.0673i	−0.532453	−	0.532453i
$699$	7.46967	+	7.46967i	0.282529	+	0.282529i
$700$	−15.6579	+	15.8033i	−0.591812	+	0.597310i
$701$			44.4522i			1.67894i	0.543409	+	0.839468i	$0.317133\pi$
$701$			44.4522i			1.67894i	−0.543409	+	0.839468i	$0.682867\pi$
$702$			6.46283i			0.243924i
$703$			4.02009i			0.151620i
$704$	3.90483	+	3.90483i	0.147169	+	0.147169i
$705$	35.1106			1.32234
$706$	−12.8444	+	12.8444i	−0.483407	+	0.483407i
$707$	−0.113207	−	24.4876i	−0.00425760	−	0.920952i
$708$	1.87111	+	1.87111i	0.0703208	+	0.0703208i
$709$		−	20.0491i		−	0.752960i	−0.926425	−	0.376480i	$-0.877134\pi$
$709$		−	20.0491i		−	0.752960i	0.926425	−	0.376480i	$-0.122866\pi$
$710$	−4.37419	−	4.37419i	−0.164160	−	0.164160i
$711$	5.39398	+	5.39398i	0.202290	+	0.202290i
$712$		−	7.03314i		−	0.263578i
$713$	−1.96673	−	1.96673i	−0.0736547	−	0.0736547i
$714$	0.0629078	+	13.6075i	0.00235427	+	0.509246i
$715$	92.4090	−	92.4090i	3.45590	−	3.45590i
$716$	12.4043			0.463571
$717$	−9.09496	−	9.09496i	−0.339657	−	0.339657i
$718$		−	25.9397i		−	0.968061i
$719$		−	29.4268i		−	1.09744i	−0.836008	−	0.548718i	$-0.815116\pi$
$719$		−	29.4268i		−	1.09744i	0.836008	−	0.548718i	$-0.184884\pi$
$720$			3.66176i			0.136466i
$721$	−23.9856	+	24.2084i	−0.893272	+	0.901569i
$722$	7.95077	+	7.95077i	0.295897	+	0.295897i
$723$	5.65015	+	5.65015i	0.210131	+	0.210131i
$724$	1.40839			0.0523424
$725$	33.6482	+	30.3011i	1.24966	+	1.12536i
$726$			19.4954i			0.723543i
$727$	6.03361	+	6.03361i	0.223774	+	0.223774i	0.810086	−	0.586311i	$-0.199421\pi$
$727$	6.03361	+	6.03361i	0.223774	+	0.223774i	−0.586311	+	0.810086i	$0.699421\pi$
$728$	0.0790487	+	17.0989i	0.00292974	+	0.633726i
$729$		−	1.00000i		−	0.0370370i
$730$			44.4421i			1.64488i
$731$	−46.2870			−1.71199
$732$	11.4397			0.422825
$733$	−17.9835	+	17.9835i	−0.664236	+	0.664236i	−0.956376	−	0.292139i	$-0.905633\pi$
$733$	−17.9835	+	17.9835i	−0.664236	+	0.664236i	0.292139	+	0.956376i	$0.405633\pi$
$734$	−24.6673			−0.910485
$735$	17.9564	−	18.2916i	0.662332	−	0.674695i
$736$	−1.33447	+	1.33447i	−0.0491894	+	0.0491894i
$737$	−3.82985	−	3.82985i	−0.141074	−	0.141074i
$738$	−10.6258			−0.391142
$739$	33.1122	−	33.1122i	1.21805	−	1.21805i	0.249736	−	0.968314i	$-0.419656\pi$
$739$	33.1122	−	33.1122i	1.21805	−	1.21805i	0.968314	−	0.249736i	$-0.0803439\pi$
$740$	−3.73760	+	3.73760i	−0.137397	+	0.137397i
$741$		−	17.9986i		−	0.661196i
$742$	35.9126	−	0.166025i	1.31839	−	0.00609498i
$743$	0.677571	+	0.677571i	0.0248577	+	0.0248577i	0.719426	−	0.694569i	$-0.244405\pi$
$743$	0.677571	+	0.677571i	0.0248577	+	0.0248577i	−0.694569	+	0.719426i	$0.744405\pi$
$744$	−1.04212	+	1.04212i	−0.0382062	+	0.0382062i
$745$		−	49.8074i		−	1.82480i
$746$	9.58285	−	9.58285i	0.350853	−	0.350853i
$747$	4.30382			0.157468
$748$		−	28.4021i		−	1.03848i
$749$	−21.6462	−	21.4470i	−0.790935	−	0.783656i
$750$	12.4809			0.455739
$751$	−0.737932	−	0.737932i	−0.0269275	−	0.0269275i	0.693515	−	0.720442i	$-0.256061\pi$
$751$	−0.737932	−	0.737932i	−0.0269275	−	0.0269275i	−0.720442	+	0.693515i	$0.756061\pi$
$752$	6.78006	−	6.78006i	0.247243	−	0.247243i
$753$			22.0297i			0.802806i
$754$	34.7558	−	1.81911i	1.26573	−	0.0662480i
$755$			49.9305i			1.81716i
$756$	−0.0122313	−	2.64572i	−0.000444848	−	0.0962240i
$757$	−9.96437	+	9.96437i	−0.362161	+	0.362161i	−0.864608	−	0.502447i	$-0.832433\pi$
$757$	−9.96437	+	9.96437i	−0.362161	+	0.362161i	0.502447	+	0.864608i	$0.332433\pi$
$758$		−	15.2447i		−	0.553713i
$759$	−10.4218			−0.378287
$760$		−	10.1978i		−	0.369913i
$761$		−	35.7110i		−	1.29452i	−0.762268	−	0.647261i	$-0.775914\pi$
$761$		−	35.7110i		−	1.29452i	0.762268	−	0.647261i	$-0.224086\pi$
$762$	−1.37247	+	1.37247i	−0.0497192	+	0.0497192i
$763$	0.741847	−	0.748739i	0.0268567	−	0.0271062i
$764$	9.13815	+	9.13815i	0.330607	+	0.330607i
$765$	13.3170	−	13.3170i	0.481478	−	0.481478i
$766$	−8.49186	+	8.49186i	−0.306823	+	0.306823i
$767$		−	17.1017i		−	0.617505i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	−18.8372	+	18.8372i	−0.679287	+	0.679287i	−0.959839	−	0.280552i	$-0.909482\pi$
$769$	−18.8372	+	18.8372i	−0.679287	+	0.679287i	0.280552	+	0.959839i	$0.409482\pi$
$770$	−37.6551	+	38.0049i	−1.35699	+	1.36960i
$771$	−1.71143	+	1.71143i	−0.0616355	+	0.0616355i
$772$	8.81474	+	8.81474i	0.317250	+	0.317250i
$773$	22.8839	+	22.8839i	0.823078	+	0.823078i	0.986548	−	0.163470i	$-0.0522687\pi$
$773$	22.8839	+	22.8839i	0.823078	+	0.823078i	−0.163470	+	0.986548i	$0.552269\pi$
$774$	8.99966			0.323486
$775$	8.76266	+	8.76266i	0.314764	+	0.314764i
$776$	−3.69799			−0.132750
$777$	2.68804	−	2.71301i	0.0964329	−	0.0973287i
$778$	−22.6008			−0.810276
$779$	29.5924			1.06026
$780$	16.7339	−	16.7339i	0.599170	−	0.599170i
$781$	−6.59668	−	6.59668i	−0.236048	−	0.236048i
$782$	9.70639			0.347100
$783$	−5.37780	+	0.281472i	−0.192187	+	0.0100590i
$784$	−0.0647212	−	6.99970i	−0.00231147	−	0.249989i
$785$	−19.8546	+	19.8546i	−0.708641	+	0.708641i
$786$	−0.645117	+	0.645117i	−0.0230106	+	0.0230106i
$787$	13.7982			0.491852			0.245926	−	0.969289i	$-0.420908\pi$
$787$	13.7982			0.491852			0.245926	+	0.969289i	$0.420908\pi$
$788$		−	7.54058i		−	0.268622i
$789$	8.10354			0.288494
$790$		−	27.9327i		−	0.993802i
$791$	−0.221703	−	47.9560i	−0.00788284	−	1.70512i
$792$			5.52226i			0.196225i
$793$	−52.2786	−	52.2786i	−1.85647	−	1.85647i
$794$	19.0807	+	19.0807i	0.677148	+	0.677148i
$795$	−35.1460	−	35.1460i	−1.24650	−	1.24650i
$796$	12.9406			0.458667
$797$	28.8679	+	28.8679i	1.02255	+	1.02255i	0.999740	+	0.0228143i	$0.00726265\pi$
$797$	28.8679	+	28.8679i	1.02255	+	1.02255i	0.0228143	+	0.999740i	$0.492737\pi$
$798$	0.0340635	+	7.36819i	0.00120583	+	0.260831i
$799$	−49.3153			−1.74465
$800$	5.94568	−	5.94568i	0.210211	−	0.210211i
$801$	4.97318	−	4.97318i	0.175719	−	0.175719i
$802$	14.8918	−	14.8918i	0.525847	−	0.525847i
$803$			67.0228i			2.36518i
$804$	−0.693528	−	0.693528i	−0.0244589	−	0.0244589i
$805$	−12.9881	−	12.8686i	−0.457772	−	0.453559i
$806$	9.52484			0.335498
$807$	15.6607			0.551281
$808$			9.25555i			0.325609i
$809$	−16.8947	−	16.8947i	−0.593987	−	0.593987i	0.344719	−	0.938706i	$-0.387974\pi$
$809$	−16.8947	−	16.8947i	−0.593987	−	0.593987i	−0.938706	+	0.344719i	$0.887974\pi$
$810$	−2.58925	+	2.58925i	−0.0909771	+	0.0909771i
$811$	−7.27465			−0.255447			−0.127724	−	0.991810i	$-0.540767\pi$
$811$	−7.27465			−0.255447			−0.127724	+	0.991810i	$0.540767\pi$
$812$	−14.2247	+	0.810475i	−0.499190	+	0.0284421i
$813$	26.1368			0.916658
$814$	−5.63665	+	5.63665i	−0.197564	+	0.197564i
$815$	−12.8873	−	12.8873i	−0.451423	−	0.451423i
$816$		−	5.14319i		−	0.180048i
$817$	−25.0636			−0.876863
$818$	−15.1299			−0.529004
$819$	−12.0348	+	12.1466i	−0.420531	+	0.424437i
$820$	27.5130	+	27.5130i	0.960795	+	0.960795i
$821$			39.4242i			1.37592i	0.725751	+	0.687958i	$0.241492\pi$
$821$			39.4242i			1.37592i	−0.725751	+	0.687958i	$0.758508\pi$
$822$	7.67530	−	7.67530i	0.267707	−	0.267707i
$823$	−29.6061	+	29.6061i	−1.03200	+	1.03200i	−0.0325327	+	0.999471i	$0.510357\pi$
$823$	−29.6061	+	29.6061i	−1.03200	+	1.03200i	−0.999471	+	0.0325327i	$0.989643\pi$
$824$	9.10792	−	9.10792i	0.317289	−	0.317289i
$825$	46.4337			1.61661
$826$	0.0323659	+	7.00100i	0.00112615	+	0.243596i
$827$	20.2990	+	20.2990i	0.705867	+	0.705867i	0.965663	−	0.259796i	$-0.0836555\pi$
$827$	20.2990	+	20.2990i	0.705867	+	0.705867i	−0.259796	+	0.965663i	$0.583655\pi$
$828$	−1.88723			−0.0655858
$829$	6.86392	+	6.86392i	0.238394	+	0.238394i	0.816185	−	0.577791i	$-0.196085\pi$
$829$	6.86392	+	6.86392i	0.238394	+	0.238394i	−0.577791	+	0.816185i	$0.696085\pi$
$830$	−11.1437	−	11.1437i	−0.386802	−	0.386802i
$831$	−8.69885	−	8.69885i	−0.301760	−	0.301760i
$832$		−	6.46283i		−	0.224058i
$833$	−25.2210	+	25.6918i	−0.873857	+	0.890168i
$834$		−	5.20671i		−	0.180294i
$835$	−40.3775			−1.39732
$836$		−	15.3792i		−	0.531901i
$837$	−1.47379			−0.0509415
$838$	−9.17910	+	9.17910i	−0.317087	+	0.317087i
$839$	−19.0512	+	19.0512i	−0.657722	+	0.657722i	−0.954840	−	0.297119i	$-0.903974\pi$
$839$	−19.0512	+	19.0512i	−0.657722	+	0.657722i	0.297119	+	0.954840i	$0.403974\pi$
$840$	−6.81877	+	6.88211i	−0.235270	+	0.237455i
$841$	3.02740	+	28.8415i	0.104393	+	0.994536i
$842$	−19.3629			−0.667289
$843$	−11.9265	−	11.9265i	−0.410770	−	0.410770i
$844$	−3.76259	+	3.76259i	−0.129514	+	0.129514i
$845$	−105.342			−3.62388
$846$	9.58845			0.329658
$847$	−36.3036	+	36.6408i	−1.24741	+	1.25899i
$848$	−13.5738			−0.466127
$849$	0.582008	+	0.582008i	0.0199745	+	0.0199745i
$850$	−43.2463			−1.48334
$851$	−1.92632	−	1.92632i	−0.0660335	−	0.0660335i
$852$	−1.19456	−	1.19456i	−0.0409250	−	0.0409250i
$853$	26.3681	−	26.3681i	0.902825	−	0.902825i	−0.0928548	−	0.995680i	$-0.529599\pi$
$853$	26.3681	−	26.3681i	0.902825	−	0.902825i	0.995680	+	0.0928548i	$0.0295992\pi$
$854$	21.5005	+	21.3026i	0.735732	+	0.728961i
$855$	7.21093	−	7.21093i	0.246608	−	0.246608i
$856$	8.14394	+	8.14394i	0.278354	+	0.278354i
$857$		−	13.6781i		−	0.467234i	−0.972329	−	0.233617i	$-0.924944\pi$
$857$		−	13.6781i		−	0.467234i	0.972329	−	0.233617i	$-0.0750563\pi$
$858$	25.2363	−	25.2363i	0.861552	−	0.861552i
$859$	−10.1041	+	10.1041i	−0.344748	+	0.344748i	−0.858149	−	0.513401i	$-0.828385\pi$
$859$	−10.1041	+	10.1041i	−0.344748	+	0.344748i	0.513401	+	0.858149i	$0.328385\pi$
$860$	−23.3024	−	23.3024i	−0.794605	−	0.794605i
$861$	−19.9708	−	19.7870i	−0.680603	−	0.674339i
$862$	−21.3261	+	21.3261i	−0.726371	+	0.726371i
$863$		−	51.8599i		−	1.76533i	−0.470003	−	0.882665i	$-0.655747\pi$
$863$		−	51.8599i		−	1.76533i	0.470003	−	0.882665i	$-0.344253\pi$
$864$			1.00000i			0.0340207i
$865$	−17.8114			−0.605607
$866$		−	18.5770i		−	0.631272i
$867$	−6.68387	+	6.68387i	−0.226996	+	0.226996i
$868$	−3.89923	+	0.0180263i	−0.132349	+	0.000611853i
$869$		−	42.1252i		−	1.42900i
$870$	14.6533	+	13.1957i	0.496793	+	0.447376i
$871$			6.33873i			0.214780i
$872$	−0.281697	+	0.281697i	−0.00953947	+	0.00953947i
$873$	−2.61488	−	2.61488i	−0.0885002	−	0.0885002i
$874$	5.25584			0.177781
$875$	23.4574	+	23.2415i	0.793004	+	0.785706i
$876$			12.1368i			0.410066i
$877$	−6.58287			−0.222288			−0.111144	−	0.993804i	$-0.535451\pi$
$877$	−6.58287			−0.222288			−0.111144	+	0.993804i	$0.535451\pi$
$878$	−20.0085	+	20.0085i	−0.675254	+	0.675254i
$879$			2.71180i			0.0914669i
$880$	14.2985	−	14.2985i	0.482004	−	0.482004i
$881$	−12.8836	−	12.8836i	−0.434060	−	0.434060i	0.455947	−	0.890007i	$-0.349301\pi$
$881$	−12.8836	−	12.8836i	−0.434060	−	0.434060i	−0.890007	+	0.455947i	$0.849301\pi$
$882$	4.90377	−	4.99530i	0.165119	−	0.168201i
$883$		−	4.45599i		−	0.149956i	−0.997185	−	0.0749779i	$-0.976111\pi$
$883$		−	4.45599i		−	0.149956i	0.997185	−	0.0749779i	$-0.0238886\pi$
$884$	−23.5039	+	23.5039i	−0.790523	+	0.790523i
$885$	6.85157	−	6.85157i	0.230313	−	0.230313i
$886$	6.27430			0.210789
$887$	22.2324	+	22.2324i	0.746491	+	0.746491i	0.973818	−	0.227327i	$-0.0729987\pi$
$887$	22.2324	+	22.2324i	0.746491	+	0.746491i	−0.227327	+	0.973818i	$0.572999\pi$
$888$	−1.02071	+	1.02071i	−0.0342529	+	0.0342529i
$889$	−5.13524	+	0.0237404i	−0.172230	+	0.000796228i
$890$	−25.7536			−0.863264
$891$	−3.90483	+	3.90483i	−0.130817	+	0.130817i
$892$	6.40263			0.214376
$893$	−26.7033			−0.893592
$894$		−	13.6021i		−	0.454921i
$895$		−	45.4216i		−	1.51828i
$896$	0.0122313	+	2.64572i	0.000408619	+	0.0883874i
$897$	8.62448	+	8.62448i	0.287963	+	0.287963i
$898$			16.9551i			0.565801i
$899$	0.414830	+	7.92574i	0.0138354	+	0.264338i
$900$	8.40845			0.280282
$901$	49.3651	+	49.3651i	1.64459	+	1.64459i
$902$	41.4921	+	41.4921i	1.38154	+	1.38154i
$903$	16.9145	+	16.7588i	0.562879	+	0.557698i
$904$			18.1259i			0.602857i
$905$		−	5.15718i		−	0.171431i
$906$			13.6357i			0.453015i
$907$	7.53055	+	7.53055i	0.250048	+	0.250048i	0.820990	−	0.570942i	$-0.193422\pi$
$907$	7.53055	+	7.53055i	0.250048	+	0.250048i	−0.570942	+	0.820990i	$0.693422\pi$
$908$	−20.2626			−0.672437
$909$	−6.54466	+	6.54466i	−0.217073	+	0.217073i
$910$	62.6119	−	0.289457i	2.07556	−	0.00959541i
$911$	−22.2789	−	22.2789i	−0.738134	−	0.738134i	0.234083	−	0.972217i	$-0.424791\pi$
$911$	−22.2789	−	22.2789i	−0.738134	−	0.738134i	−0.972217	+	0.234083i	$0.924791\pi$
$912$		−	2.78495i		−	0.0922187i
$913$	−16.8057	−	16.8057i	−0.556187	−	0.556187i
$914$	−9.82809	−	9.82809i	−0.325084	−	0.325084i
$915$		−	41.8895i		−	1.38483i
$916$	8.12556	+	8.12556i	0.268476	+	0.268476i
$917$	−2.41378	+	0.0111590i	−0.0797101	+	0.000368503i
$918$	3.63679	−	3.63679i	0.120032	−	0.120032i
$919$	37.0586			1.22245			0.611224	−	0.791457i	$-0.290677\pi$
$919$	37.0586			1.22245			0.611224	+	0.791457i	$0.290677\pi$
$920$	4.88652	+	4.88652i	0.161104	+	0.161104i
$921$		−	17.9570i		−	0.591705i
$922$		−	24.5877i		−	0.809751i
$923$			10.9181i			0.359373i
$924$	−10.2833	+	10.3789i	−0.338297	+	0.341440i
$925$	8.58262	+	8.58262i	0.282195	+	0.282195i
$926$	19.2774	+	19.2774i	0.633494	+	0.633494i
$927$	12.8805			0.423053
$928$	5.37780	−	0.281472i	0.176535	−	0.00923978i
$929$			32.4867i			1.06585i	0.846162	+	0.532926i	$0.178908\pi$
$929$			32.4867i			1.06585i	−0.846162	+	0.532926i	$0.821092\pi$
$930$	3.81601	+	3.81601i	0.125132	+	0.125132i
$931$	−13.6567	+	13.9116i	−0.447581	+	0.455936i
$932$		−	10.5637i		−	0.346026i
$933$		−	34.8518i		−	1.14100i
$934$	20.2231			0.661721
$935$	−104.001			−3.40121
$936$	4.56991	−	4.56991i	0.149372	−	0.149372i
$937$	45.9721			1.50184			0.750921	−	0.660392i	$-0.229610\pi$
$937$	45.9721			1.50184			0.750921	+	0.660392i	$0.229610\pi$
$938$	−0.0119964	−	2.59492i	−0.000391697	−	0.0847271i
$939$	6.59641	−	6.59641i	0.215266	−	0.215266i
$940$	−24.8269	−	24.8269i	−0.809765	−	0.809765i
$941$	35.6821			1.16320			0.581602	−	0.813474i	$-0.302426\pi$
$941$	35.6821			1.16320			0.581602	+	0.813474i	$0.302426\pi$
$942$	−5.42216	+	5.42216i	−0.176663	+	0.176663i
$943$	−14.1799	+	14.1799i	−0.461761	+	0.461761i
$944$		−	2.64616i		−	0.0861250i
$945$	−9.68799	+	0.0447880i	−0.315150	+	0.00145695i
$946$	−35.1422	−	35.1422i	−1.14257	−	1.14257i
$947$	15.3100	−	15.3100i	0.497509	−	0.497509i	−0.413153	−	0.910662i	$-0.635573\pi$
$947$	15.3100	−	15.3100i	0.497509	−	0.497509i	0.910662	+	0.413153i	$0.135573\pi$
$948$		−	7.62824i		−	0.247754i
$949$	55.4643	−	55.4643i	1.80045	−	1.80045i
$950$	−23.4171			−0.759751
$951$			1.04428i			0.0338629i
$952$	9.57745	−	9.66641i	0.310407	−	0.313290i
$953$	−42.6678			−1.38215			−0.691073	−	0.722785i	$-0.742862\pi$
$953$	−42.6678			−1.38215			−0.691073	+	0.722785i	$0.742862\pi$
$954$	−9.59814	−	9.59814i	−0.310751	−	0.310751i
$955$	33.4617	−	33.4617i	1.08279	−	1.08279i
$956$			12.8622i			0.415994i
$957$	22.0985	+	19.9003i	0.714344	+	0.643286i
$958$			2.40480i			0.0776955i
$959$	28.7181	−	0.132765i	0.927354	−	0.00428720i
$960$	2.58925	−	2.58925i	0.0835678	−	0.0835678i
$961$		−	28.8280i		−	0.929934i
$962$	9.32914			0.300784
$963$			11.5173i			0.371139i
$964$		−	7.99052i		−	0.257357i
$965$	32.2774	−	32.2774i	1.03905	−	1.03905i
$966$	−3.54697	−	3.51433i	−0.114122	−	0.113072i
$967$	−4.26830	−	4.26830i	−0.137259	−	0.137259i	0.635139	−	0.772398i	$-0.280943\pi$
$967$	−4.26830	−	4.26830i	−0.137259	−	0.137259i	−0.772398	+	0.635139i	$0.780943\pi$
$968$	13.7853	−	13.7853i	0.443077	−	0.443077i
$969$	−10.1282	+	10.1282i	−0.325366	+	0.325366i
$970$			13.5412i			0.434780i
$971$	23.4821	+	23.4821i	0.753577	+	0.753577i	0.975145	−	0.221568i	$-0.0711174\pi$
$971$	23.4821	+	23.4821i	0.753577	+	0.753577i	−0.221568	+	0.975145i	$0.571117\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	9.69572	−	9.78578i	0.310831	−	0.313718i
$974$	3.23761	−	3.23761i	0.103740	−	0.103740i
$975$	−38.4259	−	38.4259i	−1.23061	−	1.23061i
$976$	−8.08912	−	8.08912i	−0.258926	−	0.258926i
$977$	23.8794			0.763968			0.381984	−	0.924169i	$-0.375241\pi$
$977$	23.8794			0.763968			0.381984	+	0.924169i	$0.375241\pi$
$978$	−3.51944	−	3.51944i	−0.112539	−	0.112539i
$979$	−38.8389			−1.24130
$980$	−25.6312	+	0.236993i	−0.818758	+	0.00757047i
$981$	−0.398380			−0.0127193
$982$	23.2547			0.742088
$983$	10.5213	−	10.5213i	0.335577	−	0.335577i	−0.519122	−	0.854700i	$-0.673741\pi$
$983$	10.5213	−	10.5213i	0.335577	−	0.335577i	0.854700	+	0.519122i	$0.173741\pi$
$984$	7.51360	+	7.51360i	0.239525	+	0.239525i
$985$	−27.6117			−0.879784
$986$	−20.5816	−	18.5343i	−0.655451	−	0.590251i
$987$	18.0211	+	17.8552i	0.573618	+	0.568338i
$988$	−12.7270	+	12.7270i	−0.404898	+	0.404898i
$989$	12.0098	−	12.0098i	0.381890	−	0.381890i
$990$	20.2212			0.642671
$991$			2.81634i			0.0894639i	0.998999	+	0.0447320i	$0.0142434\pi$
$991$			2.81634i			0.0894639i	−0.998999	+	0.0447320i	$0.985757\pi$
$992$	1.47379			0.0467928
$993$			16.3118i			0.517639i
$994$	−0.0206631	−	4.46959i	−0.000655394	−	0.141767i
$995$		−	47.3852i		−	1.50221i
$996$	−3.04326	−	3.04326i	−0.0964293	−	0.0964293i
$997$	−6.06758	−	6.06758i	−0.192162	−	0.192162i	0.604468	−	0.796630i	$-0.293386\pi$
$997$	−6.06758	−	6.06758i	−0.192162	−	0.192162i	−0.796630	+	0.604468i	$0.793386\pi$
$998$	−27.0274	−	27.0274i	−0.855538	−	0.855538i
$999$	−1.44351			−0.0456705

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1218.2.m.a.307.1	✓	40
7.6	odd	2		1218.2.m.b.307.1	yes	40
29.12	odd	4		1218.2.m.b.853.1	yes	40
203.41	even	4	inner	1218.2.m.a.853.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1218.2.m.a.307.1	✓	40	1.1	even	1	trivial
1218.2.m.a.853.1	yes	40	203.41	even	4	inner
1218.2.m.b.307.1	yes	40	7.6	odd	2
1218.2.m.b.853.1	yes	40	29.12	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:	\( N \)	\(=\)	\( 1218 = 2 \cdot 3 \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1218.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} -3.66176 q^{5} -1.00000 q^{6} +(-1.87946 - 1.86216i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(2.58925 - 2.58925i) q^{10} +(3.90483 - 3.90483i) q^{11} +(0.707107 - 0.707107i) q^{12} -6.46283 q^{13} +(2.64572 - 0.0122313i) q^{14} +(-2.58925 - 2.58925i) q^{15} -1.00000 q^{16} +(3.63679 + 3.63679i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(1.96925 + 1.96925i) q^{19} +3.66176i q^{20} +(-0.0122313 - 2.64572i) q^{21} +5.52226i q^{22} -1.88723 q^{23} +1.00000i q^{24} +8.40845 q^{25} +(4.56991 - 4.56991i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.86216 + 1.87946i) q^{28} +(4.00171 + 3.60365i) q^{29} +3.66176 q^{30} +(1.04212 + 1.04212i) q^{31} +(0.707107 - 0.707107i) q^{32} +5.52226 q^{33} -5.14319 q^{34} +(6.88211 + 6.81877i) q^{35} +1.00000 q^{36} +(1.02071 + 1.02071i) q^{37} -2.78495 q^{38} +(-4.56991 - 4.56991i) q^{39} +(-2.58925 - 2.58925i) q^{40} +(7.51360 - 7.51360i) q^{41} +(1.87946 + 1.86216i) q^{42} +(-6.36372 + 6.36372i) q^{43} +(-3.90483 - 3.90483i) q^{44} -3.66176i q^{45} +(1.33447 - 1.33447i) q^{46} +(-6.78006 + 6.78006i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(0.0647212 + 6.99970i) q^{49} +(-5.94568 + 5.94568i) q^{50} +5.14319i q^{51} +6.46283i q^{52} +13.5738 q^{53} -1.00000i q^{54} +(-14.2985 + 14.2985i) q^{55} +(-0.0122313 - 2.64572i) q^{56} +2.78495i q^{57} +(-5.37780 + 0.281472i) q^{58} +2.64616i q^{59} +(-2.58925 + 2.58925i) q^{60} +(8.08912 + 8.08912i) q^{61} -1.47379 q^{62} +(1.86216 - 1.87946i) q^{63} +1.00000i q^{64} +23.6653 q^{65} +(-3.90483 + 3.90483i) q^{66} -0.980797i q^{67} +(3.63679 - 3.63679i) q^{68} +(-1.33447 - 1.33447i) q^{69} +(-9.68799 + 0.0447880i) q^{70} -1.68936i q^{71} +(-0.707107 + 0.707107i) q^{72} +(-8.58204 + 8.58204i) q^{73} -1.44351 q^{74} +(5.94568 + 5.94568i) q^{75} +(1.96925 - 1.96925i) q^{76} +(-14.6104 + 0.0675444i) q^{77} +6.46283 q^{78} +(5.39398 - 5.39398i) q^{79} +3.66176 q^{80} -1.00000 q^{81} +10.6258i q^{82} -4.30382i q^{83} +(-2.64572 + 0.0122313i) q^{84} +(-13.3170 - 13.3170i) q^{85} -8.99966i q^{86} +(0.281472 + 5.37780i) q^{87} +5.52226 q^{88} +(-4.97318 - 4.97318i) q^{89} +(2.58925 + 2.58925i) q^{90} +(12.1466 + 12.0348i) q^{91} +1.88723i q^{92} +1.47379i q^{93} -9.58845i q^{94} +(-7.21093 - 7.21093i) q^{95} +1.00000 q^{96} +(-2.61488 + 2.61488i) q^{97} +(-4.99530 - 4.90377i) q^{98} +(3.90483 + 3.90483i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{6} + 4 q^{10} + 4 q^{14} - 4 q^{15} - 40 q^{16} + 8 q^{19} - 4 q^{21} + 24 q^{25} - 12 q^{28} + 8 q^{29} - 24 q^{31} - 12 q^{35} + 40 q^{36} - 16 q^{37} - 4 q^{40} + 16 q^{41} - 20 q^{43} + 4 q^{46}+ \cdots - 8 q^{98}+O(q^{100}) \) 40 * q - 40 * q^6 + 4 * q^10 + 4 * q^14 - 4 * q^15 - 40 * q^16 + 8 * q^19 - 4 * q^21 + 24 * q^25 - 12 * q^28 + 8 * q^29 - 24 * q^31 - 12 * q^35 + 40 * q^36 - 16 * q^37 - 4 * q^40 + 16 * q^41 - 20 * q^43 + 4 * q^46 - 16 * q^47 + 28 * q^49 + 32 * q^50 + 16 * q^53 - 24 * q^55 - 4 * q^56 - 20 * q^58 - 4 * q^60 - 44 * q^61 + 12 * q^63 - 4 * q^69 - 28 * q^70 - 52 * q^73 - 32 * q^75 + 8 * q^76 + 44 * q^77 + 4 * q^79 - 40 * q^81 - 4 * q^84 - 24 * q^85 - 12 * q^87 + 24 * q^89 + 4 * q^90 - 16 * q^95 + 40 * q^96 - 68 * q^97 - 8 * q^98

Introduction

L-functions

Modular forms

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Database

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