LMFDB - Embedded newform 1218.2.m.b.307.3

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)

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")

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);

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			307.3
Character	$\chi$	$=$	1218.307
Dual form			1218.2.m.b.853.3

$q$-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} +0.964064 q^{5} +1.00000 q^{6} +(-1.12003 - 2.39698i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(-0.681696 + 0.681696i) q^{10} +(1.01614 - 1.01614i) q^{11} +(-0.707107 + 0.707107i) q^{12} -1.66411 q^{13} +(2.48690 + 0.902943i) q^{14} +(-0.681696 - 0.681696i) q^{15} -1.00000 q^{16} +(-4.23210 - 4.23210i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(-0.200133 - 0.200133i) q^{19} -0.964064i q^{20} +(-0.902943 + 2.48690i) q^{21} +1.43704i q^{22} +2.37884 q^{23} -1.00000i q^{24} -4.07058 q^{25} +(1.17671 - 1.17671i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.39698 + 1.12003i) q^{28} +(0.792373 + 5.32655i) q^{29} +0.964064 q^{30} +(2.45149 + 2.45149i) q^{31} +(0.707107 - 0.707107i) q^{32} -1.43704 q^{33} +5.98509 q^{34} +(-1.07978 - 2.31085i) q^{35} +1.00000 q^{36} +(-2.55744 - 2.55744i) q^{37} +0.283030 q^{38} +(1.17671 + 1.17671i) q^{39} +(0.681696 + 0.681696i) q^{40} +(6.53863 - 6.53863i) q^{41} +(-1.12003 - 2.39698i) q^{42} +(-5.80881 + 5.80881i) q^{43} +(-1.01614 - 1.01614i) q^{44} +0.964064i q^{45} +(-1.68209 + 1.68209i) q^{46} +(-4.08757 + 4.08757i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-4.49107 + 5.36939i) q^{49} +(2.87833 - 2.87833i) q^{50} +5.98509i q^{51} +1.66411i q^{52} -12.0147 q^{53} +1.00000i q^{54} +(0.979626 - 0.979626i) q^{55} +(0.902943 - 2.48690i) q^{56} +0.283030i q^{57} +(-4.32673 - 3.20615i) q^{58} -12.4636i q^{59} +(-0.681696 + 0.681696i) q^{60} +(-0.252020 - 0.252020i) q^{61} -3.46692 q^{62} +(2.39698 - 1.12003i) q^{63} +1.00000i q^{64} -1.60431 q^{65} +(1.01614 - 1.01614i) q^{66} -0.439521i q^{67} +(-4.23210 + 4.23210i) q^{68} +(-1.68209 - 1.68209i) q^{69} +(2.39754 + 0.870495i) q^{70} +10.6464i q^{71} +(-0.707107 + 0.707107i) q^{72} +(-9.08410 + 9.08410i) q^{73} +3.61676 q^{74} +(2.87833 + 2.87833i) q^{75} +(-0.200133 + 0.200133i) q^{76} +(-3.57379 - 1.29757i) q^{77} -1.66411 q^{78} +(-5.16289 + 5.16289i) q^{79} -0.964064 q^{80} -1.00000 q^{81} +9.24702i q^{82} -8.98566i q^{83} +(2.48690 + 0.902943i) q^{84} +(-4.08001 - 4.08001i) q^{85} -8.21489i q^{86} +(3.20615 - 4.32673i) q^{87} +1.43704 q^{88} +(-7.53183 - 7.53183i) q^{89} +(-0.681696 - 0.681696i) q^{90} +(1.86386 + 3.98886i) q^{91} -2.37884i q^{92} -3.46692i q^{93} -5.78069i q^{94} +(-0.192941 - 0.192941i) q^{95} -1.00000 q^{96} +(6.57198 - 6.57198i) q^{97} +(-0.621066 - 6.97239i) q^{98} +(1.01614 + 1.01614i) 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 - 24 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 + 20 * q^70 + 52 * q^73 + 32 * q^75 - 8 * q^76 + 20 * 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 - 24 * 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
$5$	0.964064			0.431143			0.215571	−	0.976488i	$-0.430839\pi$
$5$	0.964064			0.431143			0.215571	+	0.976488i	$0.430839\pi$
$6$	1.00000			0.408248
$7$	−1.12003	−	2.39698i	−0.423331	−	0.905975i
$7$	−1.12003	−	2.39698i	−0.423331	−	0.905975i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$			1.00000i			0.333333i
$10$	−0.681696	+	0.681696i	−0.215571	+	0.215571i
$11$	1.01614	−	1.01614i	0.306378	−	0.306378i	−0.537125	−	0.843503i	$-0.680489\pi$
$11$	1.01614	−	1.01614i	0.306378	−	0.306378i	0.843503	+	0.537125i	$0.180489\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	−1.66411			−0.461542			−0.230771	−	0.973008i	$-0.574125\pi$
$13$	−1.66411			−0.461542			−0.230771	+	0.973008i	$0.574125\pi$
$14$	2.48690	+	0.902943i	0.664653	+	0.241322i
$15$	−0.681696	−	0.681696i	−0.176013	−	0.176013i
$16$	−1.00000			−0.250000
$17$	−4.23210	−	4.23210i	−1.02643	−	1.02643i	−0.999641	−	0.0267933i	$-0.991470\pi$
$17$	−4.23210	−	4.23210i	−1.02643	−	1.02643i	−0.0267933	−	0.999641i	$-0.508530\pi$
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	−0.200133	−	0.200133i	−0.0459136	−	0.0459136i	0.683777	−	0.729691i	$-0.260336\pi$
$19$	−0.200133	−	0.200133i	−0.0459136	−	0.0459136i	−0.729691	+	0.683777i	$0.760336\pi$
$20$		−	0.964064i		−	0.215571i
$21$	−0.902943	+	2.48690i	−0.197038	+	0.542687i
$22$			1.43704i			0.306378i
$23$	2.37884			0.496022			0.248011	−	0.968757i	$-0.420223\pi$
$23$	2.37884			0.496022			0.248011	+	0.968757i	$0.420223\pi$
$24$		−	1.00000i		−	0.204124i
$25$	−4.07058			−0.814116
$26$	1.17671	−	1.17671i	0.230771	−	0.230771i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−2.39698	+	1.12003i	−0.452987	+	0.211666i
$29$	0.792373	+	5.32655i	0.147140	+	0.989116i
$29$	0.792373	+	5.32655i	0.147140	+	0.989116i
$30$	0.964064			0.176013
$31$	2.45149	+	2.45149i	0.440300	+	0.440300i	0.892113	−	0.451813i	$-0.149223\pi$
$31$	2.45149	+	2.45149i	0.440300	+	0.440300i	−0.451813	+	0.892113i	$0.649223\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−1.43704			−0.250157
$34$	5.98509			1.02643
$35$	−1.07978	−	2.31085i	−0.182516	−	0.390604i
$36$	1.00000			0.166667
$37$	−2.55744	−	2.55744i	−0.420440	−	0.420440i	0.464915	−	0.885355i	$-0.346085\pi$
$37$	−2.55744	−	2.55744i	−0.420440	−	0.420440i	−0.885355	+	0.464915i	$0.846085\pi$
$38$	0.283030			0.0459136
$39$	1.17671	+	1.17671i	0.188424	+	0.188424i
$40$	0.681696	+	0.681696i	0.107786	+	0.107786i
$41$	6.53863	−	6.53863i	1.02116	−	1.02116i	0.0213914	−	0.999771i	$-0.493190\pi$
$41$	6.53863	−	6.53863i	1.02116	−	1.02116i	0.999771	−	0.0213914i	$-0.00680962\pi$
$42$	−1.12003	−	2.39698i	−0.172824	−	0.369863i
$43$	−5.80881	+	5.80881i	−0.885834	+	0.885834i	−0.994120	−	0.108285i	$-0.965464\pi$
$43$	−5.80881	+	5.80881i	−0.885834	+	0.885834i	0.108285	+	0.994120i	$0.465464\pi$
$44$	−1.01614	−	1.01614i	−0.153189	−	0.153189i
$45$			0.964064i			0.143714i
$46$	−1.68209	+	1.68209i	−0.248011	+	0.248011i
$47$	−4.08757	+	4.08757i	−0.596233	+	0.596233i	−0.939308	−	0.343075i	$-0.888531\pi$
$47$	−4.08757	+	4.08757i	−0.596233	+	0.596233i	0.343075	+	0.939308i	$0.388531\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$	−4.49107	+	5.36939i	−0.641581	+	0.767055i
$50$	2.87833	−	2.87833i	0.407058	−	0.407058i
$51$			5.98509i			0.838080i
$52$			1.66411i			0.230771i
$53$	−12.0147			−1.65035			−0.825176	−	0.564876i	$-0.808924\pi$
$53$	−12.0147			−1.65035			−0.825176	+	0.564876i	$0.808924\pi$
$54$			1.00000i			0.136083i
$55$	0.979626	−	0.979626i	0.132093	−	0.132093i
$56$	0.902943	−	2.48690i	0.120661	−	0.332327i
$57$			0.283030i			0.0374883i
$58$	−4.32673	−	3.20615i	−0.568128	−	0.420988i
$59$		−	12.4636i		−	1.62262i	−0.584616	−	0.811310i	$-0.698755\pi$
$59$		−	12.4636i		−	1.62262i	0.584616	−	0.811310i	$-0.301245\pi$
$60$	−0.681696	+	0.681696i	−0.0880066	+	0.0880066i
$61$	−0.252020	−	0.252020i	−0.0322679	−	0.0322679i	0.690789	−	0.723057i	$-0.257263\pi$
$61$	−0.252020	−	0.252020i	−0.0322679	−	0.0322679i	−0.723057	+	0.690789i	$0.757263\pi$
$62$	−3.46692			−0.440300
$63$	2.39698	−	1.12003i	0.301992	−	0.141110i
$64$			1.00000i			0.125000i
$65$	−1.60431			−0.198991
$66$	1.01614	−	1.01614i	0.125078	−	0.125078i
$67$		−	0.439521i		−	0.0536961i	−0.999640	−	0.0268480i	$-0.991453\pi$
$67$		−	0.439521i		−	0.0536961i	0.999640	−	0.0268480i	$-0.00854702\pi$
$68$	−4.23210	+	4.23210i	−0.513217	+	0.513217i
$69$	−1.68209	−	1.68209i	−0.202500	−	0.202500i
$70$	2.39754	+	0.870495i	0.286560	+	0.104044i
$71$			10.6464i			1.26350i	0.775173	+	0.631749i	$0.217663\pi$
$71$			10.6464i			1.26350i	−0.775173	+	0.631749i	$0.782337\pi$
$72$	−0.707107	+	0.707107i	−0.0833333	+	0.0833333i
$73$	−9.08410	+	9.08410i	−1.06321	+	1.06321i	−0.0653506	+	0.997862i	$0.520817\pi$
$73$	−9.08410	+	9.08410i	−1.06321	+	1.06321i	−0.997862	+	0.0653506i	$0.979183\pi$
$74$	3.61676			0.420440
$75$	2.87833	+	2.87833i	0.332361	+	0.332361i
$76$	−0.200133	+	0.200133i	−0.0229568	+	0.0229568i
$77$	−3.57379	−	1.29757i	−0.407271	−	0.147872i
$78$	−1.66411			−0.188424
$79$	−5.16289	+	5.16289i	−0.580870	+	0.580870i	−0.935142	−	0.354272i	$-0.884729\pi$
$79$	−5.16289	+	5.16289i	−0.580870	+	0.580870i	0.354272	+	0.935142i	$0.384729\pi$
$80$	−0.964064			−0.107786
$81$	−1.00000			−0.111111
$82$			9.24702i			1.02116i
$83$		−	8.98566i		−	0.986304i	−0.869943	−	0.493152i	$-0.835845\pi$
$83$		−	8.98566i		−	0.986304i	0.869943	−	0.493152i	$-0.164155\pi$
$84$	2.48690	+	0.902943i	0.271344	+	0.0985192i
$85$	−4.08001	−	4.08001i	−0.442540	−	0.442540i
$86$		−	8.21489i		−	0.885834i
$87$	3.20615	−	4.32673i	0.343735	−	0.463874i
$88$	1.43704			0.153189
$89$	−7.53183	−	7.53183i	−0.798372	−	0.798372i	0.184467	−	0.982839i	$-0.440944\pi$
$89$	−7.53183	−	7.53183i	−0.798372	−	0.798372i	−0.982839	+	0.184467i	$0.940944\pi$
$90$	−0.681696	−	0.681696i	−0.0718571	−	0.0718571i
$91$	1.86386	+	3.98886i	0.195385	+	0.418146i
$92$		−	2.37884i		−	0.248011i
$93$		−	3.46692i		−	0.359503i
$94$		−	5.78069i		−	0.596233i
$95$	−0.192941	−	0.192941i	−0.0197953	−	0.0197953i
$96$	−1.00000			−0.102062
$97$	6.57198	−	6.57198i	0.667283	−	0.667283i	−0.289803	−	0.957086i	$-0.593590\pi$
$97$	6.57198	−	6.57198i	0.667283	−	0.667283i	0.957086	+	0.289803i	$0.0935899\pi$
$98$	−0.621066	−	6.97239i	−0.0627372	−	0.704318i
$99$	1.01614	+	1.01614i	0.102126	+	0.102126i
$100$			4.07058i			0.407058i
$101$	−9.05597	−	9.05597i	−0.901102	−	0.901102i	0.0944292	−	0.995532i	$-0.469897\pi$
$101$	−9.05597	−	9.05597i	−0.901102	−	0.901102i	−0.995532	+	0.0944292i	$0.969897\pi$
$102$	−4.23210	−	4.23210i	−0.419040	−	0.419040i
$103$			6.00327i			0.591520i	0.955262	+	0.295760i	$0.0955729\pi$
$103$			6.00327i			0.591520i	−0.955262	+	0.295760i	$0.904427\pi$
$104$	−1.17671	−	1.17671i	−0.115386	−	0.115386i
$105$	−0.870495	+	2.39754i	−0.0849516	+	0.233975i
$106$	8.49571	−	8.49571i	0.825176	−	0.825176i
$107$	5.74000			0.554906			0.277453	−	0.960739i	$-0.410510\pi$
$107$	5.74000			0.554906			0.277453	+	0.960739i	$0.410510\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$		−	12.5615i		−	1.20317i	−0.798807	−	0.601587i	$-0.794535\pi$
$109$		−	12.5615i		−	1.20317i	0.798807	−	0.601587i	$-0.205465\pi$
$110$			1.38540i			0.132093i
$111$			3.61676i			0.343288i
$112$	1.12003	+	2.39698i	0.105833	+	0.226494i
$113$	−14.2794	−	14.2794i	−1.34329	−	1.34329i	−0.892759	−	0.450535i	$-0.851233\pi$
$113$	−14.2794	−	14.2794i	−1.34329	−	1.34329i	−0.450535	−	0.892759i	$-0.648767\pi$
$114$	−0.200133	−	0.200133i	−0.0187441	−	0.0187441i
$115$	2.29335			0.213856
$116$	5.32655	−	0.792373i	0.494558	−	0.0735700i
$117$		−	1.66411i		−	0.153847i
$118$	8.81308	+	8.81308i	0.811310	+	0.811310i
$119$	−5.40420	+	14.8843i	−0.495402	+	1.36445i
$120$		−	0.964064i		−	0.0880066i
$121$			8.93491i			0.812265i
$122$	0.356410			0.0322679
$123$	−9.24702			−0.833776
$124$	2.45149	−	2.45149i	0.220150	−	0.220150i
$125$	−8.74462			−0.782143
$126$	−0.902943	+	2.48690i	−0.0804406	+	0.221551i
$127$	−3.20089	+	3.20089i	−0.284033	+	0.284033i	−0.834715	−	0.550682i	$-0.814368\pi$
$127$	−3.20089	+	3.20089i	−0.284033	+	0.284033i	0.550682	+	0.834715i	$0.314368\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	8.21489			0.723281
$130$	1.13442	−	1.13442i	0.0994953	−	0.0994953i
$131$	−7.76228	+	7.76228i	−0.678194	+	0.678194i	−0.959591	−	0.281397i	$-0.909202\pi$
$131$	−7.76228	+	7.76228i	−0.678194	+	0.678194i	0.281397	+	0.959591i	$0.409202\pi$
$132$			1.43704i			0.125078i
$133$	−0.255560	+	0.703870i	−0.0221599	+	0.0610332i
$134$	0.310789	+	0.310789i	0.0268480	+	0.0268480i
$135$	0.681696	−	0.681696i	0.0586711	−	0.0586711i
$136$		−	5.98509i		−	0.513217i
$137$	5.94573	−	5.94573i	0.507978	−	0.507978i	−0.405927	−	0.913905i	$-0.633051\pi$
$137$	5.94573	−	5.94573i	0.507978	−	0.507978i	0.913905	+	0.405927i	$0.133051\pi$
$138$	2.37884			0.202500
$139$		−	2.25836i		−	0.191552i	−0.995403	−	0.0957758i	$-0.969467\pi$
$139$		−	2.25836i		−	0.191552i	0.995403	−	0.0957758i	$-0.0305332\pi$
$140$	−2.31085	+	1.07978i	−0.195302	+	0.0912581i
$141$	5.78069			0.486822
$142$	−7.52816	−	7.52816i	−0.631749	−	0.631749i
$143$	−1.69098	+	1.69098i	−0.141407	+	0.141407i
$144$		−	1.00000i		−	0.0833333i
$145$	0.763898	+	5.13514i	0.0634383	+	0.426450i
$146$		−	12.8469i		−	1.06321i
$147$	6.97239	−	0.621066i	0.575073	−	0.0512247i
$148$	−2.55744	+	2.55744i	−0.210220	+	0.210220i
$149$		−	11.1573i		−	0.914041i	−0.889456	−	0.457020i	$-0.848917\pi$
$149$		−	11.1573i		−	0.914041i	0.889456	−	0.457020i	$-0.151083\pi$
$150$	−4.07058			−0.332361
$151$		−	7.71410i		−	0.627765i	−0.949462	−	0.313882i	$-0.898370\pi$
$151$		−	7.71410i		−	0.627765i	0.949462	−	0.313882i	$-0.101630\pi$
$152$		−	0.283030i		−	0.0229568i
$153$	4.23210	−	4.23210i	0.342145	−	0.342145i
$154$	3.44457	−	1.60953i	0.277571	−	0.129700i
$155$	2.36339	+	2.36339i	0.189832	+	0.189832i
$156$	1.17671	−	1.17671i	0.0942120	−	0.0942120i
$157$	−6.62851	+	6.62851i	−0.529012	+	0.529012i	−0.920278	−	0.391265i	$-0.872037\pi$
$157$	−6.62851	+	6.62851i	−0.529012	+	0.529012i	0.391265	+	0.920278i	$0.372037\pi$
$158$		−	7.30143i		−	0.580870i
$159$	8.49571	+	8.49571i	0.673753	+	0.673753i
$160$	0.681696	−	0.681696i	0.0538928	−	0.0538928i
$161$	−2.66437	−	5.70203i	−0.209982	−	0.449383i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	−1.20031	−	1.20031i	−0.0940153	−	0.0940153i	0.658535	−	0.752550i	$-0.271177\pi$
$163$	−1.20031	−	1.20031i	−0.0940153	−	0.0940153i	−0.752550	+	0.658535i	$0.771177\pi$
$164$	−6.53863	−	6.53863i	−0.510581	−	0.510581i
$165$	−1.38540			−0.107853
$166$	6.35382	+	6.35382i	0.493152	+	0.493152i
$167$	−3.58474			−0.277396			−0.138698	−	0.990335i	$-0.544292\pi$
$167$	−3.58474			−0.277396			−0.138698	+	0.990335i	$0.544292\pi$
$168$	−2.39698	+	1.12003i	−0.184931	+	0.0864122i
$169$	−10.2307			−0.786979
$170$	5.77001			0.442540
$171$	0.200133	−	0.200133i	0.0153045	−	0.0153045i
$172$	5.80881	+	5.80881i	0.442917	+	0.442917i
$173$	11.2490			0.855244			0.427622	−	0.903958i	$-0.359351\pi$
$173$	11.2490			0.855244			0.427622	+	0.903958i	$0.359351\pi$
$174$	0.792373	+	5.32655i	0.0600696	+	0.403805i
$175$	4.55917	+	9.75712i	0.344641	+	0.737569i
$176$	−1.01614	+	1.01614i	−0.0765946	+	0.0765946i
$177$	−8.81308	+	8.81308i	−0.662432	+	0.662432i
$178$	10.6516			0.798372
$179$			10.1493i			0.758592i	0.925275	+	0.379296i	$0.123834\pi$
$179$			10.1493i			0.758592i	−0.925275	+	0.379296i	$0.876166\pi$
$180$	0.964064			0.0718571
$181$			3.87066i			0.287704i	0.989599	+	0.143852i	$0.0459489\pi$
$181$			3.87066i			0.287704i	−0.989599	+	0.143852i	$0.954051\pi$
$182$	−4.13849	−	1.50260i	−0.306766	−	0.111380i
$183$			0.356410i			0.0263466i
$184$	1.68209	+	1.68209i	0.124005	+	0.124005i
$185$	−2.46553	−	2.46553i	−0.181269	−	0.181269i
$186$	2.45149	+	2.45149i	0.179752	+	0.179752i
$187$	−8.60082			−0.628955
$188$	4.08757	+	4.08757i	0.298116	+	0.298116i
$189$	−2.48690	−	0.902943i	−0.180896	−	0.0656795i
$190$	0.272859			0.0197953
$191$	9.44291	−	9.44291i	0.683265	−	0.683265i	−0.277470	−	0.960734i	$-0.589496\pi$
$191$	9.44291	−	9.44291i	0.683265	−	0.683265i	0.960734	+	0.277470i	$0.0894958\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	−7.99696	+	7.99696i	−0.575634	+	0.575634i	−0.933697	−	0.358064i	$-0.883437\pi$
$193$	−7.99696	+	7.99696i	−0.575634	+	0.575634i	0.358064	+	0.933697i	$0.383437\pi$
$194$			9.29418i			0.667283i
$195$	1.13442	+	1.13442i	0.0812376	+	0.0812376i
$196$	5.36939	+	4.49107i	0.383528	+	0.320790i
$197$	12.7280			0.906829			0.453415	−	0.891300i	$-0.350206\pi$
$197$	12.7280			0.906829			0.453415	+	0.891300i	$0.350206\pi$
$198$	−1.43704			−0.102126
$199$		−	21.9546i		−	1.55632i	−0.628066	−	0.778160i	$-0.716153\pi$
$199$		−	21.9546i		−	1.55632i	0.628066	−	0.778160i	$-0.283847\pi$
$200$	−2.87833	−	2.87833i	−0.203529	−	0.203529i
$201$	−0.310789	+	0.310789i	−0.0219213	+	0.0219213i
$202$	12.8071			0.901102
$203$	11.8802	−	7.86520i	0.833825	−	0.552029i
$204$	5.98509			0.419040
$205$	6.30366	−	6.30366i	0.440267	−	0.440267i
$206$	−4.24495	−	4.24495i	−0.295760	−	0.295760i
$207$			2.37884i			0.165341i
$208$	1.66411			0.115386
$209$	−0.406727			−0.0281339
$210$	−1.07978	−	2.31085i	−0.0745119	−	0.159464i
$211$	16.8267	+	16.8267i	1.15840	+	1.15840i	0.984820	+	0.173581i	$0.0555338\pi$
$211$	16.8267	+	16.8267i	1.15840	+	1.15840i	0.173581	+	0.984820i	$0.444466\pi$
$212$			12.0147i			0.825176i
$213$	7.52816	−	7.52816i	0.515821	−	0.515821i
$214$	−4.05879	+	4.05879i	−0.277453	+	0.277453i
$215$	−5.60006	+	5.60006i	−0.381921	+	0.381921i
$216$	1.00000			0.0680414
$217$	3.13044	−	8.62191i	0.212508	−	0.585293i
$218$	8.88232	+	8.88232i	0.601587	+	0.601587i
$219$	12.8469			0.868110
$220$	−0.979626	−	0.979626i	−0.0660464	−	0.0660464i
$221$	7.04270	+	7.04270i	0.473743	+	0.473743i
$222$	−2.55744	−	2.55744i	−0.171644	−	0.171644i
$223$		−	11.4633i		−	0.767638i	−0.923408	−	0.383819i	$-0.874609\pi$
$223$		−	11.4633i		−	0.767638i	0.923408	−	0.383819i	$-0.125391\pi$
$224$	−2.48690	−	0.902943i	−0.166163	−	0.0603304i
$225$		−	4.07058i		−	0.271372i
$226$	20.1941			1.34329
$227$		−	6.63942i		−	0.440674i	−0.975424	−	0.220337i	$-0.929284\pi$
$227$		−	6.63942i		−	0.440674i	0.975424	−	0.220337i	$-0.0707157\pi$
$228$	0.283030			0.0187441
$229$	−12.1043	+	12.1043i	−0.799872	+	0.799872i	−0.983075	−	0.183203i	$-0.941353\pi$
$229$	−12.1043	+	12.1043i	−0.799872	+	0.799872i	0.183203	+	0.983075i	$0.441353\pi$
$230$	−1.62164	+	1.62164i	−0.106928	+	0.106928i
$231$	1.60953	+	3.44457i	0.105899	+	0.226636i
$232$	−3.20615	+	4.32673i	−0.210494	+	0.284064i
$233$	10.8589			0.711393			0.355697	−	0.934602i	$-0.384244\pi$
$233$	10.8589			0.711393			0.355697	+	0.934602i	$0.384244\pi$
$234$	1.17671	+	1.17671i	0.0769237	+	0.0769237i
$235$	−3.94068	+	3.94068i	−0.257061	+	0.257061i
$236$	−12.4636			−0.811310
$237$	7.30143			0.474279
$238$	−6.70348	−	14.3462i	−0.434522	−	0.929924i
$239$	20.2877			1.31230			0.656152	−	0.754629i	$-0.272183\pi$
$239$	20.2877			1.31230			0.656152	+	0.754629i	$0.272183\pi$
$240$	0.681696	+	0.681696i	0.0440033	+	0.0440033i
$241$	20.7111			1.33412			0.667061	−	0.745003i	$-0.267552\pi$
$241$	20.7111			1.33412			0.667061	+	0.745003i	$0.267552\pi$
$242$	−6.31794	−	6.31794i	−0.406132	−	0.406132i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−0.252020	+	0.252020i	−0.0161339	+	0.0161339i
$245$	−4.32968	+	5.17643i	−0.276613	+	0.330710i
$246$	6.53863	−	6.53863i	0.416888	−	0.416888i
$247$	0.333044	+	0.333044i	0.0211911	+	0.0211911i
$248$			3.46692i			0.220150i
$249$	−6.35382	+	6.35382i	−0.402657	+	0.402657i
$250$	6.18338	−	6.18338i	0.391071	−	0.391071i
$251$	12.2309	+	12.2309i	0.772010	+	0.772010i	0.978458	−	0.206448i	$-0.0661903\pi$
$251$	12.2309	+	12.2309i	0.772010	+	0.772010i	−0.206448	+	0.978458i	$0.566190\pi$
$252$	−1.12003	−	2.39698i	−0.0705552	−	0.150996i
$253$	2.41724	−	2.41724i	0.151970	−	0.151970i
$254$		−	4.52674i		−	0.284033i
$255$			5.77001i			0.361332i
$256$	1.00000			0.0625000
$257$			11.8867i			0.741471i	0.928738	+	0.370736i	$0.120894\pi$
$257$			11.8867i			0.741471i	−0.928738	+	0.370736i	$0.879106\pi$
$258$	−5.80881	+	5.80881i	−0.361640	+	0.361640i
$259$	−3.26573	+	8.99453i	−0.202922	+	0.558893i
$260$			1.60431i			0.0994953i
$261$	−5.32655	+	0.792373i	−0.329705	+	0.0490467i
$262$		−	10.9775i		−	0.678194i
$263$	10.9109	−	10.9109i	0.672793	−	0.672793i	−0.285566	−	0.958359i	$-0.592182\pi$
$263$	10.9109	−	10.9109i	0.672793	−	0.672793i	0.958359	+	0.285566i	$0.0921816\pi$
$264$	−1.01614	−	1.01614i	−0.0625392	−	0.0625392i
$265$	−11.5830			−0.711537
$266$	−0.317002	−	0.678419i	−0.0194367	−	0.0415966i
$267$			10.6516i			0.651868i
$268$	−0.439521			−0.0268480
$269$	2.30415	−	2.30415i	0.140486	−	0.140486i	−0.633366	−	0.773852i	$-0.718327\pi$
$269$	2.30415	−	2.30415i	0.140486	−	0.140486i	0.773852	+	0.633366i	$0.218327\pi$
$270$			0.964064i			0.0586711i
$271$	−14.3107	+	14.3107i	−0.869311	+	0.869311i	−0.992396	−	0.123085i	$-0.960721\pi$
$271$	−14.3107	+	14.3107i	−0.869311	+	0.869311i	0.123085	+	0.992396i	$0.460721\pi$
$272$	4.23210	+	4.23210i	0.256609	+	0.256609i
$273$	1.50260	−	4.13849i	0.0909416	−	0.250473i
$274$			8.40854i			0.507978i
$275$	−4.13629	+	4.13629i	−0.249428	+	0.249428i
$276$	−1.68209	+	1.68209i	−0.101250	+	0.101250i
$277$	28.9309			1.73829			0.869145	−	0.494558i	$-0.164670\pi$
$277$	28.9309			1.73829			0.869145	+	0.494558i	$0.164670\pi$
$278$	1.59690	+	1.59690i	0.0957758	+	0.0957758i
$279$	−2.45149	+	2.45149i	−0.146767	+	0.146767i
$280$	0.870495	−	2.39754i	0.0520220	−	0.143280i
$281$	15.0360			0.896974			0.448487	−	0.893789i	$-0.351963\pi$
$281$	15.0360			0.896974			0.448487	+	0.893789i	$0.351963\pi$
$282$	−4.08757	+	4.08757i	−0.243411	+	0.243411i
$283$	−8.71282			−0.517923			−0.258962	−	0.965888i	$-0.583380\pi$
$283$	−8.71282			−0.517923			−0.258962	+	0.965888i	$0.583380\pi$
$284$	10.6464			0.631749
$285$			0.272859i			0.0161628i
$286$		−	2.39140i		−	0.141407i
$287$	−22.9965	−	8.34953i	−1.35744	−	0.492857i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$			18.8213i			1.10713i
$290$	−4.17125	−	3.09093i	−0.244944	−	0.181506i
$291$	−9.29418			−0.544834
$292$	9.08410	+	9.08410i	0.531606	+	0.531606i
$293$	−12.7513	−	12.7513i	−0.744940	−	0.744940i	0.228584	−	0.973524i	$-0.426590\pi$
$293$	−12.7513	−	12.7513i	−0.744940	−	0.744940i	−0.973524	+	0.228584i	$0.926590\pi$
$294$	−4.49107	+	5.36939i	−0.261924	+	0.313149i
$295$		−	12.0157i		−	0.699580i
$296$		−	3.61676i		−	0.210220i
$297$		−	1.43704i		−	0.0833856i
$298$	7.88939	+	7.88939i	0.457020	+	0.457020i
$299$	−3.95866			−0.228935
$300$	2.87833	−	2.87833i	0.166181	−	0.166181i
$301$	20.4296	+	7.41758i	1.17755	+	0.427542i
$302$	5.45470	+	5.45470i	0.313882	+	0.313882i
$303$			12.8071i			0.735747i
$304$	0.200133	+	0.200133i	0.0114784	+	0.0114784i
$305$	−0.242963	−	0.242963i	−0.0139120	−	0.0139120i
$306$			5.98509i			0.342145i
$307$	−17.0684	−	17.0684i	−0.974147	−	0.974147i	0.0255270	−	0.999674i	$-0.491874\pi$
$307$	−17.0684	−	17.0684i	−0.974147	−	0.974147i	−0.999674	+	0.0255270i	$0.991874\pi$
$308$	−1.29757	+	3.57379i	−0.0739358	+	0.203635i
$309$	4.24495	−	4.24495i	0.241487	−	0.241487i
$310$	−3.34234			−0.189832
$311$	10.0030	+	10.0030i	0.567216	+	0.567216i	0.931347	−	0.364132i	$-0.118634\pi$
$311$	10.0030	+	10.0030i	0.567216	+	0.567216i	−0.364132	+	0.931347i	$0.618634\pi$
$312$			1.66411i			0.0942120i
$313$			10.7799i			0.609315i	0.952462	+	0.304658i	$0.0985421\pi$
$313$			10.7799i			0.609315i	−0.952462	+	0.304658i	$0.901458\pi$
$314$		−	9.37413i		−	0.529012i
$315$	2.31085	−	1.07978i	0.130201	−	0.0608387i
$316$	5.16289	+	5.16289i	0.290435	+	0.290435i
$317$	−10.7710	−	10.7710i	−0.604958	−	0.604958i	0.336666	−	0.941624i	$-0.390701\pi$
$317$	−10.7710	−	10.7710i	−0.604958	−	0.604958i	−0.941624	+	0.336666i	$0.890701\pi$
$318$	−12.0147			−0.673753
$319$	6.21770	+	4.60737i	0.348124	+	0.257963i
$320$			0.964064i			0.0538928i
$321$	−4.05879	−	4.05879i	−0.226540	−	0.226540i
$322$	5.91594	+	2.14795i	0.329682	+	0.119701i
$323$			1.69396i			0.0942546i
$324$			1.00000i			0.0555556i
$325$	6.77391			0.375749
$326$	1.69749			0.0940153
$327$	−8.88232	+	8.88232i	−0.491194	+	0.491194i
$328$	9.24702			0.510581
$329$	14.3760	+	5.21964i	0.792576	+	0.287768i
$330$	0.979626	−	0.979626i	0.0539266	−	0.0539266i
$331$	16.9128	+	16.9128i	0.929613	+	0.929613i	0.997681	−	0.0680677i	$-0.0216834\pi$
$331$	16.9128	+	16.9128i	0.929613	+	0.929613i	−0.0680677	+	0.997681i	$0.521683\pi$
$332$	−8.98566			−0.493152
$333$	2.55744	−	2.55744i	0.140147	−	0.140147i
$334$	2.53480	−	2.53480i	0.138698	−	0.138698i
$335$		−	0.423727i		−	0.0231507i
$336$	0.902943	−	2.48690i	0.0492596	−	0.135672i
$337$	−17.1735	−	17.1735i	−0.935498	−	0.935498i	0.0625441	−	0.998042i	$-0.480079\pi$
$337$	−17.1735	−	17.1735i	−0.935498	−	0.935498i	−0.998042	+	0.0625441i	$0.980079\pi$
$338$	7.23421	−	7.23421i	0.393489	−	0.393489i
$339$			20.1941i			1.09679i
$340$	−4.08001	+	4.08001i	−0.221270	+	0.221270i
$341$	4.98212			0.269797
$342$			0.283030i			0.0153045i
$343$	17.9005	+	4.75114i	0.966534	+	0.256538i
$344$	−8.21489			−0.442917
$345$	−1.62164	−	1.62164i	−0.0873064	−	0.0873064i
$346$	−7.95423	+	7.95423i	−0.427622	+	0.427622i
$347$			19.0608i			1.02324i	0.859212	+	0.511619i	$0.170954\pi$
$347$			19.0608i			1.02324i	−0.859212	+	0.511619i	$0.829046\pi$
$348$	−4.32673	−	3.20615i	−0.231937	−	0.171868i
$349$		−	6.14089i		−	0.328714i	−0.986401	−	0.164357i	$-0.947445\pi$
$349$		−	6.14089i		−	0.328714i	0.986401	−	0.164357i	$-0.0525550\pi$
$350$	−10.1231	−	3.67550i	−0.541105	−	0.196464i
$351$	−1.17671	+	1.17671i	−0.0628080	+	0.0628080i
$352$		−	1.43704i		−	0.0765946i
$353$	20.8953			1.11214			0.556072	−	0.831134i	$-0.312308\pi$
$353$	20.8953			1.11214			0.556072	+	0.831134i	$0.312308\pi$
$354$		−	12.4636i		−	0.662432i
$355$			10.2638i			0.544748i
$356$	−7.53183	+	7.53183i	−0.399186	+	0.399186i
$357$	14.3462	−	6.70348i	0.759280	−	0.354786i
$358$	−7.17662	−	7.17662i	−0.379296	−	0.379296i
$359$	13.1158	−	13.1158i	0.692228	−	0.692228i	−0.270494	−	0.962722i	$-0.587187\pi$
$359$	13.1158	−	13.1158i	0.692228	−	0.692228i	0.962722	+	0.270494i	$0.0871870\pi$
$360$	−0.681696	+	0.681696i	−0.0359285	+	0.0359285i
$361$		−	18.9199i		−	0.995784i
$362$	−2.73697	−	2.73697i	−0.143852	−	0.143852i
$363$	6.31794	−	6.31794i	0.331606	−	0.331606i
$364$	3.98886	−	1.86386i	0.209073	−	0.0976927i
$365$	−8.75765	+	8.75765i	−0.458396	+	0.458396i
$366$	−0.252020	−	0.252020i	−0.0131733	−	0.0131733i
$367$	−7.78965	−	7.78965i	−0.406616	−	0.406616i	0.473940	−	0.880557i	$-0.342831\pi$
$367$	−7.78965	−	7.78965i	−0.406616	−	0.406616i	−0.880557	+	0.473940i	$0.842831\pi$
$368$	−2.37884			−0.124005
$369$	6.53863	+	6.53863i	0.340388	+	0.340388i
$370$	3.48679			0.181269
$371$	13.4569	+	28.7992i	0.698646	+	1.49518i
$372$	−3.46692			−0.179752
$373$	−17.8557			−0.924535			−0.462268	−	0.886740i	$-0.652964\pi$
$373$	−17.8557			−0.924535			−0.462268	+	0.886740i	$0.652964\pi$
$374$	6.08170	−	6.08170i	0.314477	−	0.314477i
$375$	6.18338	+	6.18338i	0.319308	+	0.319308i
$376$	−5.78069			−0.298116
$377$	−1.31860	−	8.86399i	−0.0679113	−	0.456519i
$378$	2.39698	−	1.12003i	0.123288	−	0.0576081i
$379$	−5.41892	+	5.41892i	−0.278351	+	0.278351i	−0.832451	−	0.554099i	$-0.813063\pi$
$379$	−5.41892	+	5.41892i	−0.278351	+	0.278351i	0.554099	+	0.832451i	$0.313063\pi$
$380$	−0.192941	+	0.192941i	−0.00989765	+	0.00989765i
$381$	4.52674			0.231912
$382$			13.3543i			0.683265i
$383$	−10.5121			−0.537143			−0.268572	−	0.963260i	$-0.586552\pi$
$383$	−10.5121			−0.537143			−0.268572	+	0.963260i	$0.586552\pi$
$384$			1.00000i			0.0510310i
$385$	−3.44536	−	1.25094i	−0.175592	−	0.0637537i
$386$		−	11.3094i		−	0.575634i
$387$	−5.80881	−	5.80881i	−0.295278	−	0.295278i
$388$	−6.57198	−	6.57198i	−0.333642	−	0.333642i
$389$	2.21704	+	2.21704i	0.112408	+	0.112408i	0.761074	−	0.648665i	$-0.224672\pi$
$389$	2.21704	+	2.21704i	0.112408	+	0.112408i	−0.648665	+	0.761074i	$0.724672\pi$
$390$	−1.60431			−0.0812376
$391$	−10.0675	−	10.0675i	−0.509134	−	0.509134i
$392$	−6.97239	+	0.621066i	−0.352159	+	0.0313686i
$393$	10.9775			0.553743
$394$	−9.00003	+	9.00003i	−0.453415	+	0.453415i
$395$	−4.97736	+	4.97736i	−0.250438	+	0.250438i
$396$	1.01614	−	1.01614i	0.0510631	−	0.0510631i
$397$			11.4076i			0.572532i	0.958150	+	0.286266i	$0.0924141\pi$
$397$			11.4076i			0.572532i	−0.958150	+	0.286266i	$0.907586\pi$
$398$	15.5243	+	15.5243i	0.778160	+	0.778160i
$399$	0.678419	−	0.317002i	0.0339635	−	0.0158700i
$400$	4.07058			0.203529
$401$	25.2084			1.25885			0.629424	−	0.777062i	$-0.283291\pi$
$401$	25.2084			1.25885			0.629424	+	0.777062i	$0.283291\pi$
$402$		−	0.439521i		−	0.0219213i
$403$	−4.07955	−	4.07955i	−0.203217	−	0.203217i
$404$	−9.05597	+	9.05597i	−0.450551	+	0.450551i
$405$	−0.964064			−0.0479047
$406$	−2.83902	+	13.9621i	−0.140898	+	0.692927i
$407$	−5.19743			−0.257627
$408$	−4.23210	+	4.23210i	−0.209520	+	0.209520i
$409$	−25.7643	−	25.7643i	−1.27396	−	1.27396i	−0.943990	−	0.329974i	$-0.892960\pi$
$409$	−25.7643	−	25.7643i	−1.27396	−	1.27396i	−0.329974	−	0.943990i	$-0.607040\pi$
$410$			8.91472i			0.440267i
$411$	−8.40854			−0.414762
$412$	6.00327			0.295760
$413$	−29.8750	+	13.9596i	−1.47005	+	0.686906i
$414$	−1.68209	−	1.68209i	−0.0826703	−	0.0826703i
$415$		−	8.66275i		−	0.425238i
$416$	−1.17671	+	1.17671i	−0.0576928	+	0.0576928i
$417$	−1.59690	+	1.59690i	−0.0782006	+	0.0782006i
$418$	0.287599	−	0.287599i	0.0140669	−	0.0140669i
$419$	−35.2790			−1.72349			−0.861746	−	0.507340i	$-0.830629\pi$
$419$	−35.2790			−1.72349			−0.861746	+	0.507340i	$0.830629\pi$
$420$	2.39754	+	0.870495i	0.116988	+	0.0424758i
$421$	−2.48282	−	2.48282i	−0.121005	−	0.121005i	0.644011	−	0.765016i	$-0.277269\pi$
$421$	−2.48282	−	2.48282i	−0.121005	−	0.121005i	−0.765016	+	0.644011i	$0.777269\pi$
$422$	−23.7966			−1.15840
$423$	−4.08757	−	4.08757i	−0.198744	−	0.198744i
$424$	−8.49571	−	8.49571i	−0.412588	−	0.412588i
$425$	17.2271	+	17.2271i	0.835637	+	0.835637i
$426$			10.6464i			0.515821i
$427$	−0.321818	+	0.886358i	−0.0155739	+	0.0428939i
$428$		−	5.74000i		−	0.277453i
$429$	2.39140			0.115458
$430$		−	7.91968i		−	0.381921i
$431$	15.7376			0.758054			0.379027	−	0.925386i	$-0.376259\pi$
$431$	15.7376			0.758054			0.379027	+	0.925386i	$0.376259\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	12.3276	−	12.3276i	0.592427	−	0.592427i	−0.345860	−	0.938286i	$-0.612413\pi$
$433$	12.3276	−	12.3276i	0.592427	−	0.592427i	0.938286	+	0.345860i	$0.112413\pi$
$434$	3.88306	+	8.31016i	0.186393	+	0.398901i
$435$	3.09093	−	4.17125i	0.148199	−	0.199996i
$436$	−12.5615			−0.601587
$437$	−0.476083	−	0.476083i	−0.0227741	−	0.0227741i
$438$	−9.08410	+	9.08410i	−0.434055	+	0.434055i
$439$	26.3216			1.25626			0.628131	−	0.778108i	$-0.283820\pi$
$439$	26.3216			1.25626			0.628131	+	0.778108i	$0.283820\pi$
$440$	1.38540			0.0660464
$441$	−5.36939	−	4.49107i	−0.255685	−	0.213860i
$442$	−9.95988			−0.473743
$443$	16.9914	+	16.9914i	0.807287	+	0.807287i	0.984222	−	0.176936i	$-0.0566185\pi$
$443$	16.9914	+	16.9914i	0.807287	+	0.807287i	−0.176936	+	0.984222i	$0.556618\pi$
$444$	3.61676			0.171644
$445$	−7.26117	−	7.26117i	−0.344212	−	0.344212i
$446$	8.10576	+	8.10576i	0.383819	+	0.383819i
$447$	−7.88939	+	7.88939i	−0.373156	+	0.373156i
$448$	2.39698	−	1.12003i	0.113247	−	0.0529164i
$449$	−19.8245	+	19.8245i	−0.935575	+	0.935575i	−0.998047	−	0.0624716i	$-0.980102\pi$
$449$	−19.8245	+	19.8245i	−0.935575	+	0.935575i	0.0624716	+	0.998047i	$0.480102\pi$
$450$	2.87833	+	2.87833i	0.135686	+	0.135686i
$451$		−	13.2884i		−	0.625724i
$452$	−14.2794	+	14.2794i	−0.671647	+	0.671647i
$453$	−5.45470	+	5.45470i	−0.256284	+	0.256284i
$454$	4.69478	+	4.69478i	0.220337	+	0.220337i
$455$	1.79688	+	3.84551i	0.0842390	+	0.180280i
$456$	−0.200133	+	0.200133i	−0.00937207	+	0.00937207i
$457$		−	15.5388i		−	0.726875i	−0.931619	−	0.363437i	$-0.881603\pi$
$457$		−	15.5388i		−	0.726875i	0.931619	−	0.363437i	$-0.118397\pi$
$458$		−	17.1180i		−	0.799872i
$459$	−5.98509			−0.279360
$460$		−	2.29335i		−	0.106928i
$461$	8.39366	−	8.39366i	0.390932	−	0.390932i	−0.484088	−	0.875019i	$-0.660848\pi$
$461$	8.39366	−	8.39366i	0.390932	−	0.390932i	0.875019	+	0.484088i	$0.160848\pi$
$462$	−3.57379	−	1.29757i	−0.166268	−	0.0603683i
$463$		−	33.7822i		−	1.56999i	−0.619500	−	0.784997i	$-0.712665\pi$
$463$		−	33.7822i		−	1.56999i	0.619500	−	0.784997i	$-0.287335\pi$
$464$	−0.792373	−	5.32655i	−0.0367850	−	0.247279i
$465$		−	3.34234i		−	0.154997i
$466$	−7.67843	+	7.67843i	−0.355697	+	0.355697i
$467$	−7.67724	−	7.67724i	−0.355260	−	0.355260i	0.506802	−	0.862062i	$-0.330828\pi$
$467$	−7.67724	−	7.67724i	−0.355260	−	0.355260i	−0.862062	+	0.506802i	$0.830828\pi$
$468$	−1.66411			−0.0769237
$469$	−1.05353	+	0.492277i	−0.0486473	+	0.0227312i
$470$		−	5.57296i		−	0.257061i
$471$	9.37413			0.431937
$472$	8.81308	−	8.81308i	0.405655	−	0.405655i
$473$			11.8051i			0.542801i
$474$	−5.16289	+	5.16289i	−0.237139	+	0.237139i
$475$	0.814656	+	0.814656i	0.0373790	+	0.0373790i
$476$	14.8843	+	5.40420i	0.682223	+	0.247701i
$477$		−	12.0147i		−	0.550117i
$478$	−14.3456	+	14.3456i	−0.656152	+	0.656152i
$479$	26.1341	−	26.1341i	1.19410	−	1.19410i	0.218189	−	0.975906i	$-0.429985\pi$
$479$	26.1341	−	26.1341i	1.19410	−	1.19410i	0.975906	−	0.218189i	$-0.0700150\pi$
$480$	−0.964064			−0.0440033
$481$	4.25587	+	4.25587i	0.194051	+	0.194051i
$482$	−14.6450	+	14.6450i	−0.667061	+	0.667061i
$483$	−2.14795	+	5.91594i	−0.0977353	+	0.269185i
$484$	8.93491			0.406132
$485$	6.33581	−	6.33581i	0.287694	−	0.287694i
$486$	−1.00000			−0.0453609
$487$	39.9490			1.81026			0.905131	−	0.425133i	$-0.139773\pi$
$487$	39.9490			1.81026			0.905131	+	0.425133i	$0.139773\pi$
$488$		−	0.356410i		−	0.0161339i
$489$			1.69749i			0.0767632i
$490$	−0.598748	−	6.72183i	−0.0270487	−	0.303662i
$491$	−23.2695	−	23.2695i	−1.05014	−	1.05014i	−0.998675	−	0.0514649i	$-0.983611\pi$
$491$	−23.2695	−	23.2695i	−1.05014	−	1.05014i	−0.0514649	−	0.998675i	$-0.516389\pi$
$492$			9.24702i			0.416888i
$493$	19.1891	−	25.8959i	0.864233	−	1.16629i
$494$	−0.470995			−0.0211911
$495$	0.979626	+	0.979626i	0.0440309	+	0.0440309i
$496$	−2.45149	−	2.45149i	−0.110075	−	0.110075i
$497$	25.5193	−	11.9243i	1.14470	−	0.534879i
$498$		−	8.98566i		−	0.402657i
$499$		−	30.6018i		−	1.36992i	−0.728579	−	0.684962i	$-0.759819\pi$
$499$		−	30.6018i		−	1.36992i	0.728579	−	0.684962i	$-0.240181\pi$
$500$			8.74462i			0.391071i
$501$	2.53480	+	2.53480i	0.113246	+	0.113246i
$502$	−17.2972			−0.772010
$503$	11.5060	−	11.5060i	0.513029	−	0.513029i	−0.402424	−	0.915453i	$-0.631832\pi$
$503$	11.5060	−	11.5060i	0.513029	−	0.513029i	0.915453	+	0.402424i	$0.131832\pi$
$504$	2.48690	+	0.902943i	0.110776	+	0.0402203i
$505$	−8.73053	−	8.73053i	−0.388504	−	0.388504i
$506$			3.41849i			0.151970i
$507$	7.23421	+	7.23421i	0.321283	+	0.321283i
$508$	3.20089	+	3.20089i	0.142016	+	0.142016i
$509$		−	15.0180i		−	0.665661i	−0.942987	−	0.332830i	$-0.891996\pi$
$509$		−	15.0180i		−	0.665661i	0.942987	−	0.332830i	$-0.108004\pi$
$510$	−4.08001	−	4.08001i	−0.180666	−	0.180666i
$511$	31.9489	+	11.6000i	1.41334	+	0.513153i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−0.283030			−0.0124961
$514$	−8.40516	−	8.40516i	−0.370736	−	0.370736i
$515$			5.78754i			0.255029i
$516$		−	8.21489i		−	0.361640i
$517$			8.30710i			0.365346i
$518$	−4.05088	−	8.66932i	−0.177985	−	0.380908i
$519$	−7.95423	−	7.95423i	−0.349152	−	0.349152i
$520$	−1.13442	−	1.13442i	−0.0497476	−	0.0497476i
$521$	−27.4497			−1.20259			−0.601296	−	0.799027i	$-0.705349\pi$
$521$	−27.4497			−1.20259			−0.601296	+	0.799027i	$0.705349\pi$
$522$	3.20615	−	4.32673i	0.140329	−	0.189376i
$523$		−	21.2786i		−	0.930450i	−0.885193	−	0.465225i	$-0.845973\pi$
$523$		−	21.2786i		−	0.930450i	0.885193	−	0.465225i	$-0.154027\pi$
$524$	7.76228	+	7.76228i	0.339097	+	0.339097i
$525$	3.67550	−	10.1231i	0.160412	−	0.441810i
$526$			15.4303i			0.672793i
$527$		−	20.7499i		−	0.903878i
$528$	1.43704			0.0625392
$529$	−17.3411			−0.753963
$530$	8.19041	−	8.19041i	0.355768	−	0.355768i
$531$	12.4636			0.540873
$532$	0.703870	+	0.255560i	0.0305166	+	0.0110799i
$533$	−10.8810	+	10.8810i	−0.471310	+	0.471310i
$534$	−7.53183	−	7.53183i	−0.325934	−	0.325934i
$535$	5.53373			0.239244
$536$	0.310789	−	0.310789i	0.0134240	−	0.0134240i
$537$	7.17662	−	7.17662i	0.309694	−	0.309694i
$538$			3.25855i			0.140486i
$539$	0.892498	+	10.0196i	0.0384426	+	0.431576i
$540$	−0.681696	−	0.681696i	−0.0293355	−	0.0293355i
$541$	−16.8886	+	16.8886i	−0.726098	+	0.726098i	−0.969840	−	0.243742i	$-0.921625\pi$
$541$	−16.8886	+	16.8886i	−0.726098	+	0.726098i	0.243742	+	0.969840i	$0.421625\pi$
$542$		−	20.2383i		−	0.869311i
$543$	2.73697	−	2.73697i	0.117455	−	0.117455i
$544$	−5.98509			−0.256609
$545$		−	12.1101i		−	0.518739i
$546$	1.86386	+	3.98886i	0.0797658	+	0.170707i
$547$	−14.8657			−0.635613			−0.317806	−	0.948156i	$-0.602946\pi$
$547$	−14.8657			−0.635613			−0.317806	+	0.948156i	$0.602946\pi$
$548$	−5.94573	−	5.94573i	−0.253989	−	0.253989i
$549$	0.252020	−	0.252020i	0.0107560	−	0.0107560i
$550$		−	5.84959i		−	0.249428i
$551$	0.907437	−	1.22460i	0.0386581	−	0.0521696i
$552$		−	2.37884i		−	0.101250i
$553$	18.1579	+	6.59277i	0.772155	+	0.280353i
$554$	−20.4572	+	20.4572i	−0.869145	+	0.869145i
$555$			3.48679i			0.148006i
$556$	−2.25836			−0.0957758
$557$		−	19.5606i		−	0.828811i	−0.910092	−	0.414406i	$-0.863990\pi$
$557$		−	19.5606i		−	0.828811i	0.910092	−	0.414406i	$-0.136010\pi$
$558$		−	3.46692i		−	0.146767i
$559$	9.66652	−	9.66652i	0.408850	−	0.408850i
$560$	1.07978	+	2.31085i	0.0456291	+	0.0976511i
$561$	6.08170	+	6.08170i	0.256770	+	0.256770i
$562$	−10.6321	+	10.6321i	−0.448487	+	0.448487i
$563$	23.7395	−	23.7395i	1.00050	−	1.00050i	0.000501710	−	1.00000i	$-0.499840\pi$
$563$	23.7395	−	23.7395i	1.00050	−	1.00050i	1.00000		0.000501710i	$-0.000159699\pi$
$564$		−	5.78069i		−	0.243411i
$565$	−13.7663	−	13.7663i	−0.579151	−	0.579151i
$566$	6.16090	−	6.16090i	0.258962	−	0.258962i
$567$	1.12003	+	2.39698i	0.0470368	+	0.100664i
$568$	−7.52816	+	7.52816i	−0.315875	+	0.315875i
$569$	−15.8417	−	15.8417i	−0.664120	−	0.664120i	0.292228	−	0.956349i	$-0.405603\pi$
$569$	−15.8417	−	15.8417i	−0.664120	−	0.664120i	−0.956349	+	0.292228i	$0.905603\pi$
$570$	−0.192941	−	0.192941i	−0.00808140	−	0.00808140i
$571$	16.1487			0.675801			0.337900	−	0.941182i	$-0.390283\pi$
$571$	16.1487			0.675801			0.337900	+	0.941182i	$0.390283\pi$
$572$	1.69098	+	1.69098i	0.0707033	+	0.0707033i
$573$	−13.3543			−0.557883
$574$	22.1650	−	10.3569i	0.925148	−	0.432290i
$575$	−9.68324			−0.403819
$576$	−1.00000			−0.0416667
$577$	−13.1093	+	13.1093i	−0.545746	+	0.545746i	−0.925208	−	0.379461i	$-0.876109\pi$
$577$	−13.1093	+	13.1093i	−0.545746	+	0.545746i	0.379461	+	0.925208i	$0.376109\pi$
$578$	−13.3087	−	13.3087i	−0.553567	−	0.553567i
$579$	11.3094			0.470003
$580$	5.13514	−	0.763898i	0.213225	−	0.0317192i
$581$	−21.5385	+	10.0642i	−0.893567	+	0.417533i
$582$	6.57198	−	6.57198i	0.272417	−	0.272417i
$583$	−12.2087	+	12.2087i	−0.505632	+	0.505632i
$584$	−12.8469			−0.531606
$585$		−	1.60431i		−	0.0663302i
$586$	18.0331			0.744940
$587$			3.73659i			0.154225i	0.997022	+	0.0771127i	$0.0245701\pi$
$587$			3.73659i			0.154225i	−0.997022	+	0.0771127i	$0.975430\pi$
$588$	−0.621066	−	6.97239i	−0.0256123	−	0.287537i
$589$		−	0.981245i		−	0.0404315i
$590$	8.49637	+	8.49637i	0.349790	+	0.349790i
$591$	−9.00003	−	9.00003i	−0.370212	−	0.370212i
$592$	2.55744	+	2.55744i	0.105110	+	0.105110i
$593$	21.6595			0.889448			0.444724	−	0.895668i	$-0.353302\pi$
$593$	21.6595			0.889448			0.444724	+	0.895668i	$0.353302\pi$
$594$	1.01614	+	1.01614i	0.0416928	+	0.0416928i
$595$	−5.20999	+	14.3495i	−0.213589	+	0.588271i
$596$	−11.1573			−0.457020
$597$	−15.5243	+	15.5243i	−0.635365	+	0.635365i
$598$	2.79919	−	2.79919i	0.114468	−	0.114468i
$599$	−17.8000	+	17.8000i	−0.727288	+	0.727288i	−0.970079	−	0.242790i	$-0.921937\pi$
$599$	−17.8000	+	17.8000i	−0.727288	+	0.727288i	0.242790	+	0.970079i	$0.421937\pi$
$600$			4.07058i			0.166181i
$601$	−11.9411	−	11.9411i	−0.487089	−	0.487089i	0.420298	−	0.907386i	$-0.361926\pi$
$601$	−11.9411	−	11.9411i	−0.487089	−	0.487089i	−0.907386	+	0.420298i	$0.861926\pi$
$602$	−19.6910	+	9.20092i	−0.802544	+	0.375002i
$603$	0.439521			0.0178987
$604$	−7.71410			−0.313882
$605$			8.61383i			0.350202i
$606$	−9.05597	−	9.05597i	−0.367874	−	0.367874i
$607$	−23.3502	+	23.3502i	−0.947756	+	0.947756i	−0.998701	−	0.0509456i	$-0.983777\pi$
$607$	−23.3502	+	23.3502i	−0.947756	+	0.947756i	0.0509456	+	0.998701i	$0.483777\pi$
$608$	−0.283030			−0.0114784
$609$	−13.9621	−	2.83902i	−0.565772	−	0.115043i
$610$	0.343602			0.0139120
$611$	6.80218	−	6.80218i	0.275187	−	0.275187i
$612$	−4.23210	−	4.23210i	−0.171072	−	0.171072i
$613$		−	27.3874i		−	1.10617i	−0.833125	−	0.553084i	$-0.813451\pi$
$613$		−	27.3874i		−	1.10617i	0.833125	−	0.553084i	$-0.186549\pi$
$614$	24.1384			0.974147
$615$	−8.91472			−0.359476
$616$	−1.60953	−	3.44457i	−0.0648498	−	0.138786i
$617$	17.6926	+	17.6926i	0.712276	+	0.712276i	0.967011	−	0.254735i	$-0.0819883\pi$
$617$	17.6926	+	17.6926i	0.712276	+	0.712276i	−0.254735	+	0.967011i	$0.581988\pi$
$618$			6.00327i			0.241487i
$619$	5.85980	−	5.85980i	0.235525	−	0.235525i	−0.579469	−	0.814994i	$-0.696740\pi$
$619$	5.85980	−	5.85980i	0.235525	−	0.235525i	0.814994	+	0.579469i	$0.196740\pi$
$620$	2.36339	−	2.36339i	0.0949160	−	0.0949160i
$621$	1.68209	−	1.68209i	0.0675000	−	0.0675000i
$622$	−14.1463			−0.567216
$623$	−9.61780	+	26.4895i	−0.385329	+	1.06128i
$624$	−1.17671	−	1.17671i	−0.0471060	−	0.0471060i
$625$	11.9225			0.476901
$626$	−7.62253	−	7.62253i	−0.304658	−	0.304658i
$627$	0.287599	+	0.287599i	0.0114856	+	0.0114856i
$628$	6.62851	+	6.62851i	0.264506	+	0.264506i
$629$			21.6466i			0.863108i
$630$	−0.870495	+	2.39754i	−0.0346814	+	0.0955201i
$631$		−	33.9510i		−	1.35157i	−0.737100	−	0.675784i	$-0.763805\pi$
$631$		−	33.9510i		−	1.35157i	0.737100	−	0.675784i	$-0.236195\pi$
$632$	−7.30143			−0.290435
$633$		−	23.7966i		−	0.945830i
$634$	15.2325			0.604958
$635$	−3.08586	+	3.08586i	−0.122459	+	0.122459i
$636$	8.49571	−	8.49571i	0.336877	−	0.336877i
$637$	7.47365	−	8.93528i	0.296117	−	0.354029i
$638$	−7.65448	+	1.13867i	−0.303044	+	0.0450805i
$639$	−10.6464			−0.421166
$640$	−0.681696	−	0.681696i	−0.0269464	−	0.0269464i
$641$	12.1238	−	12.1238i	0.478861	−	0.478861i	−0.425906	−	0.904767i	$-0.640045\pi$
$641$	12.1238	−	12.1238i	0.478861	−	0.478861i	0.904767	+	0.425906i	$0.140045\pi$
$642$	5.74000			0.226540
$643$	−32.3297			−1.27496			−0.637480	−	0.770467i	$-0.720023\pi$
$643$	−32.3297			−1.27496			−0.637480	+	0.770467i	$0.720023\pi$
$644$	−5.70203	+	2.66437i	−0.224692	+	0.104991i
$645$	7.91968			0.311837
$646$	−1.19781	−	1.19781i	−0.0471273	−	0.0471273i
$647$	7.49764			0.294763			0.147381	−	0.989080i	$-0.452916\pi$
$647$	7.49764			0.294763			0.147381	+	0.989080i	$0.452916\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	−12.6648	−	12.6648i	−0.497136	−	0.497136i
$650$	−4.78988	+	4.78988i	−0.187875	+	0.187875i
$651$	−8.31016	+	3.88306i	−0.325701	+	0.152189i
$652$	−1.20031	+	1.20031i	−0.0470077	+	0.0470077i
$653$	−19.3186	−	19.3186i	−0.755997	−	0.755997i	0.219595	−	0.975591i	$-0.429527\pi$
$653$	−19.3186	−	19.3186i	−0.755997	−	0.755997i	−0.975591	+	0.219595i	$0.929527\pi$
$654$		−	12.5615i		−	0.491194i
$655$	−7.48334	+	7.48334i	−0.292398	+	0.292398i
$656$	−6.53863	+	6.53863i	−0.255291	+	0.255291i
$657$	−9.08410	−	9.08410i	−0.354404	−	0.354404i
$658$	−13.8562	+	6.47455i	−0.540172	+	0.252404i
$659$	−19.2863	+	19.2863i	−0.751286	+	0.751286i	−0.974719	−	0.223433i	$-0.928274\pi$
$659$	−19.2863	+	19.2863i	−0.751286	+	0.751286i	0.223433	+	0.974719i	$0.428274\pi$
$660$			1.38540i			0.0539266i
$661$			40.2924i			1.56719i	0.621269	+	0.783597i	$0.286617\pi$
$661$			40.2924i			1.56719i	−0.621269	+	0.783597i	$0.713383\pi$
$662$	−23.9183			−0.929613
$663$		−	9.95988i		−	0.386810i
$664$	6.35382	−	6.35382i	0.246576	−	0.246576i
$665$	−0.246377	+	0.678575i	−0.00955407	+	0.0263140i
$666$			3.61676i			0.140147i
$667$	1.88493	+	12.6710i	0.0729846	+	0.490623i
$668$			3.58474i			0.138698i
$669$	−8.10576	+	8.10576i	−0.313387	+	0.313387i
$670$	0.299620	+	0.299620i	0.0115753	+	0.0115753i
$671$	−0.512176			−0.0197723
$672$	1.12003	+	2.39698i	0.0432061	+	0.0924657i
$673$		−	27.3159i		−	1.05295i	−0.850190	−	0.526476i	$-0.823513\pi$
$673$		−	27.3159i		−	1.05295i	0.850190	−	0.526476i	$-0.176487\pi$
$674$	24.2869			0.935498
$675$	−2.87833	+	2.87833i	−0.110787	+	0.110787i
$676$			10.2307i			0.393489i
$677$	7.13492	−	7.13492i	0.274217	−	0.274217i	−0.556578	−	0.830795i	$-0.687886\pi$
$677$	7.13492	−	7.13492i	0.274217	−	0.274217i	0.830795	+	0.556578i	$0.187886\pi$
$678$	−14.2794	−	14.2794i	−0.548397	−	0.548397i
$679$	−23.1137	−	8.39211i	−0.887024	−	0.322060i
$680$		−	5.77001i		−	0.221270i
$681$	−4.69478	+	4.69478i	−0.179904	+	0.179904i
$682$	−3.52289	+	3.52289i	−0.134898	+	0.134898i
$683$	5.42689			0.207654			0.103827	−	0.994595i	$-0.466891\pi$
$683$	5.42689			0.207654			0.103827	+	0.994595i	$0.466891\pi$
$684$	−0.200133	−	0.200133i	−0.00765227	−	0.00765227i
$685$	5.73207	−	5.73207i	0.219011	−	0.219011i
$686$	−16.0171	+	9.29797i	−0.611536	+	0.354998i
$687$	17.1180			0.653093
$688$	5.80881	−	5.80881i	0.221459	−	0.221459i
$689$	19.9939			0.761707
$690$	2.29335			0.0873064
$691$		−	29.3076i		−	1.11492i	−0.830205	−	0.557458i	$-0.811777\pi$
$691$		−	29.3076i		−	1.11492i	0.830205	−	0.557458i	$-0.188223\pi$
$692$		−	11.2490i		−	0.427622i
$693$	1.29757	−	3.57379i	0.0492905	−	0.135757i
$694$	−13.4780	−	13.4780i	−0.511619	−	0.511619i
$695$		−	2.17720i		−	0.0825860i
$696$	5.32655	−	0.792373i	0.201902	−	0.0300348i
$697$	−55.3442			−2.09631
$698$	4.34227	+	4.34227i	0.164357	+	0.164357i
$699$	−7.67843	−	7.67843i	−0.290425	−	0.290425i
$700$	9.75712	−	4.55917i	0.368784	−	0.172320i
$701$		−	1.53161i		−	0.0578482i	−0.999582	−	0.0289241i	$-0.990792\pi$
$701$		−	1.53161i		−	0.0578482i	0.999582	−	0.0289241i	$-0.00920812\pi$
$702$		−	1.66411i		−	0.0628080i
$703$			1.02365i			0.0386078i
$704$	1.01614	+	1.01614i	0.0382973	+	0.0382973i
$705$	5.57296			0.209890
$706$	−14.7752	+	14.7752i	−0.556072	+	0.556072i
$707$	−11.5641	+	31.8500i	−0.434911	+	1.19784i
$708$	8.81308	+	8.81308i	0.331216	+	0.331216i
$709$			39.9169i			1.49911i	0.661941	+	0.749556i	$0.269733\pi$
$709$			39.9169i			1.49911i	−0.661941	+	0.749556i	$0.730267\pi$
$710$	−7.25763	−	7.25763i	−0.272374	−	0.272374i
$711$	−5.16289	−	5.16289i	−0.193623	−	0.193623i
$712$		−	10.6516i		−	0.399186i
$713$	5.83168	+	5.83168i	0.218398	+	0.218398i
$714$	−5.40420	+	14.8843i	−0.202247	+	0.557033i
$715$	−1.63021	+	1.63021i	−0.0609664	+	0.0609664i
$716$	10.1493			0.379296
$717$	−14.3456	−	14.3456i	−0.535746	−	0.535746i
$718$			18.5486i			0.692228i
$719$			48.6715i			1.81514i	0.419899	+	0.907571i	$0.362066\pi$
$719$			48.6715i			1.81514i	−0.419899	+	0.907571i	$0.637934\pi$
$720$		−	0.964064i		−	0.0359285i
$721$	14.3898	−	6.72384i	0.535902	−	0.250409i
$722$	13.3784	+	13.3784i	0.497892	+	0.497892i
$723$	−14.6450	−	14.6450i	−0.544653	−	0.544653i
$724$	3.87066			0.143852
$725$	−3.22542	−	21.6822i	−0.119789	−	0.805255i
$726$			8.93491i			0.331606i
$727$	7.20162	+	7.20162i	0.267093	+	0.267093i	0.827928	−	0.560835i	$-0.189520\pi$
$727$	7.20162	+	7.20162i	0.267093	+	0.267093i	−0.560835	+	0.827928i	$0.689520\pi$
$728$	−1.50260	+	4.13849i	−0.0556901	+	0.153383i
$729$		−	1.00000i		−	0.0370370i
$730$		−	12.3852i		−	0.458396i
$731$	49.1669			1.81850
$732$	0.356410			0.0131733
$733$	13.8947	−	13.8947i	0.513211	−	0.513211i	−0.402298	−	0.915509i	$-0.631788\pi$
$733$	13.8947	−	13.8947i	0.513211	−	0.513211i	0.915509	+	0.402298i	$0.131788\pi$
$734$	11.0162			0.406616
$735$	6.72183	−	0.598748i	0.247939	−	0.0220851i
$736$	1.68209	−	1.68209i	0.0620027	−	0.0620027i
$737$	−0.446616	−	0.446616i	−0.0164513	−	0.0164513i
$738$	−9.24702			−0.340388
$739$	−14.7828	+	14.7828i	−0.543793	+	0.543793i	−0.924639	−	0.380846i	$-0.875633\pi$
$739$	−14.7828	+	14.7828i	−0.543793	+	0.543793i	0.380846	+	0.924639i	$0.375633\pi$
$740$	−2.46553	+	2.46553i	−0.0906347	+	0.0906347i
$741$		−	0.470995i		−	0.0173024i
$742$	−29.8795	−	10.8486i	−1.09691	−	0.398266i
$743$	13.9627	+	13.9627i	0.512241	+	0.512241i	0.915213	−	0.402972i	$-0.132023\pi$
$743$	13.9627	+	13.9627i	0.512241	+	0.512241i	−0.402972	+	0.915213i	$0.632023\pi$
$744$	2.45149	−	2.45149i	0.0898758	−	0.0898758i
$745$		−	10.7563i		−	0.394082i
$746$	12.6259	−	12.6259i	0.462268	−	0.462268i
$747$	8.98566			0.328768
$748$			8.60082i			0.314477i
$749$	−6.42897	−	13.7587i	−0.234909	−	0.502731i
$750$	−8.74462			−0.319308
$751$	11.3537	+	11.3537i	0.414301	+	0.414301i	0.883234	−	0.468933i	$-0.155361\pi$
$751$	11.3537	+	11.3537i	0.414301	+	0.414301i	−0.468933	+	0.883234i	$0.655361\pi$
$752$	4.08757	−	4.08757i	0.149058	−	0.149058i
$753$		−	17.2972i		−	0.630344i
$754$	7.20018	+	5.33540i	0.262215	+	0.194304i
$755$		−	7.43689i		−	0.270656i
$756$	−0.902943	+	2.48690i	−0.0328397	+	0.0904478i
$757$	−32.3617	+	32.3617i	−1.17621	+	1.17621i	−0.195503	+	0.980703i	$0.562634\pi$
$757$	−32.3617	+	32.3617i	−1.17621	+	1.17621i	−0.980703	+	0.195503i	$0.937366\pi$
$758$		−	7.66351i		−	0.278351i
$759$	−3.41849			−0.124083
$760$		−	0.272859i		−	0.00989765i
$761$		−	7.74127i		−	0.280621i	−0.990108	−	0.140310i	$-0.955190\pi$
$761$		−	7.74127i		−	0.280621i	0.990108	−	0.140310i	$-0.0448101\pi$
$762$	−3.20089	+	3.20089i	−0.115956	+	0.115956i
$763$	−30.1097	+	14.0693i	−1.09005	+	0.509341i
$764$	−9.44291	−	9.44291i	−0.341632	−	0.341632i
$765$	4.08001	−	4.08001i	0.147513	−	0.147513i
$766$	7.43318	−	7.43318i	0.268572	−	0.268572i
$767$			20.7408i			0.748908i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−6.29639	+	6.29639i	−0.227054	+	0.227054i	−0.811461	−	0.584407i	$-0.801327\pi$
$769$	−6.29639	+	6.29639i	−0.227054	+	0.227054i	0.584407	+	0.811461i	$0.301327\pi$
$770$	3.32078	−	1.55169i	0.119673	−	0.0559190i
$771$	8.40516	−	8.40516i	0.302704	−	0.302704i
$772$	7.99696	+	7.99696i	0.287817	+	0.287817i
$773$	6.68353	+	6.68353i	0.240390	+	0.240390i	0.817011	−	0.576621i	$-0.195629\pi$
$773$	6.68353	+	6.68353i	0.240390	+	0.240390i	−0.576621	+	0.817011i	$0.695629\pi$
$774$	8.21489			0.295278
$775$	−9.97897	−	9.97897i	−0.358455	−	0.358455i
$776$	9.29418			0.333642
$777$	8.66932	−	4.05088i	0.311010	−	0.145324i
$778$	−3.13537			−0.112408
$779$	−2.61719			−0.0937705
$780$	1.13442	−	1.13442i	0.0406188	−	0.0406188i
$781$	10.8183	+	10.8183i	0.387109	+	0.387109i
$782$	14.2375			0.509134
$783$	4.32673	+	3.20615i	0.154625	+	0.114578i
$784$	4.49107	−	5.36939i	0.160395	−	0.191764i
$785$	−6.39031	+	6.39031i	−0.228080	+	0.228080i
$786$	−7.76228	+	7.76228i	−0.276871	+	0.276871i
$787$	3.64304			0.129860			0.0649301	−	0.997890i	$-0.479318\pi$
$787$	3.64304			0.129860			0.0649301	+	0.997890i	$0.479318\pi$
$788$		−	12.7280i		−	0.453415i
$789$	−15.4303			−0.549333
$790$		−	7.03904i		−	0.250438i
$791$	−18.2342	+	50.2209i	−0.648332	+	1.78565i
$792$			1.43704i			0.0510631i
$793$	0.419390	+	0.419390i	0.0148930	+	0.0148930i
$794$	−8.06640	−	8.06640i	−0.286266	−	0.286266i
$795$	8.19041	+	8.19041i	0.290484	+	0.290484i
$796$	−21.9546			−0.778160
$797$	−0.0613583	−	0.0613583i	−0.00217342	−	0.00217342i	0.706019	−	0.708193i	$-0.250489\pi$
$797$	−0.0613583	−	0.0613583i	−0.00217342	−	0.00217342i	−0.708193	+	0.706019i	$0.750489\pi$
$798$	−0.255560	+	0.703870i	−0.00904674	+	0.0249167i
$799$	34.5980			1.22399
$800$	−2.87833	+	2.87833i	−0.101765	+	0.101765i
$801$	7.53183	−	7.53183i	0.266124	−	0.266124i
$802$	−17.8250	+	17.8250i	−0.629424	+	0.629424i
$803$			18.4615i			0.651491i
$804$	0.310789	+	0.310789i	0.0109607	+	0.0109607i
$805$	−2.56862	−	5.49713i	−0.0905320	−	0.193748i
$806$	5.76936			0.203217
$807$	−3.25855			−0.114707
$808$		−	12.8071i		−	0.450551i
$809$	−21.0102	−	21.0102i	−0.738680	−	0.738680i	0.233643	−	0.972323i	$-0.424935\pi$
$809$	−21.0102	−	21.0102i	−0.738680	−	0.738680i	−0.972323	+	0.233643i	$0.924935\pi$
$810$	0.681696	−	0.681696i	0.0239524	−	0.0239524i
$811$	−12.3535			−0.433789			−0.216894	−	0.976195i	$-0.569593\pi$
$811$	−12.3535			−0.433789			−0.216894	+	0.976195i	$0.569593\pi$
$812$	−7.86520	−	11.8802i	−0.276014	−	0.416912i
$813$	20.2383			0.709790
$814$	3.67514	−	3.67514i	0.128814	−	0.128814i
$815$	−1.15717	−	1.15717i	−0.0405340	−	0.0405340i
$816$		−	5.98509i		−	0.209520i
$817$	2.32506			0.0813437
$818$	36.4363			1.27396
$819$	−3.98886	+	1.86386i	−0.139382	+	0.0651285i
$820$	−6.30366	−	6.30366i	−0.220133	−	0.220133i
$821$		−	12.2386i		−	0.427129i	−0.976929	−	0.213565i	$-0.931493\pi$
$821$		−	12.2386i		−	0.427129i	0.976929	−	0.213565i	$-0.0685074\pi$
$822$	5.94573	−	5.94573i	0.207381	−	0.207381i
$823$	28.3968	−	28.3968i	0.989849	−	0.989849i	−0.0100999	−	0.999949i	$-0.503215\pi$
$823$	28.3968	−	28.3968i	0.989849	−	0.989849i	0.999949	+	0.0100999i	$0.00321494\pi$
$824$	−4.24495	+	4.24495i	−0.147880	+	0.147880i
$825$	5.84959			0.203657
$826$	11.2539	−	30.9957i	0.391573	−	1.07848i
$827$	−20.8899	−	20.8899i	−0.726412	−	0.726412i	0.243491	−	0.969903i	$-0.421707\pi$
$827$	−20.8899	−	20.8899i	−0.726412	−	0.726412i	−0.969903	+	0.243491i	$0.921707\pi$
$828$	2.37884			0.0826703
$829$	4.18667	+	4.18667i	0.145409	+	0.145409i	0.776064	−	0.630655i	$-0.217214\pi$
$829$	4.18667	+	4.18667i	0.145409	+	0.145409i	−0.630655	+	0.776064i	$0.717214\pi$
$830$	6.12549	+	6.12549i	0.212619	+	0.212619i
$831$	−20.4572	−	20.4572i	−0.709654	−	0.709654i
$832$		−	1.66411i		−	0.0576928i
$833$	41.7304	−	3.71714i	1.44587	−	0.128791i
$834$		−	2.25836i		−	0.0782006i
$835$	−3.45592			−0.119597
$836$			0.406727i			0.0140669i
$837$	3.46692			0.119834
$838$	24.9460	−	24.9460i	0.861746	−	0.861746i
$839$	−20.9050	+	20.9050i	−0.721721	+	0.721721i	−0.968956	−	0.247235i	$-0.920478\pi$
$839$	−20.9050	+	20.9050i	−0.721721	+	0.721721i	0.247235	+	0.968956i	$0.420478\pi$
$840$	−2.31085	+	1.07978i	−0.0797318	+	0.0372560i
$841$	−27.7443	+	8.44123i	−0.956700	+	0.291077i
$842$	3.51123			0.121005
$843$	−10.6321	−	10.6321i	−0.366188	−	0.366188i
$844$	16.8267	−	16.8267i	0.579200	−	0.579200i
$845$	−9.86307			−0.339300
$846$	5.78069			0.198744
$847$	21.4168	−	10.0074i	0.735891	−	0.343857i
$848$	12.0147			0.412588
$849$	6.16090	+	6.16090i	0.211441	+	0.211441i
$850$	−24.3628			−0.835637
$851$	−6.08372	−	6.08372i	−0.208547	−	0.208547i
$852$	−7.52816	−	7.52816i	−0.257910	−	0.257910i
$853$	−33.7086	+	33.7086i	−1.15416	+	1.15416i	−0.168452	+	0.985710i	$0.553877\pi$
$853$	−33.7086	+	33.7086i	−1.15416	+	1.15416i	−0.985710	+	0.168452i	$0.946123\pi$
$854$	−0.399190	−	0.854309i	−0.0136600	−	0.0292339i
$855$	0.192941	−	0.192941i	0.00659844	−	0.00659844i
$856$	4.05879	+	4.05879i	0.138727	+	0.138727i
$857$			42.4479i			1.44999i	0.688753	+	0.724996i	$0.258158\pi$
$857$			42.4479i			1.44999i	−0.688753	+	0.724996i	$0.741842\pi$
$858$	−1.69098	+	1.69098i	−0.0577290	+	0.0577290i
$859$	1.13914	−	1.13914i	0.0388670	−	0.0388670i	−0.687406	−	0.726273i	$-0.741251\pi$
$859$	1.13914	−	1.13914i	0.0388670	−	0.0388670i	0.726273	+	0.687406i	$0.241251\pi$
$860$	5.60006	+	5.60006i	0.190960	+	0.190960i
$861$	10.3569	+	22.1650i	0.352963	+	0.755380i
$862$	−11.1282	+	11.1282i	−0.379027	+	0.379027i
$863$		−	37.2710i		−	1.26872i	−0.773038	−	0.634359i	$-0.781264\pi$
$863$		−	37.2710i		−	1.26872i	0.773038	−	0.634359i	$-0.218736\pi$
$864$		−	1.00000i		−	0.0340207i
$865$	10.8447			0.368732
$866$			17.4339i			0.592427i
$867$	13.3087	−	13.3087i	0.451986	−	0.451986i
$868$	−8.62191	−	3.13044i	−0.292647	−	0.106254i
$869$			10.4925i			0.355932i
$870$	0.763898	+	5.13514i	0.0258986	+	0.174097i
$871$			0.731414i			0.0247830i
$872$	8.88232	−	8.88232i	0.300793	−	0.300793i
$873$	6.57198	+	6.57198i	0.222428	+	0.222428i
$874$	0.673283			0.0227741
$875$	9.79424	+	20.9607i	0.331106	+	0.708602i
$876$		−	12.8469i		−	0.434055i
$877$	−31.8050			−1.07398			−0.536989	−	0.843589i	$-0.680438\pi$
$877$	−31.8050			−1.07398			−0.536989	+	0.843589i	$0.680438\pi$
$878$	−18.6122	+	18.6122i	−0.628131	+	0.628131i
$879$			18.0331i			0.608241i
$880$	−0.979626	+	0.979626i	−0.0330232	+	0.0330232i
$881$	−12.4714	−	12.4714i	−0.420171	−	0.420171i	0.465091	−	0.885263i	$-0.346021\pi$
$881$	−12.4714	−	12.4714i	−0.420171	−	0.420171i	−0.885263	+	0.465091i	$0.846021\pi$
$882$	6.97239	−	0.621066i	0.234773	−	0.0209124i
$883$		−	1.51845i		−	0.0510998i	−0.999674	−	0.0255499i	$-0.991866\pi$
$883$		−	1.51845i		−	0.0510998i	0.999674	−	0.0255499i	$-0.00813368\pi$
$884$	7.04270	−	7.04270i	0.236871	−	0.236871i
$885$	−8.49637	+	8.49637i	−0.285603	+	0.285603i
$886$	−24.0295			−0.807287
$887$	0.296112	+	0.296112i	0.00994248	+	0.00994248i	0.712061	−	0.702118i	$-0.247762\pi$
$887$	0.296112	+	0.296112i	0.00994248	+	0.00994248i	−0.702118	+	0.712061i	$0.747762\pi$
$888$	−2.55744	+	2.55744i	−0.0858219	+	0.0858219i
$889$	11.2576	+	4.08739i	0.377566	+	0.137087i
$890$	10.2688			0.344212
$891$	−1.01614	+	1.01614i	−0.0340420	+	0.0340420i
$892$	−11.4633			−0.383819
$893$	1.63611			0.0547504
$894$		−	11.1573i		−	0.373156i
$895$			9.78455i			0.327061i
$896$	−0.902943	+	2.48690i	−0.0301652	+	0.0830816i
$897$	2.79919	+	2.79919i	0.0934623	+	0.0934623i
$898$		−	28.0361i		−	0.935575i
$899$	−11.1155	+	15.0005i	−0.370722	+	0.500293i
$900$	−4.07058			−0.135686
$901$	50.8476	+	50.8476i	1.69398	+	1.69398i
$902$	9.39629	+	9.39629i	0.312862	+	0.312862i
$903$	−9.20092	−	19.6910i	−0.306188	−	0.655274i
$904$		−	20.1941i		−	0.671647i
$905$			3.73157i			0.124041i
$906$		−	7.71410i		−	0.256284i
$907$	22.8118	+	22.8118i	0.757454	+	0.757454i	0.975858	−	0.218404i	$-0.0700851\pi$
$907$	22.8118	+	22.8118i	0.757454	+	0.757454i	−0.218404	+	0.975858i	$0.570085\pi$
$908$	−6.63942			−0.220337
$909$	9.05597	−	9.05597i	0.300367	−	0.300367i
$910$	−3.98977	−	1.44860i	−0.132260	−	0.0480208i
$911$	40.0810	+	40.0810i	1.32794	+	1.32794i	0.907163	+	0.420780i	$0.138244\pi$
$911$	40.0810	+	40.0810i	1.32794	+	1.32794i	0.420780	+	0.907163i	$0.361756\pi$
$912$		−	0.283030i		−	0.00937207i
$913$	−9.13070	−	9.13070i	−0.302182	−	0.302182i
$914$	10.9876	+	10.9876i	0.363437	+	0.363437i
$915$			0.343602i			0.0113591i
$916$	12.1043	+	12.1043i	0.399936	+	0.399936i
$917$	27.3001	+	9.91208i	0.901527	+	0.327326i
$918$	4.23210	−	4.23210i	0.139680	−	0.139680i
$919$	7.15196			0.235921			0.117961	−	0.993018i	$-0.462364\pi$
$919$	7.15196			0.235921			0.117961	+	0.993018i	$0.462364\pi$
$920$	1.62164	+	1.62164i	0.0534640	+	0.0534640i
$921$			24.1384i			0.795388i
$922$			11.8704i			0.390932i
$923$		−	17.7169i		−	0.583158i
$924$	3.44457	−	1.60953i	0.113318	−	0.0529496i
$925$	10.4102	+	10.4102i	0.342287	+	0.342287i
$926$	23.8876	+	23.8876i	0.784997	+	0.784997i
$927$	−6.00327			−0.197173
$928$	4.32673	+	3.20615i	0.142032	+	0.105247i
$929$		−	59.2220i		−	1.94301i	−0.237020	−	0.971505i	$-0.576171\pi$
$929$		−	59.2220i		−	1.94301i	0.237020	−	0.971505i	$-0.423829\pi$
$930$	2.36339	+	2.36339i	0.0774986	+	0.0774986i
$931$	1.97340	−	0.175781i	0.0646756	−	0.00576098i
$932$		−	10.8589i		−	0.355697i
$933$		−	14.1463i		−	0.463130i
$934$	10.8573			0.355260
$935$	−8.29175			−0.271169
$936$	1.17671	−	1.17671i	0.0384619	−	0.0384619i
$937$	−24.2941			−0.793652			−0.396826	−	0.917894i	$-0.629888\pi$
$937$	−24.2941			−0.793652			−0.396826	+	0.917894i	$0.629888\pi$
$938$	0.396863	−	1.09305i	0.0129580	−	0.0356893i
$939$	7.62253	−	7.62253i	0.248752	−	0.248752i
$940$	3.94068	+	3.94068i	0.128531	+	0.128531i
$941$	9.24786			0.301472			0.150736	−	0.988574i	$-0.451836\pi$
$941$	9.24786			0.301472			0.150736	+	0.988574i	$0.451836\pi$
$942$	−6.62851	+	6.62851i	−0.215968	+	0.215968i
$943$	15.5543	−	15.5543i	0.506519	−	0.506519i
$944$			12.4636i			0.405655i
$945$	−2.39754	−	0.870495i	−0.0779918	−	0.0283172i
$946$	−8.34750	−	8.34750i	−0.271401	−	0.271401i
$947$	15.9133	−	15.9133i	0.517111	−	0.517111i	−0.399585	−	0.916696i	$-0.630846\pi$
$947$	15.9133	−	15.9133i	0.517111	−	0.517111i	0.916696	+	0.399585i	$0.130846\pi$
$948$		−	7.30143i		−	0.237139i
$949$	15.1170	−	15.1170i	0.490718	−	0.490718i
$950$	−1.15210			−0.0373790
$951$			15.2325i			0.493946i
$952$	−14.3462	+	6.70348i	−0.464962	+	0.217261i
$953$	−23.5911			−0.764192			−0.382096	−	0.924123i	$-0.624798\pi$
$953$	−23.5911			−0.764192			−0.382096	+	0.924123i	$0.624798\pi$
$954$	8.49571	+	8.49571i	0.275059	+	0.275059i
$955$	9.10357	−	9.10357i	0.294584	−	0.294584i
$956$		−	20.2877i		−	0.656152i
$957$	−1.13867	−	7.65448i	−0.0368081	−	0.247434i
$958$			36.9591i			1.19410i
$959$	−20.9112	−	7.59243i	−0.675259	−	0.245172i
$960$	0.681696	−	0.681696i	0.0220017	−	0.0220017i
$961$		−	18.9804i		−	0.612272i
$962$	−6.01870			−0.194051
$963$			5.74000i			0.184969i
$964$		−	20.7111i		−	0.667061i
$965$	−7.70958	+	7.70958i	−0.248180	+	0.248180i
$966$	−2.66437	−	5.70203i	−0.0857246	−	0.183460i
$967$	−7.25348	−	7.25348i	−0.233256	−	0.233256i	0.580794	−	0.814050i	$-0.302742\pi$
$967$	−7.25348	−	7.25348i	−0.233256	−	0.233256i	−0.814050	+	0.580794i	$0.802742\pi$
$968$	−6.31794	+	6.31794i	−0.203066	+	0.203066i
$969$	1.19781	−	1.19781i	0.0384793	−	0.0384793i
$970$			8.96018i			0.287694i
$971$	0.353537	+	0.353537i	0.0113455	+	0.0113455i	0.712757	−	0.701411i	$-0.247446\pi$
$971$	0.353537	+	0.353537i	0.0113455	+	0.0113455i	−0.701411	+	0.712757i	$0.747446\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	−5.41325	+	2.52943i	−0.173541	+	0.0810898i
$974$	−28.2482	+	28.2482i	−0.905131	+	0.905131i
$975$	−4.78988	−	4.78988i	−0.153399	−	0.153399i
$976$	0.252020	+	0.252020i	0.00806696	+	0.00806696i
$977$	7.58272			0.242593			0.121296	−	0.992616i	$-0.461295\pi$
$977$	7.58272			0.242593			0.121296	+	0.992616i	$0.461295\pi$
$978$	−1.20031	−	1.20031i	−0.0383816	−	0.0383816i
$979$	−15.3068			−0.489208
$980$	5.17643	+	4.32968i	0.165355	+	0.138306i
$981$	12.5615			0.401058
$982$	32.9081			1.05014
$983$	−16.7975	+	16.7975i	−0.535758	+	0.535758i	−0.922280	−	0.386522i	$-0.873676\pi$
$983$	−16.7975	+	16.7975i	−0.535758	+	0.535758i	0.386522	+	0.922280i	$0.373676\pi$
$984$	−6.53863	−	6.53863i	−0.208444	−	0.208444i
$985$	12.2706			0.390973
$986$	4.74242	+	31.8799i	0.151030	+	1.01526i
$987$	−6.47455	−	13.8562i	−0.206087	−	0.441049i
$988$	0.333044	−	0.333044i	0.0105955	−	0.0105955i
$989$	−13.8182	+	13.8182i	−0.439393	+	0.439393i
$990$	−1.38540			−0.0440309
$991$		−	23.0921i		−	0.733544i	−0.930311	−	0.366772i	$-0.880463\pi$
$991$		−	23.0921i		−	0.733544i	0.930311	−	0.366772i	$-0.119537\pi$
$992$	3.46692			0.110075
$993$		−	23.9183i		−	0.759026i
$994$	−9.61312	+	26.4766i	−0.304910	+	0.839788i
$995$		−	21.1656i		−	0.670996i
$996$	6.35382	+	6.35382i	0.201328	+	0.201328i
$997$	33.6194	+	33.6194i	1.06474	+	1.06474i	0.997754	+	0.0669825i	$0.0213372\pi$
$997$	33.6194	+	33.6194i	1.06474	+	1.06474i	0.0669825	+	0.997754i	$0.478663\pi$
$998$	21.6387	+	21.6387i	0.684962	+	0.684962i
$999$	−3.61676			−0.114429

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1218.2.m.b.307.3	yes	40
7.6	odd	2		1218.2.m.a.307.3	✓	40
29.12	odd	4		1218.2.m.a.853.3	yes	40
203.41	even	4	inner	1218.2.m.b.853.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1218.2.m.a.307.3	✓	40	7.6	odd	2
1218.2.m.a.853.3	yes	40	29.12	odd	4
1218.2.m.b.307.3	yes	40	1.1	even	1	trivial
1218.2.m.b.853.3	yes	40	203.41	even	4	inner

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} +0.964064 q^{5} +1.00000 q^{6} +(-1.12003 - 2.39698i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(-0.681696 + 0.681696i) q^{10} +(1.01614 - 1.01614i) q^{11} +(-0.707107 + 0.707107i) q^{12} -1.66411 q^{13} +(2.48690 + 0.902943i) q^{14} +(-0.681696 - 0.681696i) q^{15} -1.00000 q^{16} +(-4.23210 - 4.23210i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(-0.200133 - 0.200133i) q^{19} -0.964064i q^{20} +(-0.902943 + 2.48690i) q^{21} +1.43704i q^{22} +2.37884 q^{23} -1.00000i q^{24} -4.07058 q^{25} +(1.17671 - 1.17671i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.39698 + 1.12003i) q^{28} +(0.792373 + 5.32655i) q^{29} +0.964064 q^{30} +(2.45149 + 2.45149i) q^{31} +(0.707107 - 0.707107i) q^{32} -1.43704 q^{33} +5.98509 q^{34} +(-1.07978 - 2.31085i) q^{35} +1.00000 q^{36} +(-2.55744 - 2.55744i) q^{37} +0.283030 q^{38} +(1.17671 + 1.17671i) q^{39} +(0.681696 + 0.681696i) q^{40} +(6.53863 - 6.53863i) q^{41} +(-1.12003 - 2.39698i) q^{42} +(-5.80881 + 5.80881i) q^{43} +(-1.01614 - 1.01614i) q^{44} +0.964064i q^{45} +(-1.68209 + 1.68209i) q^{46} +(-4.08757 + 4.08757i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-4.49107 + 5.36939i) q^{49} +(2.87833 - 2.87833i) q^{50} +5.98509i q^{51} +1.66411i q^{52} -12.0147 q^{53} +1.00000i q^{54} +(0.979626 - 0.979626i) q^{55} +(0.902943 - 2.48690i) q^{56} +0.283030i q^{57} +(-4.32673 - 3.20615i) q^{58} -12.4636i q^{59} +(-0.681696 + 0.681696i) q^{60} +(-0.252020 - 0.252020i) q^{61} -3.46692 q^{62} +(2.39698 - 1.12003i) q^{63} +1.00000i q^{64} -1.60431 q^{65} +(1.01614 - 1.01614i) q^{66} -0.439521i q^{67} +(-4.23210 + 4.23210i) q^{68} +(-1.68209 - 1.68209i) q^{69} +(2.39754 + 0.870495i) q^{70} +10.6464i q^{71} +(-0.707107 + 0.707107i) q^{72} +(-9.08410 + 9.08410i) q^{73} +3.61676 q^{74} +(2.87833 + 2.87833i) q^{75} +(-0.200133 + 0.200133i) q^{76} +(-3.57379 - 1.29757i) q^{77} -1.66411 q^{78} +(-5.16289 + 5.16289i) q^{79} -0.964064 q^{80} -1.00000 q^{81} +9.24702i q^{82} -8.98566i q^{83} +(2.48690 + 0.902943i) q^{84} +(-4.08001 - 4.08001i) q^{85} -8.21489i q^{86} +(3.20615 - 4.32673i) q^{87} +1.43704 q^{88} +(-7.53183 - 7.53183i) q^{89} +(-0.681696 - 0.681696i) q^{90} +(1.86386 + 3.98886i) q^{91} -2.37884i q^{92} -3.46692i q^{93} -5.78069i q^{94} +(-0.192941 - 0.192941i) q^{95} -1.00000 q^{96} +(6.57198 - 6.57198i) q^{97} +(-0.621066 - 6.97239i) q^{98} +(1.01614 + 1.01614i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{6} - 4 q^{10} + 4 q^{14} - 4 q^{15} - 40 q^{16} - 8 q^{19} + 4 q^{21} + 24 q^{25} + 12 q^{28} + 8 q^{29} + 24 q^{31} + 12 q^{35} + 40 q^{36} - 16 q^{37} + 4 q^{40} - 16 q^{41} - 20 q^{43} + 4 q^{46}+ \cdots - 24 q^{98}+O(q^{100}) \) 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 + 20 * q^70 + 52 * q^73 + 32 * q^75 - 8 * q^76 + 20 * 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 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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