LMFDB - Embedded newform 336.2.w.b.253.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(85,336)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("336.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.w (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.5
Character	$\chi$	$=$	336.253
Dual form			336.2.w.b.85.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.819262 - 1.15274i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-0.657621 + 1.88879i) q^{4} +(-0.979857 + 0.979857i) q^{5} +(-0.235805 + 1.39442i) q^{6} +1.00000i q^{7} +(2.71605 - 0.789348i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.819262 - 1.15274i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-0.657621 + 1.88879i) q^{4} +(-0.979857 + 0.979857i) q^{5} +(-0.235805 + 1.39442i) q^{6} +1.00000i q^{7} +(2.71605 - 0.789348i) q^{8} +1.00000i q^{9} +(1.93228 + 0.326762i) q^{10} +(2.99092 - 2.99092i) q^{11} +(1.80059 - 0.870569i) q^{12} +(-0.686333 - 0.686333i) q^{13} +(1.15274 - 0.819262i) q^{14} +1.38573 q^{15} +(-3.13507 - 2.48422i) q^{16} +7.74860 q^{17} +(1.15274 - 0.819262i) q^{18} +(2.46495 + 2.46495i) q^{19} +(-1.20637 - 2.49512i) q^{20} +(0.707107 - 0.707107i) q^{21} +(-5.89810 - 0.997408i) q^{22} -8.35641i q^{23} +(-2.47869 - 1.36238i) q^{24} +3.07976i q^{25} +(-0.228878 + 1.35345i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.88879 - 0.657621i) q^{28} +(-3.68876 - 3.68876i) q^{29} +(-1.13527 - 1.59738i) q^{30} +7.60568 q^{31} +(-0.295218 + 5.64915i) q^{32} -4.22980 q^{33} +(-6.34813 - 8.93212i) q^{34} +(-0.979857 - 0.979857i) q^{35} +(-1.88879 - 0.657621i) q^{36} +(-4.63198 + 4.63198i) q^{37} +(0.822008 - 4.86088i) q^{38} +0.970621i q^{39} +(-1.88789 + 3.43479i) q^{40} +7.39378i q^{41} +(-1.39442 - 0.235805i) q^{42} +(7.06672 - 7.06672i) q^{43} +(3.68233 + 7.61611i) q^{44} +(-0.979857 - 0.979857i) q^{45} +(-9.63277 + 6.84608i) q^{46} +2.46578 q^{47} +(0.460221 + 3.97344i) q^{48} -1.00000 q^{49} +(3.55016 - 2.52313i) q^{50} +(-5.47909 - 5.47909i) q^{51} +(1.74769 - 0.844993i) q^{52} +(6.50509 - 6.50509i) q^{53} +(-1.39442 - 0.235805i) q^{54} +5.86134i q^{55} +(0.789348 + 2.71605i) q^{56} -3.48596i q^{57} +(-1.23012 + 7.27423i) q^{58} +(2.18485 - 2.18485i) q^{59} +(-0.911283 + 2.61735i) q^{60} +(-1.02350 - 1.02350i) q^{61} +(-6.23104 - 8.76737i) q^{62} -1.00000 q^{63} +(6.75386 - 4.28782i) q^{64} +1.34502 q^{65} +(3.46531 + 4.87586i) q^{66} +(2.22728 + 2.22728i) q^{67} +(-5.09564 + 14.6355i) q^{68} +(-5.90887 + 5.90887i) q^{69} +(-0.326762 + 1.93228i) q^{70} +14.1741i q^{71} +(0.789348 + 2.71605i) q^{72} +5.93888i q^{73} +(9.13427 + 1.54467i) q^{74} +(2.17772 - 2.17772i) q^{75} +(-6.27678 + 3.03477i) q^{76} +(2.99092 + 2.99092i) q^{77} +(1.11887 - 0.795193i) q^{78} -2.58459 q^{79} +(5.50610 - 0.637740i) q^{80} -1.00000 q^{81} +(8.52311 - 6.05744i) q^{82} +(-4.80684 - 4.80684i) q^{83} +(0.870569 + 1.80059i) q^{84} +(-7.59252 + 7.59252i) q^{85} +(-13.9356 - 2.35660i) q^{86} +5.21669i q^{87} +(5.76261 - 10.4844i) q^{88} +5.96557i q^{89} +(-0.326762 + 1.93228i) q^{90} +(0.686333 - 0.686333i) q^{91} +(15.7835 + 5.49535i) q^{92} +(-5.37803 - 5.37803i) q^{93} +(-2.02012 - 2.84241i) q^{94} -4.83059 q^{95} +(4.20330 - 3.78580i) q^{96} +11.2310 q^{97} +(0.819262 + 1.15274i) q^{98} +(2.99092 + 2.99092i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q+O(q^{10}) $ 28 * q	$ 28 q - 4 q^{10} - 4 q^{11} - 8 q^{12} + 8 q^{15} + 4 q^{16} + 8 q^{19} - 28 q^{20} - 8 q^{22} - 16 q^{24} - 20 q^{26} + 4 q^{28} + 4 q^{29} + 8 q^{30} + 24 q^{33} + 12 q^{34} + 4 q^{36} + 4 q^{37} + 60 q^{38} - 56 q^{40} - 4 q^{42} + 20 q^{43} + 56 q^{44} - 44 q^{46} + 16 q^{48} - 28 q^{49} + 20 q^{50} - 8 q^{51} - 32 q^{52} + 20 q^{53} - 4 q^{54} - 12 q^{56} - 12 q^{58} - 12 q^{60} - 40 q^{61} - 60 q^{62} - 28 q^{63} + 60 q^{64} + 16 q^{65} + 24 q^{66} + 4 q^{67} - 108 q^{68} - 16 q^{69} - 4 q^{70} - 12 q^{72} + 28 q^{74} - 16 q^{75} - 8 q^{76} - 4 q^{77} + 12 q^{78} + 24 q^{79} - 72 q^{80} - 28 q^{81} + 36 q^{82} + 40 q^{83} + 48 q^{85} + 24 q^{86} + 4 q^{88} - 4 q^{90} + 52 q^{92} - 8 q^{94} + 40 q^{96} + 72 q^{97} - 4 q^{99}+O(q^{100}) $ 28 * q - 4 * q^10 - 4 * q^11 - 8 * q^12 + 8 * q^15 + 4 * q^16 + 8 * q^19 - 28 * q^20 - 8 * q^22 - 16 * q^24 - 20 * q^26 + 4 * q^28 + 4 * q^29 + 8 * q^30 + 24 * q^33 + 12 * q^34 + 4 * q^36 + 4 * q^37 + 60 * q^38 - 56 * q^40 - 4 * q^42 + 20 * q^43 + 56 * q^44 - 44 * q^46 + 16 * q^48 - 28 * q^49 + 20 * q^50 - 8 * q^51 - 32 * q^52 + 20 * q^53 - 4 * q^54 - 12 * q^56 - 12 * q^58 - 12 * q^60 - 40 * q^61 - 60 * q^62 - 28 * q^63 + 60 * q^64 + 16 * q^65 + 24 * q^66 + 4 * q^67 - 108 * q^68 - 16 * q^69 - 4 * q^70 - 12 * q^72 + 28 * q^74 - 16 * q^75 - 8 * q^76 - 4 * q^77 + 12 * q^78 + 24 * q^79 - 72 * q^80 - 28 * q^81 + 36 * q^82 + 40 * q^83 + 48 * q^85 + 24 * q^86 + 4 * q^88 - 4 * q^90 + 52 * q^92 - 8 * q^94 + 40 * q^96 + 72 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$1$

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 $

$2$	−0.819262	−	1.15274i	−0.579305	−	0.815111i
$2$	−0.819262	−	1.15274i	−0.579305	−	0.815111i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−0.657621	+	1.88879i	−0.328811	+	0.944396i
$5$	−0.979857	+	0.979857i	−0.438205	+	0.438205i	−0.891408	−	0.453202i	$-0.850282\pi$
$5$	−0.979857	+	0.979857i	−0.438205	+	0.438205i	0.453202	+	0.891408i	$0.350282\pi$
$6$	−0.235805	+	1.39442i	−0.0962671	+	0.569268i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	2.71605	−	0.789348i	0.960269	−	0.279077i
$9$			1.00000i			0.333333i
$10$	1.93228	+	0.326762i	0.611041	+	0.103331i
$11$	2.99092	−	2.99092i	0.901796	−	0.901796i	−0.0937956	−	0.995591i	$-0.529900\pi$
$11$	2.99092	−	2.99092i	0.901796	−	0.901796i	0.995591	+	0.0937956i	$0.0299000\pi$
$12$	1.80059	−	0.870569i	0.519784	−	0.251312i
$13$	−0.686333	−	0.686333i	−0.190355	−	0.190355i	0.605495	−	0.795849i	$-0.292975\pi$
$13$	−0.686333	−	0.686333i	−0.190355	−	0.190355i	−0.795849	+	0.605495i	$0.792975\pi$
$14$	1.15274	−	0.819262i	0.308083	−	0.218957i
$15$	1.38573			0.357793
$16$	−3.13507	−	2.48422i	−0.783767	−	0.621055i
$17$	7.74860			1.87931			0.939655	−	0.342122i	$-0.111146\pi$
$17$	7.74860			1.87931			0.939655	+	0.342122i	$0.111146\pi$
$18$	1.15274	−	0.819262i	0.271704	−	0.193102i
$19$	2.46495	+	2.46495i	0.565498	+	0.565498i	0.930864	−	0.365366i	$-0.119056\pi$
$19$	2.46495	+	2.46495i	0.565498	+	0.565498i	−0.365366	+	0.930864i	$0.619056\pi$
$20$	−1.20637	−	2.49512i	−0.269753	−	0.557926i
$21$	0.707107	−	0.707107i	0.154303	−	0.154303i
$22$	−5.89810	−	0.997408i	−1.25748	−	0.212648i
$23$		−	8.35641i		−	1.74243i	−0.490900	−	0.871216i	$-0.663332\pi$
$23$		−	8.35641i		−	1.74243i	0.490900	−	0.871216i	$-0.336668\pi$
$24$	−2.47869	−	1.36238i	−0.505961	−	0.278096i
$25$			3.07976i			0.615952i
$26$	−0.228878	+	1.35345i	−0.0448866	+	0.265433i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−1.88879	−	0.657621i	−0.356948	−	0.124279i
$29$	−3.68876	−	3.68876i	−0.684985	−	0.684985i	0.276134	−	0.961119i	$-0.410947\pi$
$29$	−3.68876	−	3.68876i	−0.684985	−	0.684985i	−0.961119	+	0.276134i	$0.910947\pi$
$30$	−1.13527	−	1.59738i	−0.207271	−	0.291641i
$31$	7.60568			1.36602			0.683010	−	0.730409i	$-0.260671\pi$
$31$	7.60568			1.36602			0.683010	+	0.730409i	$0.260671\pi$
$32$	−0.295218	+	5.64915i	−0.0521877	+	0.998637i
$33$	−4.22980			−0.736313
$34$	−6.34813	−	8.93212i	−1.08869	−	1.53185i
$35$	−0.979857	−	0.979857i	−0.165626	−	0.165626i
$36$	−1.88879	−	0.657621i	−0.314799	−	0.109604i
$37$	−4.63198	+	4.63198i	−0.761492	+	0.761492i	−0.976592	−	0.215100i	$-0.930992\pi$
$37$	−4.63198	+	4.63198i	−0.761492	+	0.761492i	0.215100	+	0.976592i	$0.430992\pi$
$38$	0.822008	−	4.86088i	0.133347	−	0.788539i
$39$			0.970621i			0.155424i
$40$	−1.88789	+	3.43479i	−0.298502	+	0.543088i
$41$			7.39378i			1.15471i	0.816492	+	0.577357i	$0.195916\pi$
$41$			7.39378i			1.15471i	−0.816492	+	0.577357i	$0.804084\pi$
$42$	−1.39442	−	0.235805i	−0.215163	−	0.0363855i
$43$	7.06672	−	7.06672i	1.07767	−	1.07767i	0.0809467	−	0.996718i	$-0.474206\pi$
$43$	7.06672	−	7.06672i	1.07767	−	1.07767i	0.996718	−	0.0809467i	$-0.0257944\pi$
$44$	3.68233	+	7.61611i	0.555132	+	1.14817i
$45$	−0.979857	−	0.979857i	−0.146068	−	0.146068i
$46$	−9.63277	+	6.84608i	−1.42027	+	1.00940i
$47$	2.46578			0.359671			0.179836	−	0.983697i	$-0.442443\pi$
$47$	2.46578			0.359671			0.179836	+	0.983697i	$0.442443\pi$
$48$	0.460221	+	3.97344i	0.0664271	+	0.573516i
$49$	−1.00000			−0.142857
$50$	3.55016	−	2.52313i	0.502069	−	0.356824i
$51$	−5.47909	−	5.47909i	−0.767225	−	0.767225i
$52$	1.74769	−	0.844993i	0.242361	−	0.117179i
$53$	6.50509	−	6.50509i	0.893543	−	0.893543i	−0.101312	−	0.994855i	$-0.532304\pi$
$53$	6.50509	−	6.50509i	0.893543	−	0.893543i	0.994855	+	0.101312i	$0.0323040\pi$
$54$	−1.39442	−	0.235805i	−0.189756	−	0.0320890i
$55$			5.86134i			0.790343i
$56$	0.789348	+	2.71605i	0.105481	+	0.362948i
$57$		−	3.48596i		−	0.461727i
$58$	−1.23012	+	7.27423i	−0.161523	+	0.955154i
$59$	2.18485	−	2.18485i	0.284443	−	0.284443i	−0.550435	−	0.834878i	$-0.685538\pi$
$59$	2.18485	−	2.18485i	0.284443	−	0.284443i	0.834878	+	0.550435i	$0.185538\pi$
$60$	−0.911283	+	2.61735i	−0.117646	+	0.337898i
$61$	−1.02350	−	1.02350i	−0.131045	−	0.131045i	0.638542	−	0.769587i	$-0.279538\pi$
$61$	−1.02350	−	1.02350i	−0.131045	−	0.131045i	−0.769587	+	0.638542i	$0.779538\pi$
$62$	−6.23104	−	8.76737i	−0.791343	−	1.11346i
$63$	−1.00000			−0.125988
$64$	6.75386	−	4.28782i	0.844232	−	0.535977i
$65$	1.34502			0.166829
$66$	3.46531	+	4.87586i	0.426550	+	0.600177i
$67$	2.22728	+	2.22728i	0.272106	+	0.272106i	0.829947	−	0.557842i	$-0.188370\pi$
$67$	2.22728	+	2.22728i	0.272106	+	0.272106i	−0.557842	+	0.829947i	$0.688370\pi$
$68$	−5.09564	+	14.6355i	−0.617937	+	1.77481i
$69$	−5.90887	+	5.90887i	−0.711345	+	0.711345i
$70$	−0.326762	+	1.93228i	−0.0390555	+	0.230952i
$71$			14.1741i			1.68216i	0.540914	+	0.841078i	$0.318078\pi$
$71$			14.1741i			1.68216i	−0.540914	+	0.841078i	$0.681922\pi$
$72$	0.789348	+	2.71605i	0.0930255	+	0.320090i
$73$			5.93888i			0.695093i	0.937663	+	0.347546i	$0.112985\pi$
$73$			5.93888i			0.695093i	−0.937663	+	0.347546i	$0.887015\pi$
$74$	9.13427	+	1.54467i	1.06184	+	0.179564i
$75$	2.17772	−	2.17772i	0.251461	−	0.251461i
$76$	−6.27678	+	3.03477i	−0.719996	+	0.348112i
$77$	2.99092	+	2.99092i	0.340847	+	0.340847i
$78$	1.11887	−	0.795193i	0.126688	−	0.0900378i
$79$	−2.58459			−0.290789			−0.145394	−	0.989374i	$-0.546445\pi$
$79$	−2.58459			−0.290789			−0.145394	+	0.989374i	$0.546445\pi$
$80$	5.50610	−	0.637740i	0.615600	−	0.0713015i
$81$	−1.00000			−0.111111
$82$	8.52311	−	6.05744i	0.941220	−	0.668932i
$83$	−4.80684	−	4.80684i	−0.527619	−	0.527619i	0.392243	−	0.919862i	$-0.371699\pi$
$83$	−4.80684	−	4.80684i	−0.527619	−	0.527619i	−0.919862	+	0.392243i	$0.871699\pi$
$84$	0.870569	+	1.80059i	0.0949869	+	0.196460i
$85$	−7.59252	+	7.59252i	−0.823524	+	0.823524i
$86$	−13.9356	−	2.35660i	−1.50271	−	0.254119i
$87$			5.21669i			0.559288i
$88$	5.76261	−	10.4844i	0.614296	−	1.11764i
$89$			5.96557i			0.632349i	0.948701	+	0.316174i	$0.102398\pi$
$89$			5.96557i			0.632349i	−0.948701	+	0.316174i	$0.897602\pi$
$90$	−0.326762	+	1.93228i	−0.0344437	+	0.203680i
$91$	0.686333	−	0.686333i	0.0719472	−	0.0719472i
$92$	15.7835	+	5.49535i	1.64555	+	0.572930i
$93$	−5.37803	−	5.37803i	−0.557675	−	0.557675i
$94$	−2.02012	−	2.84241i	−0.208360	−	0.293172i
$95$	−4.83059			−0.495608
$96$	4.20330	−	3.78580i	0.428998	−	0.386386i
$97$	11.2310			1.14033			0.570166	−	0.821529i	$-0.306879\pi$
$97$	11.2310			1.14033			0.570166	+	0.821529i	$0.306879\pi$
$98$	0.819262	+	1.15274i	0.0827579	+	0.116444i
$99$	2.99092	+	2.99092i	0.300599	+	0.300599i
$100$	−5.81703	−	2.02532i	−0.581703	−	0.202532i
$101$	−10.0023	+	10.0023i	−0.995271	+	0.995271i	−0.999989	−	0.00471790i	$-0.998498\pi$
$101$	−10.0023	+	10.0023i	−0.995271	+	0.995271i	0.00471790	+	0.999989i	$0.498498\pi$
$102$	−1.82716	+	10.8048i	−0.180916	+	1.06983i
$103$		−	7.61089i		−	0.749924i	−0.927040	−	0.374962i	$-0.877656\pi$
$103$		−	7.61089i		−	0.749924i	0.927040	−	0.374962i	$-0.122344\pi$
$104$	−2.40587	−	1.32236i	−0.235915	−	0.129668i
$105$			1.38573i			0.135233i
$106$	−12.8280	−	2.16931i	−1.24597	−	0.210702i
$107$	−2.75768	+	2.75768i	−0.266595	+	0.266595i	−0.827727	−	0.561132i	$-0.810366\pi$
$107$	−2.75768	+	2.75768i	−0.266595	+	0.266595i	0.561132	+	0.827727i	$0.310366\pi$
$108$	0.870569	+	1.80059i	0.0837706	+	0.173261i
$109$	−7.69583	−	7.69583i	−0.737127	−	0.737127i	0.234894	−	0.972021i	$-0.424526\pi$
$109$	−7.69583	−	7.69583i	−0.737127	−	0.737127i	−0.972021	+	0.234894i	$0.924526\pi$
$110$	6.75661	−	4.80197i	0.644217	−	0.457850i
$111$	6.55060			0.621756
$112$	2.48422	−	3.13507i	0.234737	−	0.296236i
$113$	−4.68183			−0.440430			−0.220215	−	0.975451i	$-0.570676\pi$
$113$	−4.68183			−0.440430			−0.220215	+	0.975451i	$0.570676\pi$
$114$	−4.01841	+	2.85592i	−0.376359	+	0.267481i
$115$	8.18808	+	8.18808i	0.763543	+	0.763543i
$116$	9.39310	−	4.54149i	0.872127	−	0.421667i
$117$	0.686333	−	0.686333i	0.0634515	−	0.0634515i
$118$	−4.30852	−	0.728600i	−0.396631	−	0.0670731i
$119$			7.74860i			0.710313i
$120$	3.76370	−	1.09382i	0.343578	−	0.0998517i
$121$		−	6.89119i		−	0.626472i
$122$	−0.341314	+	2.01834i	−0.0309011	+	0.182732i
$123$	5.22819	−	5.22819i	0.471410	−	0.471410i
$124$	−5.00165	+	14.3655i	−0.449162	+	1.29006i
$125$	−7.91701	−	7.91701i	−0.708119	−	0.708119i
$126$	0.819262	+	1.15274i	0.0729856	+	0.102694i
$127$	−1.79855			−0.159596			−0.0797978	−	0.996811i	$-0.525427\pi$
$127$	−1.79855			−0.159596			−0.0797978	+	0.996811i	$0.525427\pi$
$128$	−10.4759	−	4.27260i	−0.925949	−	0.377648i
$129$	−9.99386			−0.879910
$130$	−1.10192	−	1.55045i	−0.0966448	−	0.135984i
$131$	−12.8298	−	12.8298i	−1.12094	−	1.12094i	−0.991600	−	0.129344i	$-0.958713\pi$
$131$	−12.8298	−	12.8298i	−1.12094	−	1.12094i	−0.129344	−	0.991600i	$-0.541287\pi$
$132$	2.78160	−	7.98921i	0.242108	−	0.695371i
$133$	−2.46495	+	2.46495i	−0.213738	+	0.213738i
$134$	0.742752	−	4.39220i	0.0641640	−	0.379429i
$135$			1.38573i			0.119264i
$136$	21.0456	−	6.11634i	1.80464	−	0.524472i
$137$		−	14.2550i		−	1.21789i	−0.793213	−	0.608944i	$-0.791593\pi$
$137$		−	14.2550i		−	1.21789i	0.793213	−	0.608944i	$-0.208407\pi$
$138$	11.6523	+	1.97048i	0.991910	+	0.167739i
$139$	−6.97271	+	6.97271i	−0.591418	+	0.591418i	−0.938014	−	0.346597i	$-0.887337\pi$
$139$	−6.97271	+	6.97271i	−0.591418	+	0.591418i	0.346597	+	0.938014i	$0.387337\pi$
$140$	2.49512	−	1.20637i	0.210876	−	0.101957i
$141$	−1.74357	−	1.74357i	−0.146835	−	0.146835i
$142$	16.3391	−	11.6123i	1.37114	−	0.974482i
$143$	−4.10553			−0.343322
$144$	2.48422	−	3.13507i	0.207018	−	0.261256i
$145$	7.22891			0.600328
$146$	6.84598	−	4.86549i	0.566578	−	0.402671i
$147$	0.707107	+	0.707107i	0.0583212	+	0.0583212i
$148$	−5.70275	−	11.7949i	−0.468764	−	0.969537i
$149$	1.43696	−	1.43696i	0.117721	−	0.117721i	−0.645792	−	0.763513i	$-0.723473\pi$
$149$	1.43696	−	1.43696i	0.117721	−	0.117721i	0.763513	+	0.645792i	$0.223473\pi$
$150$	−4.29447	−	0.726224i	−0.350642	−	0.0592959i
$151$		−	7.09120i		−	0.577073i	−0.957469	−	0.288537i	$-0.906831\pi$
$151$		−	7.09120i		−	0.577073i	0.957469	−	0.288537i	$-0.0931687\pi$
$152$	8.64063	+	4.74922i	0.700847	+	0.385213i
$153$			7.74860i			0.626437i
$154$	0.997408	−	5.89810i	0.0803735	−	0.475282i
$155$	−7.45248	+	7.45248i	−0.598597	+	0.598597i
$156$	−1.83330	−	0.638301i	−0.146782	−	0.0511050i
$157$	12.1843	+	12.1843i	0.972413	+	0.972413i	0.999630	−	0.0272169i	$-0.00866448\pi$
$157$	12.1843	+	12.1843i	0.972413	+	0.972413i	−0.0272169	+	0.999630i	$0.508664\pi$
$158$	2.11745	+	2.97936i	0.168455	+	0.237025i
$159$	−9.19959			−0.729575
$160$	−5.24608	−	5.82463i	−0.414739	−	0.460477i
$161$	8.35641			0.658577
$162$	0.819262	+	1.15274i	0.0643673	+	0.0905678i
$163$	−6.78971	−	6.78971i	−0.531811	−	0.531811i	0.389300	−	0.921111i	$-0.372717\pi$
$163$	−6.78971	−	6.78971i	−0.531811	−	0.531811i	−0.921111	+	0.389300i	$0.872717\pi$
$164$	−13.9653	−	4.86231i	−1.09051	−	0.379682i
$165$	4.14460	−	4.14460i	0.322656	−	0.322656i
$166$	−1.60298	+	9.47910i	−0.124415	+	0.735721i
$167$		−	5.53606i		−	0.428393i	−0.976791	−	0.214197i	$-0.931287\pi$
$167$		−	5.53606i		−	0.428393i	0.976791	−	0.214197i	$-0.0687133\pi$
$168$	1.36238	−	2.47869i	0.105110	−	0.191235i
$169$		−	12.0579i		−	0.927530i
$170$	14.9725	+	2.53194i	1.14834	+	0.194191i
$171$	−2.46495	+	2.46495i	−0.188499	+	0.188499i
$172$	8.70034	+	17.9948i	0.663395	+	1.37209i
$173$	7.62433	+	7.62433i	0.579667	+	0.579667i	0.934812	−	0.355144i	$-0.115568\pi$
$173$	7.62433	+	7.62433i	0.579667	+	0.579667i	−0.355144	+	0.934812i	$0.615568\pi$
$174$	6.01349	−	4.27383i	0.455881	−	0.323998i
$175$	−3.07976			−0.232808
$176$	−16.8068	+	1.94664i	−1.26686	+	0.146733i
$177$	−3.08984			−0.232246
$178$	6.87675	−	4.88736i	0.515434	−	0.366323i
$179$	−8.96337	−	8.96337i	−0.669954	−	0.669954i	0.287751	−	0.957705i	$-0.407092\pi$
$179$	−8.96337	−	8.96337i	−0.669954	−	0.669954i	−0.957705	+	0.287751i	$0.907092\pi$
$180$	2.49512	−	1.20637i	0.185975	−	0.0899176i
$181$	−5.90281	+	5.90281i	−0.438752	+	0.438752i	−0.891592	−	0.452840i	$-0.850411\pi$
$181$	−5.90281	+	5.90281i	−0.438752	+	0.438752i	0.452840	+	0.891592i	$0.350411\pi$
$182$	−1.35345	−	0.228878i	−0.100324	−	0.0169655i
$183$			1.44744i			0.106998i
$184$	−6.59611	−	22.6964i	−0.486272	−	1.67320i
$185$		−	9.07735i		−	0.667380i
$186$	−1.79346	+	10.6055i	−0.131503	+	0.777631i
$187$	23.1754	−	23.1754i	1.69475	−	1.69475i
$188$	−1.62155	+	4.65735i	−0.118264	+	0.339672i
$189$	0.707107	+	0.707107i	0.0514344	+	0.0514344i
$190$	3.95752	+	5.56842i	0.287109	+	0.403976i
$191$	−21.8175			−1.57866			−0.789330	−	0.613969i	$-0.789572\pi$
$191$	−21.8175			−1.57866			−0.789330	+	0.613969i	$0.789572\pi$
$192$	−7.80764	−	1.74376i	−0.563468	−	0.125845i
$193$	6.18705			0.445354			0.222677	−	0.974892i	$-0.428521\pi$
$193$	6.18705			0.445354			0.222677	+	0.974892i	$0.428521\pi$
$194$	−9.20110	−	12.9464i	−0.660601	−	0.929497i
$195$	−0.951070	−	0.951070i	−0.0681075	−	0.0681075i
$196$	0.657621	−	1.88879i	0.0469729	−	0.134914i
$197$	4.73831	−	4.73831i	0.337590	−	0.337590i	−0.517869	−	0.855460i	$-0.673275\pi$
$197$	4.73831	−	4.73831i	0.337590	−	0.337590i	0.855460	+	0.517869i	$0.173275\pi$
$198$	0.997408	−	5.89810i	0.0708827	−	0.419160i
$199$			17.6373i			1.25027i	0.780516	+	0.625136i	$0.214957\pi$
$199$			17.6373i			1.25027i	−0.780516	+	0.625136i	$0.785043\pi$
$200$	2.43100	+	8.36479i	0.171898	+	0.591480i
$201$		−	3.14985i		−	0.222173i
$202$	19.7247	+	3.33557i	1.38782	+	0.234690i
$203$	3.68876	−	3.68876i	0.258900	−	0.258900i
$204$	13.9520	−	6.74569i	0.976836	−	0.472293i
$205$	−7.24485	−	7.24485i	−0.506002	−	0.506002i
$206$	−8.77338	+	6.23531i	−0.611271	+	0.434435i
$207$	8.35641			0.580811
$208$	0.446700	+	3.85670i	0.0309731	+	0.267414i
$209$	14.7449			1.01993
$210$	1.59738	−	1.13527i	0.110230	−	0.0783413i
$211$	16.9192	+	16.9192i	1.16476	+	1.16476i	0.983420	+	0.181344i	$0.0580449\pi$
$211$	16.9192	+	16.9192i	1.16476	+	1.16476i	0.181344	+	0.983420i	$0.441955\pi$
$212$	8.00888	+	16.5646i	0.550052	+	1.13766i
$213$	10.0226	−	10.0226i	0.686737	−	0.686737i
$214$	5.43815	+	0.919628i	0.371744	+	0.0628645i
$215$			13.8488i			0.944477i
$216$	1.36238	−	2.47869i	0.0926985	−	0.168654i
$217$			7.60568i			0.516307i
$218$	−2.56640	+	15.1762i	−0.173818	+	1.02786i
$219$	4.19942	−	4.19942i	0.283770	−	0.283770i
$220$	−11.0709	−	3.85454i	−0.746397	−	0.259873i
$221$	−5.31812	−	5.31812i	−0.357735	−	0.357735i
$222$	−5.36666	−	7.55115i	−0.360187	−	0.506800i
$223$	−10.0690			−0.674271			−0.337136	−	0.941456i	$-0.609458\pi$
$223$	−10.0690			−0.674271			−0.337136	+	0.941456i	$0.609458\pi$
$224$	−5.64915	−	0.295218i	−0.377449	−	0.0197251i
$225$	−3.07976			−0.205317
$226$	3.83565	+	5.39694i	0.255143	+	0.358999i
$227$	−14.9150	−	14.9150i	−0.989946	−	0.989946i	0.0100043	−	0.999950i	$-0.496815\pi$
$227$	−14.9150	−	14.9150i	−0.989946	−	0.989946i	−0.999950	+	0.0100043i	$0.996815\pi$
$228$	6.58426	+	2.29244i	0.436053	+	0.151821i
$229$	−3.15436	+	3.15436i	−0.208446	+	0.208446i	−0.803607	−	0.595161i	$-0.797088\pi$
$229$	−3.15436	+	3.15436i	−0.208446	+	0.208446i	0.595161	+	0.803607i	$0.297088\pi$
$230$	2.73055	−	16.1469i	0.180047	−	1.06470i
$231$		−	4.22980i		−	0.278300i
$232$	−12.9306	−	7.10714i	−0.848933	−	0.466606i
$233$			7.66530i			0.502171i	0.967965	+	0.251085i	$0.0807875\pi$
$233$			7.66530i			0.502171i	−0.967965	+	0.251085i	$0.919213\pi$
$234$	−1.35345	−	0.228878i	−0.0884778	−	0.0149622i
$235$	−2.41612	+	2.41612i	−0.157610	+	0.157610i
$236$	2.68992	+	5.56352i	0.175099	+	0.362154i
$237$	1.82758	+	1.82758i	0.118714	+	0.118714i
$238$	8.93212	−	6.34813i	0.578983	−	0.411488i
$239$	3.16599			0.204791			0.102396	−	0.994744i	$-0.467349\pi$
$239$	3.16599			0.204791			0.102396	+	0.994744i	$0.467349\pi$
$240$	−4.34435	−	3.44245i	−0.280427	−	0.222209i
$241$	−11.6790			−0.752313			−0.376157	−	0.926556i	$-0.622755\pi$
$241$	−11.6790			−0.752313			−0.376157	+	0.926556i	$0.622755\pi$
$242$	−7.94375	+	5.64568i	−0.510644	+	0.362918i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	2.60624	−	1.26010i	0.166848	−	0.0806695i
$245$	0.979857	−	0.979857i	0.0626008	−	0.0626008i
$246$	−10.3100	−	1.74349i	−0.657342	−	0.111161i
$247$		−	3.38355i		−	0.215290i
$248$	20.6574	−	6.00353i	1.31175	−	0.381224i
$249$			6.79790i			0.430799i
$250$	−2.64016	+	15.6124i	−0.166978	+	0.987412i
$251$	−2.02154	+	2.02154i	−0.127599	+	0.127599i	−0.768022	−	0.640423i	$-0.778759\pi$
$251$	−2.02154	+	2.02154i	−0.127599	+	0.127599i	0.640423	+	0.768022i	$0.278759\pi$
$252$	0.657621	−	1.88879i	0.0414262	−	0.118983i
$253$	−24.9933	−	24.9933i	−1.57132	−	1.57132i
$254$	1.47348	+	2.07326i	0.0924546	+	0.130088i
$255$	10.7374			0.672405
$256$	3.65731	+	15.5764i	0.228582	+	0.973525i
$257$	−3.57377			−0.222926			−0.111463	−	0.993769i	$-0.535554\pi$
$257$	−3.57377			−0.222926			−0.111463	+	0.993769i	$0.535554\pi$
$258$	8.18758	+	11.5203i	0.509737	+	0.717224i
$259$	−4.63198	−	4.63198i	−0.287817	−	0.287817i
$260$	−0.884511	+	2.54046i	−0.0548550	+	0.157552i
$261$	3.68876	−	3.68876i	0.228328	−	0.228328i
$262$	−4.27847	+	25.3004i	−0.264324	+	1.56306i
$263$			4.46531i			0.275343i	0.990478	+	0.137672i	$0.0439618\pi$
$263$			4.46531i			0.275343i	−0.990478	+	0.137672i	$0.956038\pi$
$264$	−11.4883	+	3.33878i	−0.707059	+	0.205488i
$265$			12.7481i			0.783110i
$266$	4.86088	+	0.822008i	0.298040	+	0.0504006i
$267$	4.21829	−	4.21829i	0.258155	−	0.258155i
$268$	−5.67158	+	2.74216i	−0.346447	+	0.167504i
$269$	11.0579	+	11.0579i	0.674211	+	0.674211i	0.958684	−	0.284473i	$-0.0918185\pi$
$269$	11.0579	+	11.0579i	0.674211	+	0.674211i	−0.284473	+	0.958684i	$0.591819\pi$
$270$	1.59738	−	1.13527i	0.0972137	−	0.0690905i
$271$	7.19248			0.436912			0.218456	−	0.975847i	$-0.429898\pi$
$271$	7.19248			0.436912			0.218456	+	0.975847i	$0.429898\pi$
$272$	−24.2924	−	19.2492i	−1.47294	−	1.16715i
$273$	−0.970621			−0.0587447
$274$	−16.4323	+	11.6786i	−0.992714	+	0.705529i
$275$	9.21131	+	9.21131i	0.555463	+	0.555463i
$276$	−7.27483	−	15.0464i	−0.437893	−	0.905689i
$277$	−6.19860	+	6.19860i	−0.372438	+	0.372438i	−0.868364	−	0.495927i	$-0.834828\pi$
$277$	−6.19860	+	6.19860i	−0.372438	+	0.372438i	0.495927	+	0.868364i	$0.334828\pi$
$278$	13.7502	+	2.32525i	0.824682	+	0.139459i
$279$			7.60568i			0.455340i
$280$	−3.43479	−	1.88789i	−0.205268	−	0.112823i
$281$			12.6024i			0.751795i	0.926661	+	0.375898i	$0.122666\pi$
$281$			12.6024i			0.751795i	−0.926661	+	0.375898i	$0.877334\pi$
$282$	−0.581445	+	3.43833i	−0.0346245	+	0.204749i
$283$	−6.24349	+	6.24349i	−0.371137	+	0.371137i	−0.867891	−	0.496754i	$-0.834525\pi$
$283$	−6.24349	+	6.24349i	−0.371137	+	0.371137i	0.496754	+	0.867891i	$0.334525\pi$
$284$	−26.7719	−	9.32118i	−1.58862	−	0.553111i
$285$	3.41575	+	3.41575i	0.202331	+	0.202331i
$286$	3.36350	+	4.73261i	0.198888	+	0.279845i
$287$	−7.39378			−0.436441
$288$	−5.64915	−	0.295218i	−0.332879	−	0.0173959i
$289$	43.0408			2.53181
$290$	−5.92236	−	8.33305i	−0.347773	−	0.489334i
$291$	−7.94149	−	7.94149i	−0.465539	−	0.465539i
$292$	−11.2173	−	3.90553i	−0.656443	−	0.228554i
$293$	10.7496	−	10.7496i	0.627997	−	0.627997i	−0.319567	−	0.947564i	$-0.603537\pi$
$293$	10.7496	−	10.7496i	0.627997	−	0.627997i	0.947564	+	0.319567i	$0.103537\pi$
$294$	0.235805	−	1.39442i	0.0137524	−	0.0813240i
$295$			4.28167i			0.249289i
$296$	−8.92444	+	16.2369i	−0.518723	+	0.943752i
$297$		−	4.22980i		−	0.245438i
$298$	−2.83369	−	0.479197i	−0.164151	−	0.0277591i
$299$	−5.73528	+	5.73528i	−0.331680	+	0.331680i
$300$	2.68114	+	5.54537i	0.154796	+	0.320162i
$301$	7.06672	+	7.06672i	0.407319	+	0.407319i
$302$	−8.17431	+	5.80954i	−0.470379	+	0.334302i
$303$	14.1455			0.812635
$304$	−1.60431	−	13.8513i	−0.0920136	−	0.794424i
$305$	2.00576			0.114849
$306$	8.93212	−	6.34813i	0.510615	−	0.362898i
$307$	18.4139	+	18.4139i	1.05094	+	1.05094i	0.998631	+	0.0523045i	$0.0166566\pi$
$307$	18.4139	+	18.4139i	1.05094	+	1.05094i	0.0523045	+	0.998631i	$0.483343\pi$
$308$	−7.61611	+	3.68233i	−0.433968	+	0.209820i
$309$	−5.38171	+	5.38171i	−0.306155	+	0.306155i
$310$	14.6963	+	2.48524i	0.834694	+	0.141152i
$311$			19.1317i			1.08486i	0.840101	+	0.542430i	$0.182496\pi$
$311$			19.1317i			1.08486i	−0.840101	+	0.542430i	$0.817504\pi$
$312$	0.766158	+	2.63626i	0.0433752	+	0.149249i
$313$		−	32.5993i		−	1.84262i	−0.388827	−	0.921311i	$-0.627120\pi$
$313$		−	32.5993i		−	1.84262i	0.388827	−	0.921311i	$-0.372880\pi$
$314$	4.06321	−	24.0275i	0.229300	−	1.35595i
$315$	0.979857	−	0.979857i	0.0552087	−	0.0552087i
$316$	1.69968	−	4.88174i	0.0956143	−	0.274619i
$317$	16.8042	+	16.8042i	0.943819	+	0.943819i	0.998504	−	0.0546847i	$-0.0174154\pi$
$317$	16.8042	+	16.8042i	0.943819	+	0.943819i	−0.0546847	+	0.998504i	$0.517415\pi$
$318$	7.53687	+	10.6047i	0.422646	+	0.594684i
$319$	−22.0655			−1.23543
$320$	−2.41637	+	10.8193i	−0.135079	+	0.604815i
$321$	3.89995			0.217674
$322$	−6.84608	−	9.63277i	−0.381517	−	0.536813i
$323$	19.0999	+	19.0999i	1.06275	+	1.06275i
$324$	0.657621	−	1.88879i	0.0365345	−	0.104933i
$325$	2.11374	−	2.11374i	0.117249	−	0.117249i
$326$	−2.26422	+	13.3893i	−0.125404	+	0.741565i
$327$			10.8835i			0.601861i
$328$	5.83627	+	20.0819i	0.322254	+	1.10884i
$329$			2.46578i			0.135943i
$330$	−8.17315	−	1.38214i	−0.449917	−	0.0760841i
$331$	−23.2036	+	23.2036i	−1.27539	+	1.27539i	−0.332165	+	0.943221i	$0.607779\pi$
$331$	−23.2036	+	23.2036i	−1.27539	+	1.27539i	−0.943221	+	0.332165i	$0.892221\pi$
$332$	12.2402	−	5.91804i	0.671768	−	0.324795i
$333$	−4.63198	−	4.63198i	−0.253831	−	0.253831i
$334$	−6.38164	+	4.53548i	−0.349188	+	0.248171i
$335$	−4.36484			−0.238476
$336$	−3.97344	+	0.460221i	−0.216769	+	0.0251071i
$337$	2.77461			0.151143			0.0755714	−	0.997140i	$-0.475922\pi$
$337$	2.77461			0.151143			0.0755714	+	0.997140i	$0.475922\pi$
$338$	−13.8996	+	9.87857i	−0.756040	+	0.537323i
$339$	3.31056	+	3.31056i	0.179805	+	0.179805i
$340$	−9.34768	−	19.3337i	−0.506949	−	1.04852i
$341$	22.7480	−	22.7480i	1.23187	−	1.23187i
$342$	4.86088	+	0.822008i	0.262846	+	0.0444491i
$343$		−	1.00000i		−	0.0539949i
$344$	13.6155	−	24.7717i	0.734097	−	1.33560i
$345$		−	11.5797i		−	0.623430i
$346$	2.54255	−	15.0352i	0.136689	−	0.808297i
$347$	4.58489	−	4.58489i	0.246130	−	0.246130i	−0.573250	−	0.819380i	$-0.694318\pi$
$347$	4.58489	−	4.58489i	0.246130	−	0.246130i	0.819380	+	0.573250i	$0.194318\pi$
$348$	−9.85324	−	3.43060i	−0.528189	−	0.183900i
$349$	7.19823	+	7.19823i	0.385313	+	0.385313i	0.873012	−	0.487699i	$-0.162164\pi$
$349$	7.19823	+	7.19823i	0.385313	+	0.385313i	−0.487699	+	0.873012i	$0.662164\pi$
$350$	2.52313	+	3.55016i	0.134867	+	0.189764i
$351$	−0.970621			−0.0518079
$352$	16.0132	+	17.7791i	0.853504	+	0.947630i
$353$	−33.3957			−1.77748			−0.888738	−	0.458416i	$-0.848417\pi$
$353$	−33.3957			−1.77748			−0.888738	+	0.458416i	$0.848417\pi$
$354$	2.53139	+	3.56178i	0.134542	+	0.189307i
$355$	−13.8886	−	13.8886i	−0.737130	−	0.737130i
$356$	−11.2677	−	3.92308i	−0.597188	−	0.207923i
$357$	5.47909	−	5.47909i	0.289984	−	0.289984i
$358$	−2.98909	+	17.6758i	−0.157979	+	0.934194i
$359$		−	30.4485i		−	1.60701i	−0.595296	−	0.803506i	$-0.702965\pi$
$359$		−	30.4485i		−	1.60701i	0.595296	−	0.803506i	$-0.297035\pi$
$360$	−3.43479	−	1.88789i	−0.181029	−	0.0995007i
$361$		−	6.84806i		−	0.360424i
$362$	11.6403	+	1.96846i	0.611803	+	0.103460i
$363$	−4.87280	+	4.87280i	−0.255756	+	0.255756i
$364$	0.844993	+	1.74769i	0.0442897	+	0.0916037i
$365$	−5.81925	−	5.81925i	−0.304593	−	0.304593i
$366$	1.66852	−	1.18583i	0.0872152	−	0.0619845i
$367$	−7.37192			−0.384811			−0.192405	−	0.981316i	$-0.561629\pi$
$367$	−7.37192			−0.384811			−0.192405	+	0.981316i	$0.561629\pi$
$368$	−20.7591	+	26.1979i	−1.08215	+	1.36566i
$369$	−7.39378			−0.384905
$370$	−10.4638	+	7.43672i	−0.543988	+	0.386617i
$371$	6.50509	+	6.50509i	0.337727	+	0.337727i
$372$	13.6947	−	6.62127i	0.710036	−	0.343297i
$373$	−12.6122	+	12.6122i	−0.653034	+	0.653034i	−0.953722	−	0.300688i	$-0.902784\pi$
$373$	−12.6122	+	12.6122i	−0.653034	+	0.653034i	0.300688	+	0.953722i	$0.402784\pi$
$374$	−45.7020	−	7.72852i	−2.36319	−	0.399632i
$375$			11.1963i			0.578177i
$376$	6.69719	−	1.94636i	0.345381	−	0.100376i
$377$			5.06343i			0.260780i
$378$	0.235805	−	1.39442i	0.0121285	−	0.0717210i
$379$	−9.17933	+	9.17933i	−0.471511	+	0.471511i	−0.902403	−	0.430893i	$-0.858199\pi$
$379$	−9.17933	+	9.17933i	−0.471511	+	0.471511i	0.430893	+	0.902403i	$0.358199\pi$
$380$	3.17670	−	9.12399i	0.162961	−	0.468051i
$381$	1.27177	+	1.27177i	0.0651546	+	0.0651546i
$382$	17.8742	+	25.1499i	0.914526	+	1.28678i
$383$	−6.35061			−0.324501			−0.162251	−	0.986750i	$-0.551875\pi$
$383$	−6.35061			−0.324501			−0.162251	+	0.986750i	$0.551875\pi$
$384$	4.38641	+	10.4288i	0.223843	+	0.532191i
$385$	−5.86134			−0.298722
$386$	−5.06881	−	7.13206i	−0.257996	−	0.363012i
$387$	7.06672	+	7.06672i	0.359222	+	0.359222i
$388$	−7.38572	+	21.2130i	−0.374953	+	1.07693i
$389$	10.1588	−	10.1588i	0.515070	−	0.515070i	−0.401006	−	0.916076i	$-0.631339\pi$
$389$	10.1588	−	10.1588i	0.515070	−	0.515070i	0.916076	+	0.401006i	$0.131339\pi$
$390$	−0.317162	+	1.87551i	−0.0160601	+	0.0949702i
$391$		−	64.7504i		−	3.27457i
$392$	−2.71605	+	0.789348i	−0.137181	+	0.0398681i
$393$			18.1441i			0.915247i
$394$	−9.34395	−	1.58013i	−0.470741	−	0.0796056i
$395$	2.53252	−	2.53252i	0.127425	−	0.127425i
$396$	−7.61611	+	3.68233i	−0.382724	+	0.185044i
$397$	14.2143	+	14.2143i	0.713397	+	0.713397i	0.967244	−	0.253847i	$-0.0816961\pi$
$397$	14.2143	+	14.2143i	0.713397	+	0.713397i	−0.253847	+	0.967244i	$0.581696\pi$
$398$	20.3312	−	14.4495i	1.01911	−	0.724290i
$399$	3.48596			0.174516
$400$	7.65080	−	9.65526i	0.382540	−	0.482763i
$401$	17.0760			0.852733			0.426367	−	0.904550i	$-0.359793\pi$
$401$	17.0760			0.852733			0.426367	+	0.904550i	$0.359793\pi$
$402$	−3.63096	+	2.58055i	−0.181096	+	0.128706i
$403$	−5.22003	−	5.22003i	−0.260028	−	0.260028i
$404$	−12.3146	−	25.4701i	−0.612674	−	1.26719i
$405$	0.979857	−	0.979857i	0.0486895	−	0.0486895i
$406$	−7.27423	−	1.23012i	−0.361014	−	0.0610500i
$407$			27.7077i			1.37342i
$408$	−19.2064	−	10.5566i	−0.950857	−	0.522628i
$409$		−	35.3057i		−	1.74575i	−0.487941	−	0.872877i	$-0.662252\pi$
$409$		−	35.3057i		−	1.74575i	0.487941	−	0.872877i	$-0.337748\pi$
$410$	−2.41600	+	14.2869i	−0.119318	+	0.705578i
$411$	−10.0798	+	10.0798i	−0.497201	+	0.497201i
$412$	14.3754	+	5.00508i	0.708225	+	0.246583i
$413$	2.18485	+	2.18485i	0.107509	+	0.107509i
$414$	−6.84608	−	9.63277i	−0.336467	−	0.473425i
$415$	9.42003			0.462411
$416$	4.07981	−	3.67458i	0.200029	−	0.180161i
$417$	9.86090			0.482890
$418$	−12.0799	−	16.9971i	−0.590849	−	0.831354i
$419$	−17.0370	−	17.0370i	−0.832314	−	0.832314i	0.155519	−	0.987833i	$-0.450295\pi$
$419$	−17.0370	−	17.0370i	−0.832314	−	0.832314i	−0.987833	+	0.155519i	$0.950295\pi$
$420$	−2.61735	−	0.911283i	−0.127714	−	0.0444661i
$421$	5.35804	−	5.35804i	0.261135	−	0.261135i	−0.564380	−	0.825515i	$-0.690885\pi$
$421$	5.35804	−	5.35804i	0.261135	−	0.261135i	0.825515	+	0.564380i	$0.190885\pi$
$422$	5.64219	−	33.3646i	0.274657	−	1.62417i
$423$			2.46578i			0.119890i
$424$	12.5334	−	22.8029i	0.608674	−	1.10741i
$425$			23.8638i			1.15757i
$426$	−19.7646	−	3.34233i	−0.957597	−	0.161936i
$427$	1.02350	−	1.02350i	0.0495304	−	0.0495304i
$428$	−3.39517	−	7.02219i	−0.164112	−	0.339430i
$429$	2.90305	+	2.90305i	0.140161	+	0.140161i
$430$	15.9640	−	11.3458i	0.769853	−	0.547141i
$431$	8.52604			0.410685			0.205342	−	0.978690i	$-0.434169\pi$
$431$	8.52604			0.410685			0.205342	+	0.978690i	$0.434169\pi$
$432$	−3.97344	+	0.460221i	−0.191172	+	0.0221424i
$433$	−2.15043			−0.103343			−0.0516715	−	0.998664i	$-0.516455\pi$
$433$	−2.15043			−0.103343			−0.0516715	+	0.998664i	$0.516455\pi$
$434$	8.76737	−	6.23104i	0.420847	−	0.299099i
$435$	−5.11161	−	5.11161i	−0.245083	−	0.245083i
$436$	19.5968	−	9.47488i	0.938514	−	0.453764i
$437$	20.5981	−	20.5981i	0.985342	−	0.985342i
$438$	−8.28126	−	1.40042i	−0.395694	−	0.0669146i
$439$		−	23.1132i		−	1.10313i	−0.834132	−	0.551566i	$-0.814031\pi$
$439$		−	23.1132i		−	1.10313i	0.834132	−	0.551566i	$-0.185969\pi$
$440$	4.62664	+	15.9197i	0.220566	+	0.758942i
$441$		−	1.00000i		−	0.0476190i
$442$	−1.77348	+	10.4873i	−0.0843558	+	0.498832i
$443$	−1.94184	+	1.94184i	−0.0922594	+	0.0922594i	−0.751730	−	0.659471i	$-0.770780\pi$
$443$	−1.94184	+	1.94184i	−0.0922594	+	0.0922594i	0.659471	+	0.751730i	$0.270780\pi$
$444$	−4.30782	+	12.3727i	−0.204440	+	0.587184i
$445$	−5.84540	−	5.84540i	−0.277099	−	0.277099i
$446$	8.24916	+	11.6070i	0.390609	+	0.549606i
$447$	−2.03217			−0.0961185
$448$	4.28782	+	6.75386i	0.202580	+	0.319090i
$449$	4.34764			0.205178			0.102589	−	0.994724i	$-0.467287\pi$
$449$	4.34764			0.205178			0.102589	+	0.994724i	$0.467287\pi$
$450$	2.52313	+	3.55016i	0.118941	+	0.167356i
$451$	22.1142	+	22.1142i	1.04132	+	1.04132i
$452$	3.07887	−	8.84301i	0.144818	−	0.415940i
$453$	−5.01423	+	5.01423i	−0.235589	+	0.235589i
$454$	−4.97385	+	29.4125i	−0.233434	+	1.38040i
$455$			1.34502i			0.0630553i
$456$	−2.75164	−	9.46805i	−0.128857	−	0.443382i
$457$			2.90858i			0.136057i	0.997683	+	0.0680287i	$0.0216710\pi$
$457$			2.90858i			0.136057i	−0.997683	+	0.0680287i	$0.978329\pi$
$458$	6.22040	+	1.05191i	0.290660	+	0.0491526i
$459$	5.47909	−	5.47909i	0.255742	−	0.255742i
$460$	−20.8502	+	10.0809i	−0.972148	+	0.470026i
$461$	−0.855011	−	0.855011i	−0.0398218	−	0.0398218i	0.686915	−	0.726737i	$-0.258964\pi$
$461$	−0.855011	−	0.855011i	−0.0398218	−	0.0398218i	−0.726737	+	0.686915i	$0.758964\pi$
$462$	−4.87586	+	3.46531i	−0.226845	+	0.161221i
$463$	18.1432			0.843185			0.421592	−	0.906785i	$-0.361471\pi$
$463$	18.1432			0.843185			0.421592	+	0.906785i	$0.361471\pi$
$464$	2.40083	+	20.7282i	0.111456	+	0.962282i
$465$	10.5394			0.488753
$466$	8.83610	−	6.27989i	0.409325	−	0.290910i
$467$	−9.77872	−	9.77872i	−0.452505	−	0.452505i	0.443680	−	0.896185i	$-0.353673\pi$
$467$	−9.77872	−	9.77872i	−0.452505	−	0.452505i	−0.896185	+	0.443680i	$0.853673\pi$
$468$	0.844993	+	1.74769i	0.0390598	+	0.0807869i
$469$	−2.22728	+	2.22728i	−0.102846	+	0.102846i
$470$	4.76458	+	0.805723i	0.219774	+	0.0371653i
$471$		−	17.2312i		−	0.793972i
$472$	4.20955	−	7.65875i	0.193760	−	0.352523i
$473$		−	42.2720i		−	1.94367i
$474$	0.609459	−	3.60399i	0.0279934	−	0.165537i
$475$	−7.59145	+	7.59145i	−0.348320	+	0.348320i
$476$	−14.6355	−	5.09564i	−0.670816	−	0.233558i
$477$	6.50509	+	6.50509i	0.297848	+	0.297848i
$478$	−2.59378	−	3.64957i	−0.118637	−	0.166927i
$479$	23.4030			1.06931			0.534655	−	0.845071i	$-0.320442\pi$
$479$	23.4030			1.06931			0.534655	+	0.845071i	$0.320442\pi$
$480$	−0.409092	+	7.82817i	−0.0186724	+	0.357306i
$481$	6.35816			0.289907
$482$	9.56819	+	13.4629i	0.435819	+	0.613218i
$483$	−5.90887	−	5.90887i	−0.268863	−	0.268863i
$484$	13.0160	+	4.53179i	0.591637	+	0.205990i
$485$	−11.0047	+	11.0047i	−0.499700	+	0.499700i
$486$	0.235805	−	1.39442i	0.0106963	−	0.0632520i
$487$			16.2734i			0.737420i	0.929544	+	0.368710i	$0.120200\pi$
$487$			16.2734i			0.737420i	−0.929544	+	0.368710i	$0.879800\pi$
$488$	−3.58776	−	1.97197i	−0.162410	−	0.0892670i
$489$			9.60209i			0.434222i
$490$	−1.93228	−	0.326762i	−0.0872915	−	0.0147616i
$491$	0.0270638	−	0.0270638i	0.00122137	−	0.00122137i	−0.706496	−	0.707717i	$-0.749725\pi$
$491$	0.0270638	−	0.0270638i	0.00122137	−	0.00122137i	0.707717	+	0.706496i	$0.249725\pi$
$492$	6.43680	+	13.3131i	0.290193	+	0.600203i
$493$	−28.5827	−	28.5827i	−1.28730	−	1.28730i
$494$	−3.90036	+	2.77201i	−0.175485	+	0.124719i
$495$	−5.86134			−0.263448
$496$	−23.8443	−	18.8942i	−1.07064	−	0.848373i
$497$	−14.1741			−0.635795
$498$	7.83621	−	5.56926i	0.351149	−	0.249564i
$499$	19.4506	+	19.4506i	0.870729	+	0.870729i	0.992552	−	0.121823i	$-0.0388740\pi$
$499$	19.4506	+	19.4506i	0.870729	+	0.870729i	−0.121823	+	0.992552i	$0.538874\pi$
$500$	20.1600	−	9.74719i	0.901582	−	0.435908i
$501$	−3.91459	+	3.91459i	−0.174891	+	0.174891i
$502$	3.98648	+	0.674142i	0.177926	+	0.0300884i
$503$			11.5571i			0.515305i	0.966238	+	0.257652i	$0.0829490\pi$
$503$			11.5571i			0.515305i	−0.966238	+	0.257652i	$0.917051\pi$
$504$	−2.71605	+	0.789348i	−0.120983	+	0.0351604i
$505$		−	19.6017i		−	0.872266i
$506$	−8.33475	+	49.2869i	−0.370525	+	2.19107i
$507$	−8.52622	+	8.52622i	−0.378663	+	0.378663i
$508$	1.18276	−	3.39709i	0.0524767	−	0.150721i
$509$	22.3367	+	22.3367i	0.990056	+	0.990056i	0.999951	−	0.00989464i	$-0.00314961\pi$
$509$	22.3367	+	22.3367i	0.990056	+	0.990056i	−0.00989464	+	0.999951i	$0.503150\pi$
$510$	−8.79677	−	12.3775i	−0.389528	−	0.548084i
$511$	−5.93888			−0.262720
$512$	14.9592	−	16.9771i	0.661111	−	0.750288i
$513$	3.48596			0.153909
$514$	2.92785	+	4.11963i	0.129142	+	0.181709i
$515$	7.45759	+	7.45759i	0.328620	+	0.328620i
$516$	6.57217	−	18.8763i	0.289324	−	0.830983i
$517$	7.37496	−	7.37496i	0.324350	−	0.324350i
$518$	−1.54467	+	9.13427i	−0.0678688	+	0.401337i
$519$		−	10.7824i		−	0.473296i
$520$	3.65313	−	1.06169i	0.160200	−	0.0465580i
$521$			17.5991i			0.771031i	0.922701	+	0.385516i	$0.125976\pi$
$521$			17.5991i			0.771031i	−0.922701	+	0.385516i	$0.874024\pi$
$522$	−7.27423	−	1.23012i	−0.318385	−	0.0538410i
$523$	−11.8194	+	11.8194i	−0.516828	+	0.516828i	−0.916610	−	0.399782i	$-0.869086\pi$
$523$	−11.8194	+	11.8194i	−0.516828	+	0.516828i	0.399782	+	0.916610i	$0.369086\pi$
$524$	32.6699	−	15.7957i	1.42719	−	0.690037i
$525$	2.17772	+	2.17772i	0.0950435	+	0.0950435i
$526$	5.14735	−	3.65826i	0.224435	−	0.159508i
$527$	58.9333			2.56718
$528$	13.2607	+	10.5077i	0.577098	+	0.457291i
$529$	−46.8296			−2.03607
$530$	14.6953	−	10.4440i	0.638322	−	0.453660i
$531$	2.18485	+	2.18485i	0.0948142	+	0.0948142i
$532$	−3.03477	−	6.27678i	−0.131574	−	0.272133i
$533$	5.07460	−	5.07460i	0.219805	−	0.219805i
$534$	−8.31848	−	1.40671i	−0.359976	−	0.0608744i
$535$		−	5.40426i		−	0.233647i
$536$	7.80751	+	4.29131i	0.337233	+	0.185356i
$537$			12.6761i			0.547015i
$538$	3.68757	−	21.8062i	0.158983	−	0.940131i
$539$	−2.99092	+	2.99092i	−0.128828	+	0.128828i
$540$	−2.61735	−	0.911283i	−0.112633	−	0.0392154i
$541$	−17.1403	−	17.1403i	−0.736919	−	0.736919i	0.235061	−	0.971981i	$-0.424471\pi$
$541$	−17.1403	−	17.1403i	−0.736919	−	0.736919i	−0.971981	+	0.235061i	$0.924471\pi$
$542$	−5.89252	−	8.29107i	−0.253106	−	0.356132i
$543$	8.34783			0.358240
$544$	−2.28753	+	43.7730i	−0.0980769	+	1.87675i
$545$	15.0816			0.646026
$546$	0.795193	+	1.11887i	0.0340311	+	0.0478834i
$547$	−10.3324	−	10.3324i	−0.441782	−	0.441782i	0.450828	−	0.892611i	$-0.351129\pi$
$547$	−10.3324	−	10.3324i	−0.441782	−	0.441782i	−0.892611	+	0.450828i	$0.851129\pi$
$548$	26.9248	+	9.37440i	1.15017	+	0.400455i
$549$	1.02350	−	1.02350i	0.0436817	−	0.0436817i
$550$	3.07178	−	18.1647i	0.130981	−	0.774547i
$551$		−	18.1852i		−	0.774715i
$552$	−11.3846	+	20.7130i	−0.484562	+	0.881602i
$553$		−	2.58459i		−	0.109908i
$554$	12.2236	+	2.06710i	0.519333	+	0.0878228i
$555$	−6.41866	+	6.41866i	−0.272457	+	0.272457i
$556$	−8.58460	−	17.7554i	−0.364068	−	0.752997i
$557$	6.71091	+	6.71091i	0.284351	+	0.284351i	0.834841	−	0.550491i	$-0.185559\pi$
$557$	6.71091	+	6.71091i	0.284351	+	0.284351i	−0.550491	+	0.834841i	$0.685559\pi$
$558$	8.76737	−	6.23104i	0.371152	−	0.263781i
$559$	−9.70025			−0.410277
$560$	0.637740	+	5.50610i	0.0269494	+	0.232675i
$561$	−32.7750			−1.38376
$562$	14.5273	−	10.3246i	0.612796	−	0.435519i
$563$	0.997484	+	0.997484i	0.0420389	+	0.0420389i	0.727814	−	0.685775i	$-0.240537\pi$
$563$	0.997484	+	0.997484i	0.0420389	+	0.0420389i	−0.685775	+	0.727814i	$0.740537\pi$
$564$	4.43986	−	2.14664i	0.186952	−	0.0903896i
$565$	4.58753	−	4.58753i	0.192999	−	0.192999i
$566$	12.3122	+	2.08207i	0.517520	+	0.0875161i
$567$		−	1.00000i		−	0.0419961i
$568$	11.1883	+	38.4976i	0.469450	+	1.61532i
$569$			33.8927i			1.42085i	0.703771	+	0.710427i	$0.251498\pi$
$569$			33.8927i			1.42085i	−0.703771	+	0.710427i	$0.748502\pi$
$570$	1.13908	−	6.73586i	0.0477108	−	0.282134i
$571$	29.0688	−	29.0688i	1.21649	−	1.21649i	0.247638	−	0.968853i	$-0.420346\pi$
$571$	29.0688	−	29.0688i	1.21649	−	1.21649i	0.968853	−	0.247638i	$-0.0796544\pi$
$572$	2.69988	−	7.75449i	0.112888	−	0.324232i
$573$	15.4273	+	15.4273i	0.644485	+	0.644485i
$574$	6.05744	+	8.52311i	0.252833	+	0.355748i
$575$	25.7357			1.07325
$576$	4.28782	+	6.75386i	0.178659	+	0.281411i
$577$	−35.6352			−1.48351			−0.741756	−	0.670670i	$-0.766007\pi$
$577$	−35.6352			−1.48351			−0.741756	+	0.670670i	$0.766007\pi$
$578$	−35.2616	−	49.6148i	−1.46669	−	2.06370i
$579$	−4.37490	−	4.37490i	−0.181815	−	0.181815i
$580$	−4.75388	+	13.6539i	−0.197394	+	0.566947i
$581$	4.80684	−	4.80684i	0.199421	−	0.199421i
$582$	−2.64832	+	15.6606i	−0.109776	+	0.649155i
$583$		−	38.9124i		−	1.61159i
$584$	4.68784	+	16.1303i	0.193984	+	0.667476i
$585$			1.34502i			0.0556096i
$586$	−21.1982	−	3.58476i	−0.875688	−	0.148085i
$587$	−6.05112	+	6.05112i	−0.249756	+	0.249756i	−0.820871	−	0.571114i	$-0.806511\pi$
$587$	−6.05112	+	6.05112i	−0.249756	+	0.249756i	0.571114	+	0.820871i	$0.306511\pi$
$588$	−1.80059	+	0.870569i	−0.0742549	+	0.0359017i
$589$	18.7476	+	18.7476i	0.772482	+	0.772482i
$590$	4.93566	−	3.50781i	0.203198	−	0.144414i
$591$	−6.70098			−0.275641
$592$	26.0284	−	3.01472i	1.06976	−	0.123904i
$593$	−42.5490			−1.74728			−0.873639	−	0.486575i	$-0.838246\pi$
$593$	−42.5490			−1.74728			−0.873639	+	0.486575i	$0.838246\pi$
$594$	−4.87586	+	3.46531i	−0.200059	+	0.142183i
$595$	−7.59252	−	7.59252i	−0.311263	−	0.311263i
$596$	1.76915	+	3.65910i	0.0724671	+	0.149883i
$597$	12.4714	−	12.4714i	0.510422	−	0.510422i
$598$	11.3100	+	1.91259i	0.462499	+	0.0782118i
$599$		−	14.9804i		−	0.612082i	−0.952018	−	0.306041i	$-0.900995\pi$
$599$		−	14.9804i		−	0.612082i	0.952018	−	0.306041i	$-0.0990045\pi$
$600$	4.19582	−	7.63378i	0.171294	−	0.311648i
$601$			43.3018i			1.76632i	0.469075	+	0.883158i	$0.344587\pi$
$601$			43.3018i			1.76632i	−0.469075	+	0.883158i	$0.655413\pi$
$602$	2.35660	−	13.9356i	0.0960480	−	0.567972i
$603$	−2.22728	+	2.22728i	−0.0907019	+	0.0907019i
$604$	13.3938	+	4.66332i	0.544986	+	0.189748i
$605$	6.75238	+	6.75238i	0.274523	+	0.274523i
$606$	−11.5888	−	16.3060i	−0.470764	−	0.662388i
$607$	−40.4798			−1.64303			−0.821513	−	0.570190i	$-0.806870\pi$
$607$	−40.4798			−1.64303			−0.821513	+	0.570190i	$0.806870\pi$
$608$	−14.6526	+	13.1972i	−0.594239	+	0.535215i
$609$	−5.21669			−0.211391
$610$	−1.64324	−	2.31212i	−0.0665329	−	0.0936150i
$611$	−1.69235	−	1.69235i	−0.0684651	−	0.0684651i
$612$	−14.6355	−	5.09564i	−0.591604	−	0.205979i
$613$	−8.87961	+	8.87961i	−0.358644	+	0.358644i	−0.863313	−	0.504669i	$-0.831615\pi$
$613$	−8.87961	+	8.87961i	−0.358644	+	0.358644i	0.504669	+	0.863313i	$0.331615\pi$
$614$	6.14064	−	36.3122i	0.247816	−	1.46544i
$615$			10.2458i			0.413149i
$616$	10.4844	+	5.76261i	0.422427	+	0.232182i
$617$		−	24.7983i		−	0.998342i	−0.866503	−	0.499171i	$-0.833638\pi$
$617$		−	24.7983i		−	0.998342i	0.866503	−	0.499171i	$-0.166362\pi$
$618$	10.6128	+	1.79469i	0.426907	+	0.0721929i
$619$	−19.1531	+	19.1531i	−0.769830	+	0.769830i	−0.978076	−	0.208246i	$-0.933224\pi$
$619$	−19.1531	+	19.1531i	−0.769830	+	0.769830i	0.208246	+	0.978076i	$0.433224\pi$
$620$	−9.17527	−	18.9771i	−0.368488	−	0.762138i
$621$	−5.90887	−	5.90887i	−0.237115	−	0.237115i
$622$	22.0539	−	15.6739i	0.884281	−	0.628465i
$623$	−5.96557			−0.239005
$624$	2.41124	−	3.04296i	0.0965267	−	0.121816i
$625$	0.116268			0.00465074
$626$	−37.5785	+	26.7073i	−1.50194	+	1.06744i
$627$	−10.4262	−	10.4262i	−0.416384	−	0.416384i
$628$	−31.0262	+	15.0009i	−1.23808	+	0.598603i
$629$	−35.8913	+	35.8913i	−1.43108	+	1.43108i
$630$	−1.93228	−	0.326762i	−0.0769839	−	0.0130185i
$631$		−	24.9707i		−	0.994068i	−0.867731	−	0.497034i	$-0.834422\pi$
$631$		−	24.9707i		−	0.994068i	0.867731	−	0.497034i	$-0.165578\pi$
$632$	−7.01986	+	2.04014i	−0.279235	+	0.0811523i
$633$		−	23.9273i		−	0.951026i
$634$	5.60385	−	33.1380i	0.222557	−	1.31608i
$635$	1.76232	−	1.76232i	0.0699356	−	0.0699356i
$636$	6.04984	−	17.3761i	0.239892	−	0.689007i
$637$	0.686333	+	0.686333i	0.0271935	+	0.0271935i
$638$	18.0774	+	25.4358i	0.715693	+	1.00701i
$639$	−14.1741			−0.560719
$640$	14.4514	−	6.07836i	0.571243	−	0.240268i
$641$	−46.6091			−1.84095			−0.920474	−	0.390805i	$-0.872197\pi$
$641$	−46.6091			−1.84095			−0.920474	+	0.390805i	$0.872197\pi$
$642$	−3.19508	−	4.49563i	−0.126100	−	0.177428i
$643$	11.0061	+	11.0061i	0.434037	+	0.434037i	0.889999	−	0.455962i	$-0.150705\pi$
$643$	11.0061	+	11.0061i	0.434037	+	0.434037i	−0.455962	+	0.889999i	$0.650705\pi$
$644$	−5.49535	+	15.7835i	−0.216547	+	0.621958i
$645$	9.79255	−	9.79255i	0.385581	−	0.385581i
$646$	6.36941	−	37.6650i	0.250601	−	1.48191i
$647$		−	38.4788i		−	1.51276i	−0.654133	−	0.756379i	$-0.726967\pi$
$647$		−	38.4788i		−	1.51276i	0.654133	−	0.756379i	$-0.273033\pi$
$648$	−2.71605	+	0.789348i	−0.106697	+	0.0310085i
$649$		−	13.0694i		−	0.513018i
$650$	−4.16830	−	0.704888i	−0.163494	−	0.0276480i
$651$	5.37803	−	5.37803i	0.210781	−	0.210781i
$652$	17.2894	−	8.35929i	0.677105	−	0.327375i
$653$	−8.40405	−	8.40405i	−0.328876	−	0.328876i	0.523283	−	0.852159i	$-0.324707\pi$
$653$	−8.40405	−	8.40405i	−0.328876	−	0.328876i	−0.852159	+	0.523283i	$0.824707\pi$
$654$	12.5459	−	8.91647i	0.490584	−	0.348662i
$655$	25.1427			0.982407
$656$	18.3678	−	23.1800i	0.717141	−	0.905028i
$657$	−5.93888			−0.231698
$658$	2.84241	−	2.02012i	0.110809	−	0.0787525i
$659$	28.9012	+	28.9012i	1.12583	+	1.12583i	0.990848	+	0.134985i	$0.0430985\pi$
$659$	28.9012	+	28.9012i	1.12583	+	1.12583i	0.134985	+	0.990848i	$0.456902\pi$
$660$	5.10271	+	10.5539i	0.198623	+	0.410808i
$661$	−13.2673	+	13.2673i	−0.516037	+	0.516037i	−0.916370	−	0.400333i	$-0.868895\pi$
$661$	−13.2673	+	13.2673i	−0.516037	+	0.516037i	0.400333	+	0.916370i	$0.368895\pi$
$662$	45.7576	+	7.73792i	1.77842	+	0.300743i
$663$			7.52095i			0.292090i
$664$	−16.8499	−	9.26135i	−0.653903	−	0.359410i
$665$		−	4.83059i		−	0.187322i
$666$	−1.54467	+	9.13427i	−0.0598546	+	0.353946i
$667$	−30.8248	+	30.8248i	−1.19354	+	1.19354i
$668$	10.4565	+	3.64063i	0.404573	+	0.140860i
$669$	7.11987	+	7.11987i	0.275270	+	0.275270i
$670$	3.57594	+	5.03152i	0.138151	+	0.194385i
$671$	−6.12238			−0.236352
$672$	3.78580	+	4.20330i	0.146040	+	0.162146i
$673$	17.5478			0.676417			0.338209	−	0.941071i	$-0.390179\pi$
$673$	17.5478			0.676417			0.338209	+	0.941071i	$0.390179\pi$
$674$	−2.27313	−	3.19841i	−0.0875578	−	0.123198i
$675$	2.17772	+	2.17772i	0.0838205	+	0.0838205i
$676$	22.7749	+	7.92953i	0.875956	+	0.304982i
$677$	−33.3465	+	33.3465i	−1.28161	+	1.28161i	−0.341858	+	0.939752i	$0.611056\pi$
$677$	−33.3465	+	33.3465i	−1.28161	+	1.28161i	−0.939752	+	0.341858i	$0.888944\pi$
$678$	1.10400	−	6.52842i	0.0423989	−	0.250723i
$679$			11.2310i			0.431005i
$680$	−14.6285	+	26.6148i	−0.560978	+	1.02063i
$681$			21.0930i			0.808287i
$682$	−44.8590	−	7.58597i	−1.71774	−	0.290482i
$683$	−17.1553	+	17.1553i	−0.656431	+	0.656431i	−0.954534	−	0.298103i	$-0.903646\pi$
$683$	−17.1553	+	17.1553i	−0.656431	+	0.656431i	0.298103	+	0.954534i	$0.403646\pi$
$684$	−3.03477	−	6.27678i	−0.116037	−	0.239999i
$685$	13.9679	+	13.9679i	0.533685	+	0.533685i
$686$	−1.15274	+	0.819262i	−0.0440118	+	0.0312796i
$687$	4.46094			0.170195
$688$	−39.7099	+	4.59938i	−1.51393	+	0.175350i
$689$	−8.92931			−0.340180
$690$	−13.3484	+	9.48680i	−0.508164	+	0.361156i
$691$	−20.0455	−	20.0455i	−0.762566	−	0.762566i	0.214220	−	0.976786i	$-0.431279\pi$
$691$	−20.0455	−	20.0455i	−0.762566	−	0.762566i	−0.976786	+	0.214220i	$0.931279\pi$
$692$	−19.4147	+	9.38685i	−0.738036	+	0.356835i
$693$	−2.99092	+	2.99092i	−0.113616	+	0.113616i
$694$	−9.04141	−	1.52896i	−0.343207	−	0.0580387i
$695$		−	13.6645i		−	0.518325i
$696$	4.11778	+	14.1688i	0.156084	+	0.537067i
$697$			57.2914i			2.17007i
$698$	2.40046	−	14.1949i	0.0908587	−	0.537286i
$699$	5.42019	−	5.42019i	0.205010	−	0.205010i
$700$	2.02532	−	5.81703i	0.0765497	−	0.219863i
$701$	−34.1260	−	34.1260i	−1.28892	−	1.28892i	−0.935442	−	0.353481i	$-0.884998\pi$
$701$	−34.1260	−	34.1260i	−1.28892	−	1.28892i	−0.353481	−	0.935442i	$-0.615002\pi$
$702$	0.795193	+	1.11887i	0.0300126	+	0.0422292i
$703$	−22.8352			−0.861245
$704$	7.37573	−	33.0248i	0.277983	−	1.24467i
$705$	3.41690			0.128688
$706$	27.3598	+	38.4966i	1.02970	+	1.44884i
$707$	−10.0023	−	10.0023i	−0.376177	−	0.376177i
$708$	2.03194	−	5.83606i	0.0763651	−	0.219333i
$709$	−21.5424	+	21.5424i	−0.809040	+	0.809040i	−0.984489	−	0.175448i	$-0.943862\pi$
$709$	−21.5424	+	21.5424i	−0.809040	+	0.809040i	0.175448	+	0.984489i	$0.443862\pi$
$710$	−4.63155	+	27.3883i	−0.173819	+	1.02787i
$711$		−	2.58459i		−	0.0969295i
$712$	4.70891	+	16.2028i	0.176474	+	0.607225i
$713$		−	63.5562i		−	2.38020i
$714$	−10.8048	−	1.82716i	−0.404358	−	0.0683797i
$715$	4.02283	−	4.02283i	0.150445	−	0.150445i
$716$	22.8244	−	11.0354i	0.852989	−	0.412414i
$717$	−2.23870	−	2.23870i	−0.0836056	−	0.0836056i
$718$	−35.0993	+	24.9453i	−1.30989	+	0.930951i
$719$	−18.3813			−0.685505			−0.342752	−	0.939426i	$-0.611359\pi$
$719$	−18.3813			−0.685505			−0.342752	+	0.939426i	$0.611359\pi$
$720$	0.637740	+	5.50610i	0.0237672	+	0.205200i
$721$	7.61089			0.283444
$722$	−7.89403	+	5.61035i	−0.293785	+	0.208796i
$723$	8.25833	+	8.25833i	0.307131	+	0.307131i
$724$	−7.26736	−	15.0310i	−0.270089	−	0.558622i
$725$	11.3605	−	11.3605i	0.421918	−	0.421918i
$726$	9.60918	+	1.62498i	0.356630	+	0.0603086i
$727$		−	14.8076i		−	0.549185i	−0.961561	−	0.274593i	$-0.911457\pi$
$727$		−	14.8076i		−	0.549185i	0.961561	−	0.274593i	$-0.0885430\pi$
$728$	1.32236	−	2.40587i	0.0490099	−	0.0891675i
$729$		−	1.00000i		−	0.0370370i
$730$	−1.94060	+	11.4756i	−0.0718247	+	0.424730i
$731$	54.7572	−	54.7572i	2.02527	−	2.02527i
$732$	−2.73392	−	0.951868i	−0.101048	−	0.0351821i
$733$	4.58173	+	4.58173i	0.169230	+	0.169230i	0.786641	−	0.617411i	$-0.211818\pi$
$733$	4.58173	+	4.58173i	0.169230	+	0.169230i	−0.617411	+	0.786641i	$0.711818\pi$
$734$	6.03953	+	8.49791i	0.222923	+	0.313663i
$735$	−1.38573			−0.0511133
$736$	47.2066	+	2.46696i	1.74006	+	0.0909335i
$737$	13.3232			0.490768
$738$	6.05744	+	8.52311i	0.222977	+	0.313740i
$739$	20.3064	+	20.3064i	0.746984	+	0.746984i	0.973912	−	0.226927i	$-0.0728680\pi$
$739$	20.3064	+	20.3064i	0.746984	+	0.746984i	−0.226927	+	0.973912i	$0.572868\pi$
$740$	17.1452	+	5.96946i	0.630271	+	0.219442i
$741$	−2.39253	+	2.39253i	−0.0878918	+	0.0878918i
$742$	2.16931	−	12.8280i	0.0796379	−	0.470933i
$743$		−	12.7830i		−	0.468964i	−0.972120	−	0.234482i	$-0.924661\pi$
$743$		−	12.7830i		−	0.468964i	0.972120	−	0.234482i	$-0.0753394\pi$
$744$	−18.8521	−	10.3619i	−0.691152	−	0.379884i
$745$			2.81604i			0.103172i
$746$	24.8712	+	4.20590i	0.910601	+	0.153989i
$747$	4.80684	−	4.80684i	0.175873	−	0.175873i
$748$	28.5329	+	59.0142i	1.04327	+	2.15777i
$749$	−2.75768	−	2.75768i	−0.100763	−	0.100763i
$750$	12.9065	−	9.17273i	0.471278	−	0.334941i
$751$	−34.4832			−1.25831			−0.629155	−	0.777280i	$-0.716599\pi$
$751$	−34.4832			−1.25831			−0.629155	+	0.777280i	$0.716599\pi$
$752$	−7.73040	−	6.12555i	−0.281899	−	0.223376i
$753$	2.85889			0.104184
$754$	5.83682	−	4.14827i	0.212564	−	0.151071i
$755$	6.94836	+	6.94836i	0.252877	+	0.252877i
$756$	−1.80059	+	0.870569i	−0.0654867	+	0.0316623i
$757$	0.510274	−	0.510274i	0.0185462	−	0.0185462i	−0.697773	−	0.716319i	$-0.745826\pi$
$757$	0.510274	−	0.510274i	0.0185462	−	0.0185462i	0.716319	+	0.697773i	$0.245826\pi$
$758$	18.1017	+	3.06111i	0.657482	+	0.111185i
$759$			35.3459i			1.28298i
$760$	−13.1201	+	3.81302i	−0.475917	+	0.138313i
$761$			27.0730i			0.981396i	0.871330	+	0.490698i	$0.163258\pi$
$761$			27.0730i			0.981396i	−0.871330	+	0.490698i	$0.836742\pi$
$762$	0.424108	−	2.50793i	0.0153638	−	0.0908526i
$763$	7.69583	−	7.69583i	0.278608	−	0.278608i
$764$	14.3477	−	41.2087i	0.519080	−	1.49088i
$765$	−7.59252	−	7.59252i	−0.274508	−	0.274508i
$766$	5.20281	+	7.32061i	0.187985	+	0.264504i
$767$	−2.99906			−0.108290
$768$	8.42806	−	13.6003i	0.304122	−	0.490758i
$769$	−8.47674			−0.305679			−0.152840	−	0.988251i	$-0.548842\pi$
$769$	−8.47674			−0.305679			−0.152840	+	0.988251i	$0.548842\pi$
$770$	4.80197	+	6.75661i	0.173051	+	0.243491i
$771$	2.52704	+	2.52704i	0.0910091	+	0.0910091i
$772$	−4.06873	+	11.6860i	−0.146437	+	0.420590i
$773$	−6.94565	+	6.94565i	−0.249818	+	0.249818i	−0.820896	−	0.571078i	$-0.806525\pi$
$773$	−6.94565	+	6.94565i	−0.249818	+	0.249818i	0.571078	+	0.820896i	$0.306525\pi$
$774$	2.35660	−	13.9356i	0.0847064	−	0.500904i
$775$			23.4237i			0.841403i
$776$	30.5039	−	8.86514i	1.09503	−	0.318240i
$777$			6.55060i			0.235002i
$778$	−20.0331	−	3.38773i	−0.718221	−	0.121456i
$779$	−18.2253	+	18.2253i	−0.652989	+	0.652989i
$780$	2.42182	−	1.17093i	0.0867150	−	0.0419260i
$781$	42.3936	+	42.3936i	1.51696	+	1.51696i
$782$	−74.6405	+	53.0475i	−2.66914	+	1.89698i
$783$	−5.21669			−0.186429
$784$	3.13507	+	2.48422i	0.111967	+	0.0887221i
$785$	−23.8777			−0.852233
$786$	20.9154	−	14.8647i	0.746028	−	0.530208i
$787$	−25.0044	−	25.0044i	−0.891310	−	0.891310i	0.103336	−	0.994646i	$-0.467048\pi$
$787$	−25.0044	−	25.0044i	−0.891310	−	0.891310i	−0.994646	+	0.103336i	$0.967048\pi$
$788$	5.83367	+	12.0657i	0.207816	+	0.429822i
$789$	3.15745	−	3.15745i	0.112408	−	0.112408i
$790$	−4.99414	−	0.844543i	−0.177684	−	0.0300475i
$791$		−	4.68183i		−	0.166467i
$792$	10.4844	+	5.76261i	0.372546	+	0.204765i
$793$			1.40492i			0.0498901i
$794$	4.74018	−	28.0307i	0.168223	−	0.994772i
$795$	9.01428	−	9.01428i	0.319703	−	0.319703i
$796$	−33.3131	−	11.5986i	−1.18075	−	0.411103i
$797$	−14.3282	−	14.3282i	−0.507533	−	0.507533i	0.406236	−	0.913768i	$-0.366841\pi$
$797$	−14.3282	−	14.3282i	−0.507533	−	0.507533i	−0.913768	+	0.406236i	$0.866841\pi$
$798$	−2.85592	−	4.01841i	−0.101098	−	0.142250i
$799$	19.1064			0.675935
$800$	−17.3980	−	0.909202i	−0.615113	−	0.0321451i
$801$	−5.96557			−0.210783
$802$	−13.9897	−	19.6842i	−0.493993	−	0.695072i
$803$	17.7627	+	17.7627i	0.626832	+	0.626832i
$804$	5.94942	+	2.07141i	0.209820	+	0.0730530i
$805$	−8.18808	+	8.18808i	−0.288592	+	0.288592i
$806$	−1.74077	+	10.2939i	−0.0613160	+	0.362587i
$807$		−	15.6382i		−	0.550491i
$808$	−19.2716	+	35.0622i	−0.677971	+	1.23348i
$809$			33.4003i			1.17429i	0.809481	+	0.587146i	$0.199749\pi$
$809$			33.4003i			1.17429i	−0.809481	+	0.587146i	$0.800251\pi$
$810$	−1.93228	−	0.326762i	−0.0678934	−	0.0114812i
$811$	21.6080	−	21.6080i	0.758758	−	0.758758i	−0.217339	−	0.976096i	$-0.569738\pi$
$811$	21.6080	−	21.6080i	0.758758	−	0.758758i	0.976096	+	0.217339i	$0.0697376\pi$
$812$	4.54149	+	9.39310i	0.159375	+	0.329633i
$813$	−5.08585	−	5.08585i	−0.178369	−	0.178369i
$814$	31.9398	−	22.6999i	1.11949	−	0.795630i
$815$	13.3059			0.466085
$816$	3.56606	+	30.7886i	0.124837	+	1.07782i
$817$	34.8382			1.21883
$818$	−40.6983	+	28.9246i	−1.42298	+	1.01132i
$819$	0.686333	+	0.686333i	0.0239824	+	0.0239824i
$820$	18.4484	−	8.91965i	0.644245	−	0.311488i
$821$	−19.8197	+	19.8197i	−0.691713	+	0.691713i	−0.962609	−	0.270896i	$-0.912680\pi$
$821$	−19.8197	+	19.8197i	−0.691713	+	0.691713i	0.270896	+	0.962609i	$0.412680\pi$
$822$	19.8774	+	3.36141i	0.693305	+	0.117243i
$823$			23.2507i			0.810470i	0.914213	+	0.405235i	$0.132810\pi$
$823$			23.2507i			0.810470i	−0.914213	+	0.405235i	$0.867190\pi$
$824$	−6.00764	−	20.6716i	−0.209286	−	0.720128i
$825$		−	13.0268i		−	0.453534i
$826$	0.728600	−	4.30852i	0.0253512	−	0.149913i
$827$	−15.1321	+	15.1321i	−0.526196	+	0.526196i	−0.919436	−	0.393240i	$-0.871354\pi$
$827$	−15.1321	+	15.1321i	−0.526196	+	0.526196i	0.393240	+	0.919436i	$0.371354\pi$
$828$	−5.49535	+	15.7835i	−0.190977	+	0.548515i
$829$	30.4205	+	30.4205i	1.05655	+	1.05655i	0.998302	+	0.0582469i	$0.0185511\pi$
$829$	30.4205	+	30.4205i	1.05655	+	1.05655i	0.0582469	+	0.998302i	$0.481449\pi$
$830$	−7.71747	−	10.8589i	−0.267877	−	0.376916i
$831$	8.76614			0.304094
$832$	−7.57827	−	1.69253i	−0.262729	−	0.0586778i
$833$	−7.74860			−0.268473
$834$	−8.07866	−	11.3671i	−0.279741	−	0.393609i
$835$	5.42455	+	5.42455i	0.187724	+	0.187724i
$836$	−9.69657	+	27.8501i	−0.335363	+	0.963215i
$837$	5.37803	−	5.37803i	0.185892	−	0.185892i
$838$	−5.68150	+	33.5971i	−0.196264	+	1.16059i
$839$			10.3618i			0.357728i	0.983874	+	0.178864i	$0.0572423\pi$
$839$			10.3618i			0.357728i	−0.983874	+	0.178864i	$0.942758\pi$
$840$	1.09382	+	3.76370i	0.0377404	+	0.129860i
$841$		−	1.78616i		−	0.0615916i
$842$	−10.5661	−	1.78680i	−0.364131	−	0.0615770i
$843$	8.91123	−	8.91123i	0.306919	−	0.306919i
$844$	−43.0832	+	20.8304i	−1.48299	+	0.717012i
$845$	11.8150	+	11.8150i	0.406449	+	0.406449i
$846$	2.84241	−	2.02012i	0.0977240	−	0.0694532i
$847$	6.89119			0.236784
$848$	−36.5540	+	4.23384i	−1.25527	+	0.145391i
$849$	8.82963			0.303032
$850$	27.5088	−	19.5507i	0.943544	−	0.670584i
$851$	38.7067	+	38.7067i	1.32685	+	1.32685i
$852$	12.3395	+	25.5217i	0.422745	+	0.874358i
$853$	24.1840	−	24.1840i	0.828045	−	0.828045i	−0.159201	−	0.987246i	$-0.550892\pi$
$853$	24.1840	−	24.1840i	0.828045	−	0.828045i	0.987246	+	0.159201i	$0.0508918\pi$
$854$	−2.01834	−	0.341314i	−0.0690660	−	0.0116795i
$855$		−	4.83059i		−	0.165203i
$856$	−5.31323	+	9.66676i	−0.181602	+	0.330403i
$857$			24.0977i			0.823163i	0.911373	+	0.411581i	$0.135023\pi$
$857$			24.0977i			0.823163i	−0.911373	+	0.411581i	$0.864977\pi$
$858$	0.968106	−	5.72482i	0.0330506	−	0.195442i
$859$	31.4576	−	31.4576i	1.07332	−	1.07332i	0.0762289	−	0.997090i	$-0.475712\pi$
$859$	31.4576	−	31.4576i	1.07332	−	1.07332i	0.997090	−	0.0762289i	$-0.0242880\pi$
$860$	−26.1574	−	9.10723i	−0.891960	−	0.310554i
$861$	5.22819	+	5.22819i	0.178176	+	0.178176i
$862$	−6.98505	−	9.82831i	−0.237912	−	0.334754i
$863$	20.4551			0.696299			0.348149	−	0.937439i	$-0.386810\pi$
$863$	20.4551			0.696299			0.348149	+	0.937439i	$0.386810\pi$
$864$	3.78580	+	4.20330i	0.128795	+	0.142999i
$865$	−14.9415			−0.508027
$866$	1.76176	+	2.47889i	0.0598671	+	0.0842360i
$867$	−30.4344	−	30.4344i	−1.03361	−	1.03361i
$868$	−14.3655	−	5.00165i	−0.487598	−	0.169767i
$869$	−7.73028	+	7.73028i	−0.262232	+	0.262232i
$870$	−1.70461	+	10.0801i	−0.0577918	+	0.341747i
$871$		−	3.05731i		−	0.103593i
$872$	−26.9769	−	14.8276i	−0.913555	−	0.502125i
$873$			11.2310i			0.380111i
$874$	−40.6195	−	6.86904i	−1.37398	−	0.232349i
$875$	7.91701	−	7.91701i	0.267644	−	0.267644i
$876$	5.17020	+	10.6935i	0.174685	+	0.361298i
$877$	0.277805	+	0.277805i	0.00938082	+	0.00938082i	0.711782	−	0.702401i	$-0.247889\pi$
$877$	0.277805	+	0.277805i	0.00938082	+	0.00938082i	−0.702401	+	0.711782i	$0.747889\pi$
$878$	−26.6435	+	18.9357i	−0.899174	+	0.639050i
$879$	−15.2022			−0.512757
$880$	14.5609	−	18.3757i	0.490847	−	0.619445i
$881$	22.5049			0.758208			0.379104	−	0.925354i	$-0.376232\pi$
$881$	22.5049			0.758208			0.379104	+	0.925354i	$0.376232\pi$
$882$	−1.15274	+	0.819262i	−0.0388148	+	0.0275860i
$883$	5.44565	+	5.44565i	0.183261	+	0.183261i	0.792775	−	0.609514i	$-0.208636\pi$
$883$	5.44565	+	5.44565i	0.183261	+	0.183261i	−0.609514	+	0.792775i	$0.708636\pi$
$884$	13.5421	−	6.54751i	0.455471	−	0.220217i
$885$	3.02760	−	3.02760i	0.101772	−	0.101772i
$886$	3.82930	+	0.647561i	0.128648	+	0.0217552i
$887$		−	4.18811i		−	0.140623i	−0.997525	−	0.0703114i	$-0.977601\pi$
$887$		−	4.18811i		−	0.140623i	0.997525	−	0.0703114i	$-0.0223993\pi$
$888$	17.7918	−	5.17071i	0.597053	−	0.173518i
$889$		−	1.79855i		−	0.0603214i
$890$	−1.94932	+	11.5271i	−0.0653413	+	0.386391i
$891$	−2.99092	+	2.99092i	−0.100200	+	0.100200i
$892$	6.62160	−	19.0183i	0.221708	−	0.636779i
$893$	6.07803	+	6.07803i	0.203394	+	0.203394i
$894$	1.66488	+	2.34257i	0.0556819	+	0.0783472i
$895$	17.5656			0.587155
$896$	4.27260	−	10.4759i	0.142738	−	0.349976i
$897$	8.11091			0.270815
$898$	−3.56185	−	5.01170i	−0.118861	−	0.167243i
$899$	−28.0555	−	28.0555i	−0.935703	−	0.935703i
$900$	2.02532	−	5.81703i	0.0675105	−	0.193901i
$901$	50.4053	−	50.4053i	1.67924	−	1.67924i
$902$	7.37462	−	43.6092i	0.245548	−	1.45203i
$903$		−	9.99386i		−	0.332575i
$904$	−12.7161	+	3.69560i	−0.422931	+	0.122914i
$905$		−	11.5678i		−	0.384527i
$906$	9.88808	+	1.67214i	0.328509	+	0.0555532i
$907$	−36.9451	+	36.9451i	−1.22674	+	1.22674i	−0.261553	+	0.965189i	$0.584235\pi$
$907$	−36.9451	+	36.9451i	−1.22674	+	1.22674i	−0.965189	+	0.261553i	$0.915765\pi$
$908$	37.9798	−	18.3630i	1.26041	−	0.609396i
$909$	−10.0023	−	10.0023i	−0.331757	−	0.331757i
$910$	1.55045	−	1.10192i	0.0513971	−	0.0365283i
$911$	−18.8612			−0.624900			−0.312450	−	0.949934i	$-0.601150\pi$
$911$	−18.8612			−0.624900			−0.312450	+	0.949934i	$0.601150\pi$
$912$	−8.65990	+	10.9287i	−0.286758	+	0.361887i
$913$	−28.7537			−0.951610
$914$	3.35283	−	2.38288i	0.110902	−	0.0788188i
$915$	−1.41829	−	1.41829i	−0.0468871	−	0.0468871i
$916$	−3.88355	−	8.03230i	−0.128316	−	0.265395i
$917$	12.8298	−	12.8298i	0.423677	−	0.423677i
$918$	−10.8048	−	1.82716i	−0.356610	−	0.0603053i
$919$			37.4649i			1.23585i	0.786236	+	0.617926i	$0.212027\pi$
$919$			37.4649i			1.23585i	−0.786236	+	0.617926i	$0.787973\pi$
$920$	28.7025	+	15.7760i	0.946293	+	0.520119i
$921$		−	26.0412i		−	0.858085i
$922$	−0.285128	+	1.68608i	−0.00939020	+	0.0555282i
$923$	9.72815	−	9.72815i	0.320206	−	0.320206i
$924$	7.98921	+	2.78160i	0.262826	+	0.0915081i
$925$	−14.2654	−	14.2654i	−0.469043	−	0.469043i
$926$	−14.8640	−	20.9144i	−0.488461	−	0.687289i
$927$	7.61089			0.249975
$928$	21.9273	−	19.7493i	0.719799	−	0.648304i
$929$	−36.1739			−1.18683			−0.593413	−	0.804898i	$-0.702220\pi$
$929$	−36.1739			−1.18683			−0.593413	+	0.804898i	$0.702220\pi$
$930$	−8.63452	−	12.1492i	−0.283137	−	0.398387i
$931$	−2.46495	−	2.46495i	−0.0807854	−	0.0807854i
$932$	−14.4782	−	5.04086i	−0.474248	−	0.165119i
$933$	13.5282	−	13.5282i	0.442892	−	0.442892i
$934$	−3.26100	+	19.2836i	−0.106703	+	0.630980i
$935$			45.4172i			1.48530i
$936$	1.32236	−	2.40587i	0.0432227	−	0.0786383i
$937$		−	50.8408i		−	1.66090i	−0.557096	−	0.830448i	$-0.688084\pi$
$937$		−	50.8408i		−	1.66090i	0.557096	−	0.830448i	$-0.311916\pi$
$938$	4.39220	+	0.742752i	0.143411	+	0.0242517i
$939$	−23.0512	+	23.0512i	−0.752247	+	0.752247i
$940$	−2.97465	−	6.15243i	−0.0970224	−	0.200670i
$941$	24.8105	+	24.8105i	0.808801	+	0.808801i	0.984452	−	0.175652i	$-0.0562033\pi$
$941$	24.8105	+	24.8105i	0.808801	+	0.808801i	−0.175652	+	0.984452i	$0.556203\pi$
$942$	−19.8631	+	14.1169i	−0.647175	+	0.459952i
$943$	61.7855			2.01201
$944$	−12.2773	+	1.42201i	−0.399591	+	0.0462824i
$945$	−1.38573			−0.0450777
$946$	−48.7286	+	34.6318i	−1.58430	+	1.12598i
$947$	−9.91506	−	9.91506i	−0.322196	−	0.322196i	0.527413	−	0.849609i	$-0.323162\pi$
$947$	−9.91506	−	9.91506i	−0.322196	−	0.322196i	−0.849609	+	0.527413i	$0.823162\pi$
$948$	−4.65377	+	2.25006i	−0.151147	+	0.0730785i
$949$	4.07605	−	4.07605i	0.132314	−	0.132314i
$950$	14.9704	+	2.53159i	0.485703	+	0.0821356i
$951$		−	23.7648i		−	0.770625i
$952$	6.11634	+	21.0456i	0.198232	+	0.682091i
$953$		−	28.5778i		−	0.925726i	−0.886430	−	0.462863i	$-0.846822\pi$
$953$		−	28.5778i		−	0.925726i	0.886430	−	0.462863i	$-0.153178\pi$
$954$	2.16931	−	12.8280i	0.0702340	−	0.415323i
$955$	21.3780	−	21.3780i	0.691777	−	0.691777i
$956$	−2.08202	+	5.97990i	−0.0673375	+	0.193404i
$957$	15.6027	+	15.6027i	0.504363	+	0.504363i
$958$	−19.1732	−	26.9776i	−0.619457	−	0.871605i
$959$	14.2550			0.460319
$960$	9.35901	−	5.94174i	0.302061	−	0.191769i
$961$	26.8463			0.866011
$962$	−5.20899	−	7.32930i	−0.167945	−	0.236306i
$963$	−2.75768	−	2.75768i	−0.0888649	−	0.0888649i
$964$	7.68038	−	22.0593i	0.247368	−	0.710481i
$965$	−6.06242	+	6.06242i	−0.195156	+	0.195156i
$966$	−1.97048	+	11.6523i	−0.0633993	+	0.374907i
$967$		−	20.7125i		−	0.666068i	−0.942915	−	0.333034i	$-0.891928\pi$
$967$		−	20.7125i		−	0.666068i	0.942915	−	0.333034i	$-0.108072\pi$
$968$	−5.43954	−	18.7168i	−0.174834	−	0.601581i
$969$		−	27.0113i		−	0.867729i
$970$	21.7014	+	3.66985i	0.696789	+	0.117832i
$971$	−3.26325	+	3.26325i	−0.104723	+	0.104723i	−0.757527	−	0.652804i	$-0.773592\pi$
$971$	−3.26325	+	3.26325i	−0.104723	+	0.104723i	0.652804	+	0.757527i	$0.273592\pi$
$972$	−1.80059	+	0.870569i	−0.0577538	+	0.0279235i
$973$	−6.97271	−	6.97271i	−0.223535	−	0.223535i
$974$	18.7591	−	13.3322i	0.601079	−	0.427191i
$975$	−2.98928			−0.0957336
$976$	0.666142	+	5.75132i	0.0213227	+	0.184095i
$977$	−5.01098			−0.160315			−0.0801577	−	0.996782i	$-0.525542\pi$
$977$	−5.01098			−0.160315			−0.0801577	+	0.996782i	$0.525542\pi$
$978$	11.0687	−	7.86663i	0.353939	−	0.251547i
$979$	17.8425	+	17.8425i	0.570250	+	0.570250i
$980$	1.20637	+	2.49512i	0.0385361	+	0.0797037i
$981$	7.69583	−	7.69583i	0.245709	−	0.245709i
$982$	−0.0533699	−	0.00902522i	−0.00170310	−	0.000288006i
$983$			29.7225i			0.947999i	0.880525	+	0.474000i	$0.157190\pi$
$983$			29.7225i			0.947999i	−0.880525	+	0.474000i	$0.842810\pi$
$984$	10.0732	−	18.3269i	0.321121	−	0.584240i
$985$			9.28573i			0.295868i
$986$	−9.53172	+	56.3651i	−0.303552	+	1.79503i
$987$	1.74357	−	1.74357i	0.0554985	−	0.0554985i
$988$	6.39082	+	2.22509i	0.203319	+	0.0707897i
$989$	−59.0524	−	59.0524i	−1.87776	−	1.87776i
$990$	4.80197	+	6.75661i	0.152617	+	0.214739i
$991$	−56.2320			−1.78627			−0.893135	−	0.449789i	$-0.851499\pi$
$991$	−56.2320			−1.78627			−0.893135	+	0.449789i	$0.851499\pi$
$992$	−2.24533	+	42.9656i	−0.0712894	+	1.36416i
$993$	32.8149			1.04135
$994$	11.6123	+	16.3391i	0.368319	+	0.518243i
$995$	−17.2820	−	17.2820i	−0.547876	−	0.547876i
$996$	−12.8398	−	4.47044i	−0.406845	−	0.141651i
$997$	27.0545	−	27.0545i	0.856826	−	0.856826i	−0.134137	−	0.990963i	$-0.542826\pi$
$997$	27.0545	−	27.0545i	0.856826	−	0.856826i	0.990963	+	0.134137i	$0.0428262\pi$
$998$	6.48637	−	38.3566i	0.205322	−	1.21416i
$999$			6.55060i			0.207252i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.w.b.253.5	yes	28
4.3	odd	2		1344.2.w.b.337.10		28
8.3	odd	2		2688.2.w.c.673.5		28
8.5	even	2		2688.2.w.d.673.10		28
16.3	odd	4		2688.2.w.c.2017.5		28
16.5	even	4	inner	336.2.w.b.85.5	✓	28
16.11	odd	4		1344.2.w.b.1009.10		28
16.13	even	4		2688.2.w.d.2017.10		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.w.b.85.5	✓	28	16.5	even	4	inner
336.2.w.b.253.5	yes	28	1.1	even	1	trivial
1344.2.w.b.337.10		28	4.3	odd	2
1344.2.w.b.1009.10		28	16.11	odd	4
2688.2.w.c.673.5		28	8.3	odd	2
2688.2.w.c.2017.5		28	16.3	odd	4
2688.2.w.d.673.10		28	8.5	even	2
2688.2.w.d.2017.10		28	16.13	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.819262 - 1.15274i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-0.657621 + 1.88879i) q^{4} +(-0.979857 + 0.979857i) q^{5} +(-0.235805 + 1.39442i) q^{6} +1.00000i q^{7} +(2.71605 - 0.789348i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.819262 - 1.15274i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-0.657621 + 1.88879i) q^{4} +(-0.979857 + 0.979857i) q^{5} +(-0.235805 + 1.39442i) q^{6} +1.00000i q^{7} +(2.71605 - 0.789348i) q^{8} +1.00000i q^{9} +(1.93228 + 0.326762i) q^{10} +(2.99092 - 2.99092i) q^{11} +(1.80059 - 0.870569i) q^{12} +(-0.686333 - 0.686333i) q^{13} +(1.15274 - 0.819262i) q^{14} +1.38573 q^{15} +(-3.13507 - 2.48422i) q^{16} +7.74860 q^{17} +(1.15274 - 0.819262i) q^{18} +(2.46495 + 2.46495i) q^{19} +(-1.20637 - 2.49512i) q^{20} +(0.707107 - 0.707107i) q^{21} +(-5.89810 - 0.997408i) q^{22} -8.35641i q^{23} +(-2.47869 - 1.36238i) q^{24} +3.07976i q^{25} +(-0.228878 + 1.35345i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.88879 - 0.657621i) q^{28} +(-3.68876 - 3.68876i) q^{29} +(-1.13527 - 1.59738i) q^{30} +7.60568 q^{31} +(-0.295218 + 5.64915i) q^{32} -4.22980 q^{33} +(-6.34813 - 8.93212i) q^{34} +(-0.979857 - 0.979857i) q^{35} +(-1.88879 - 0.657621i) q^{36} +(-4.63198 + 4.63198i) q^{37} +(0.822008 - 4.86088i) q^{38} +0.970621i q^{39} +(-1.88789 + 3.43479i) q^{40} +7.39378i q^{41} +(-1.39442 - 0.235805i) q^{42} +(7.06672 - 7.06672i) q^{43} +(3.68233 + 7.61611i) q^{44} +(-0.979857 - 0.979857i) q^{45} +(-9.63277 + 6.84608i) q^{46} +2.46578 q^{47} +(0.460221 + 3.97344i) q^{48} -1.00000 q^{49} +(3.55016 - 2.52313i) q^{50} +(-5.47909 - 5.47909i) q^{51} +(1.74769 - 0.844993i) q^{52} +(6.50509 - 6.50509i) q^{53} +(-1.39442 - 0.235805i) q^{54} +5.86134i q^{55} +(0.789348 + 2.71605i) q^{56} -3.48596i q^{57} +(-1.23012 + 7.27423i) q^{58} +(2.18485 - 2.18485i) q^{59} +(-0.911283 + 2.61735i) q^{60} +(-1.02350 - 1.02350i) q^{61} +(-6.23104 - 8.76737i) q^{62} -1.00000 q^{63} +(6.75386 - 4.28782i) q^{64} +1.34502 q^{65} +(3.46531 + 4.87586i) q^{66} +(2.22728 + 2.22728i) q^{67} +(-5.09564 + 14.6355i) q^{68} +(-5.90887 + 5.90887i) q^{69} +(-0.326762 + 1.93228i) q^{70} +14.1741i q^{71} +(0.789348 + 2.71605i) q^{72} +5.93888i q^{73} +(9.13427 + 1.54467i) q^{74} +(2.17772 - 2.17772i) q^{75} +(-6.27678 + 3.03477i) q^{76} +(2.99092 + 2.99092i) q^{77} +(1.11887 - 0.795193i) q^{78} -2.58459 q^{79} +(5.50610 - 0.637740i) q^{80} -1.00000 q^{81} +(8.52311 - 6.05744i) q^{82} +(-4.80684 - 4.80684i) q^{83} +(0.870569 + 1.80059i) q^{84} +(-7.59252 + 7.59252i) q^{85} +(-13.9356 - 2.35660i) q^{86} +5.21669i q^{87} +(5.76261 - 10.4844i) q^{88} +5.96557i q^{89} +(-0.326762 + 1.93228i) q^{90} +(0.686333 - 0.686333i) q^{91} +(15.7835 + 5.49535i) q^{92} +(-5.37803 - 5.37803i) q^{93} +(-2.02012 - 2.84241i) q^{94} -4.83059 q^{95} +(4.20330 - 3.78580i) q^{96} +11.2310 q^{97} +(0.819262 + 1.15274i) q^{98} +(2.99092 + 2.99092i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q+O(q^{10}) \) 28 * q	\( 28 q - 4 q^{10} - 4 q^{11} - 8 q^{12} + 8 q^{15} + 4 q^{16} + 8 q^{19} - 28 q^{20} - 8 q^{22} - 16 q^{24} - 20 q^{26} + 4 q^{28} + 4 q^{29} + 8 q^{30} + 24 q^{33} + 12 q^{34} + 4 q^{36} + 4 q^{37} + 60 q^{38} - 56 q^{40} - 4 q^{42} + 20 q^{43} + 56 q^{44} - 44 q^{46} + 16 q^{48} - 28 q^{49} + 20 q^{50} - 8 q^{51} - 32 q^{52} + 20 q^{53} - 4 q^{54} - 12 q^{56} - 12 q^{58} - 12 q^{60} - 40 q^{61} - 60 q^{62} - 28 q^{63} + 60 q^{64} + 16 q^{65} + 24 q^{66} + 4 q^{67} - 108 q^{68} - 16 q^{69} - 4 q^{70} - 12 q^{72} + 28 q^{74} - 16 q^{75} - 8 q^{76} - 4 q^{77} + 12 q^{78} + 24 q^{79} - 72 q^{80} - 28 q^{81} + 36 q^{82} + 40 q^{83} + 48 q^{85} + 24 q^{86} + 4 q^{88} - 4 q^{90} + 52 q^{92} - 8 q^{94} + 40 q^{96} + 72 q^{97} - 4 q^{99}+O(q^{100}) \) 28 * q - 4 * q^10 - 4 * q^11 - 8 * q^12 + 8 * q^15 + 4 * q^16 + 8 * q^19 - 28 * q^20 - 8 * q^22 - 16 * q^24 - 20 * q^26 + 4 * q^28 + 4 * q^29 + 8 * q^30 + 24 * q^33 + 12 * q^34 + 4 * q^36 + 4 * q^37 + 60 * q^38 - 56 * q^40 - 4 * q^42 + 20 * q^43 + 56 * q^44 - 44 * q^46 + 16 * q^48 - 28 * q^49 + 20 * q^50 - 8 * q^51 - 32 * q^52 + 20 * q^53 - 4 * q^54 - 12 * q^56 - 12 * q^58 - 12 * q^60 - 40 * q^61 - 60 * q^62 - 28 * q^63 + 60 * q^64 + 16 * q^65 + 24 * q^66 + 4 * q^67 - 108 * q^68 - 16 * q^69 - 4 * q^70 - 12 * q^72 + 28 * q^74 - 16 * q^75 - 8 * q^76 - 4 * q^77 + 12 * q^78 + 24 * q^79 - 72 * q^80 - 28 * q^81 + 36 * q^82 + 40 * q^83 + 48 * q^85 + 24 * q^86 + 4 * q^88 - 4 * q^90 + 52 * q^92 - 8 * q^94 + 40 * q^96 + 72 * q^97 - 4 * q^99

Introduction

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