LMFDB - Embedded newform 546.2.p.b.281.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(239,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("546.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.p (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.45474709504.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 38x^{6} + 481x^{4} + 2112x^{2} + 1024 $ x^8 + 38x^6 + 481x^4 + 2112*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			281.4
Root			$-3.90842i$ of defining polynomial
Character	$\chi$	$=$	546.281
Dual form			546.2.p.b.239.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(1.41421 + 1.00000i) q^{3} -1.00000i q^{4} +(2.76367 - 2.76367i) q^{5} +(1.70711 - 0.292893i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(1.41421 + 1.00000i) q^{3} -1.00000i q^{4} +(2.76367 - 2.76367i) q^{5} +(1.70711 - 0.292893i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} -3.90842i q^{10} +(3.14475 + 3.14475i) q^{11} +(1.00000 - 1.41421i) q^{12} +(-3.47078 + 0.976570i) q^{13} +1.00000i q^{14} +(6.67210 - 1.14475i) q^{15} -1.00000 q^{16} +1.90842 q^{17} +(2.70711 + 1.29289i) q^{18} +(-4.76367 - 4.76367i) q^{19} +(-2.76367 - 2.76367i) q^{20} +(-1.70711 + 0.292893i) q^{21} +4.44735 q^{22} -4.56048 q^{23} +(-0.292893 - 1.70711i) q^{24} -10.2758i q^{25} +(-1.76367 + 3.14475i) q^{26} +(-1.41421 + 5.00000i) q^{27} +(0.707107 + 0.707107i) q^{28} -1.03314i q^{29} +(3.90842 - 5.52735i) q^{30} +(0.585786 + 0.585786i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(1.30260 + 7.59210i) q^{33} +(1.34946 - 1.34946i) q^{34} +3.90842i q^{35} +(2.82843 - 1.00000i) q^{36} +(-3.73054 + 3.73054i) q^{37} -6.73685 q^{38} +(-5.88499 - 2.08970i) q^{39} -3.90842 q^{40} +(4.03314 - 4.03314i) q^{41} +(-1.00000 + 1.41421i) q^{42} +3.14627i q^{43} +(3.14475 - 3.14475i) q^{44} +(10.5805 + 5.05317i) q^{45} +(-3.22475 + 3.22475i) q^{46} +(4.24264 + 4.24264i) q^{47} +(-1.41421 - 1.00000i) q^{48} -1.00000i q^{49} +(-7.26607 - 7.26607i) q^{50} +(2.69892 + 1.90842i) q^{51} +(0.976570 + 3.47078i) q^{52} -9.60999i q^{53} +(2.53553 + 4.53553i) q^{54} +17.3821 q^{55} +1.00000 q^{56} +(-1.97318 - 11.5005i) q^{57} +(-0.730537 - 0.730537i) q^{58} +(5.98842 + 5.98842i) q^{59} +(-1.14475 - 6.67210i) q^{60} -15.2058 q^{61} +0.828427 q^{62} +(-2.70711 - 1.29289i) q^{63} +1.00000i q^{64} +(-6.89318 + 12.2910i) q^{65} +(6.28950 + 4.44735i) q^{66} +(8.70372 + 8.70372i) q^{67} -1.90842i q^{68} +(-6.44949 - 4.56048i) q^{69} +(2.76367 + 2.76367i) q^{70} +(-6.49421 + 6.49421i) q^{71} +(1.29289 - 2.70711i) q^{72} +(1.60103 - 1.60103i) q^{73} +5.27578i q^{74} +(10.2758 - 14.5321i) q^{75} +(-4.76367 + 4.76367i) q^{76} -4.44735 q^{77} +(-5.63896 + 2.68368i) q^{78} -4.35577 q^{79} +(-2.76367 + 2.76367i) q^{80} +(-7.00000 + 5.65685i) q^{81} -5.70372i q^{82} +(-0.908424 + 0.908424i) q^{83} +(0.292893 + 1.70711i) q^{84} +(5.27426 - 5.27426i) q^{85} +(2.22475 + 2.22475i) q^{86} +(1.03314 - 1.46107i) q^{87} -4.44735i q^{88} +(-13.0595 - 13.0595i) q^{89} +(11.0547 - 3.90842i) q^{90} +(1.76367 - 3.14475i) q^{91} +4.56048i q^{92} +(0.242641 + 1.41421i) q^{93} +6.00000 q^{94} -26.3305 q^{95} +(-1.70711 + 0.292893i) q^{96} +(5.41421 + 5.41421i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(-5.74995 + 12.0394i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{5} + 8 q^{6} + 8 q^{9}+O(q^{10}) $ 8 * q + 4 * q^5 + 8 * q^6 + 8 * q^9	$ 8 q + 4 q^{5} + 8 q^{6} + 8 q^{9} + 8 q^{11} + 8 q^{12} - 4 q^{13} - 8 q^{16} - 20 q^{17} + 16 q^{18} - 20 q^{19} - 4 q^{20} - 8 q^{21} + 12 q^{22} + 12 q^{23} - 8 q^{24} + 4 q^{26} - 4 q^{30} + 16 q^{31} + 4 q^{33} + 4 q^{34} - 24 q^{37} + 4 q^{38} - 12 q^{39} + 4 q^{40} + 20 q^{41} - 8 q^{42} + 8 q^{44} - 4 q^{45} + 4 q^{46} - 24 q^{50} + 8 q^{51} + 8 q^{52} - 8 q^{54} - 12 q^{55} + 8 q^{56} + 24 q^{57} + 8 q^{60} + 20 q^{61} - 16 q^{62} - 16 q^{63} - 28 q^{65} + 16 q^{66} + 24 q^{67} + 8 q^{69} + 4 q^{70} - 28 q^{71} + 16 q^{72} + 16 q^{73} + 36 q^{75} - 20 q^{76} - 12 q^{77} - 4 q^{78} + 24 q^{79} - 4 q^{80} - 56 q^{81} + 28 q^{83} + 8 q^{84} + 16 q^{85} - 12 q^{86} - 4 q^{87} + 16 q^{90} - 4 q^{91} - 32 q^{93} + 48 q^{94} - 92 q^{95} - 8 q^{96} + 32 q^{97} - 16 q^{99}+O(q^{100}) $ 8 * q + 4 * q^5 + 8 * q^6 + 8 * q^9 + 8 * q^11 + 8 * q^12 - 4 * q^13 - 8 * q^16 - 20 * q^17 + 16 * q^18 - 20 * q^19 - 4 * q^20 - 8 * q^21 + 12 * q^22 + 12 * q^23 - 8 * q^24 + 4 * q^26 - 4 * q^30 + 16 * q^31 + 4 * q^33 + 4 * q^34 - 24 * q^37 + 4 * q^38 - 12 * q^39 + 4 * q^40 + 20 * q^41 - 8 * q^42 + 8 * q^44 - 4 * q^45 + 4 * q^46 - 24 * q^50 + 8 * q^51 + 8 * q^52 - 8 * q^54 - 12 * q^55 + 8 * q^56 + 24 * q^57 + 8 * q^60 + 20 * q^61 - 16 * q^62 - 16 * q^63 - 28 * q^65 + 16 * q^66 + 24 * q^67 + 8 * q^69 + 4 * q^70 - 28 * q^71 + 16 * q^72 + 16 * q^73 + 36 * q^75 - 20 * q^76 - 12 * q^77 - 4 * q^78 + 24 * q^79 - 4 * q^80 - 56 * q^81 + 28 * q^83 + 8 * q^84 + 16 * q^85 - 12 * q^86 - 4 * q^87 + 16 * q^90 - 4 * q^91 - 32 * q^93 + 48 * q^94 - 92 * q^95 - 8 * q^96 + 32 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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
$3$	1.41421	+	1.00000i	0.816497	+	0.577350i
$3$	1.41421	+	1.00000i	0.816497	+	0.577350i
$4$		−	1.00000i		−	0.500000i
$5$	2.76367	−	2.76367i	1.23595	−	1.23595i	0.274311	−	0.961641i	$-0.411550\pi$
$5$	2.76367	−	2.76367i	1.23595	−	1.23595i	0.961641	−	0.274311i	$-0.0884498\pi$
$6$	1.70711	−	0.292893i	0.696923	−	0.119573i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	1.00000	+	2.82843i	0.333333	+	0.942809i
$10$		−	3.90842i		−	1.23595i
$11$	3.14475	+	3.14475i	0.948178	+	0.948178i	0.998722	−	0.0505438i	$-0.0160954\pi$
$11$	3.14475	+	3.14475i	0.948178	+	0.948178i	−0.0505438	+	0.998722i	$0.516095\pi$
$12$	1.00000	−	1.41421i	0.288675	−	0.408248i
$13$	−3.47078	+	0.976570i	−0.962621	+	0.270852i
$13$	−3.47078	+	0.976570i	−0.962621	+	0.270852i
$14$			1.00000i			0.267261i
$15$	6.67210	−	1.14475i	1.72273	−	0.295573i
$16$	−1.00000			−0.250000
$17$	1.90842			0.462861			0.231430	−	0.972851i	$-0.425659\pi$
$17$	1.90842			0.462861			0.231430	+	0.972851i	$0.425659\pi$
$18$	2.70711	+	1.29289i	0.638071	+	0.304738i
$19$	−4.76367	−	4.76367i	−1.09286	−	1.09286i	−0.995222	−	0.0976397i	$-0.968871\pi$
$19$	−4.76367	−	4.76367i	−1.09286	−	1.09286i	−0.0976397	−	0.995222i	$-0.531129\pi$
$20$	−2.76367	−	2.76367i	−0.617976	−	0.617976i
$21$	−1.70711	+	0.292893i	−0.372521	+	0.0639145i
$22$	4.44735			0.948178
$23$	−4.56048			−0.950926			−0.475463	−	0.879736i	$-0.657719\pi$
$23$	−4.56048			−0.950926			−0.475463	+	0.879736i	$0.657719\pi$
$24$	−0.292893	−	1.70711i	−0.0597866	−	0.348462i
$25$		−	10.2758i		−	2.05516i
$26$	−1.76367	+	3.14475i	−0.345885	+	0.616736i
$27$	−1.41421	+	5.00000i	−0.272166	+	0.962250i
$28$	0.707107	+	0.707107i	0.133631	+	0.133631i
$29$		−	1.03314i		−	0.191848i	−0.995389	−	0.0959242i	$-0.969419\pi$
$29$		−	1.03314i		−	0.191848i	0.995389	−	0.0959242i	$-0.0305807\pi$
$30$	3.90842	−	5.52735i	0.713577	−	1.00915i
$31$	0.585786	+	0.585786i	0.105210	+	0.105210i	0.757752	−	0.652542i	$-0.226297\pi$
$31$	0.585786	+	0.585786i	0.105210	+	0.105210i	−0.652542	+	0.757752i	$0.726297\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	1.30260	+	7.59210i	0.226753	+	1.32161i
$34$	1.34946	−	1.34946i	0.231430	−	0.231430i
$35$			3.90842i			0.660644i
$36$	2.82843	−	1.00000i	0.471405	−	0.166667i
$37$	−3.73054	+	3.73054i	−0.613297	+	0.613297i	−0.943804	−	0.330507i	$-0.892780\pi$
$37$	−3.73054	+	3.73054i	−0.613297	+	0.613297i	0.330507	+	0.943804i	$0.392780\pi$
$38$	−6.73685			−1.09286
$39$	−5.88499	−	2.08970i	−0.942353	−	0.334620i
$40$	−3.90842			−0.617976
$41$	4.03314	−	4.03314i	0.629870	−	0.629870i	−0.318165	−	0.948035i	$-0.603067\pi$
$41$	4.03314	−	4.03314i	0.629870	−	0.629870i	0.948035	+	0.318165i	$0.103067\pi$
$42$	−1.00000	+	1.41421i	−0.154303	+	0.218218i
$43$			3.14627i			0.479801i	0.970797	+	0.239901i	$0.0771149\pi$
$43$			3.14627i			0.479801i	−0.970797	+	0.239901i	$0.922885\pi$
$44$	3.14475	−	3.14475i	0.474089	−	0.474089i
$45$	10.5805	+	5.05317i	1.57725	+	0.753283i
$46$	−3.22475	+	3.22475i	−0.475463	+	0.475463i
$47$	4.24264	+	4.24264i	0.618853	+	0.618853i	0.945237	−	0.326384i	$-0.105830\pi$
$47$	4.24264	+	4.24264i	0.618853	+	0.618853i	−0.326384	+	0.945237i	$0.605830\pi$
$48$	−1.41421	−	1.00000i	−0.204124	−	0.144338i
$49$		−	1.00000i		−	0.142857i
$50$	−7.26607	−	7.26607i	−1.02758	−	1.02758i
$51$	2.69892	+	1.90842i	0.377924	+	0.267233i
$52$	0.976570	+	3.47078i	0.135426	+	0.481311i
$53$		−	9.60999i		−	1.32003i	−0.751251	−	0.660017i	$-0.770549\pi$
$53$		−	9.60999i		−	1.32003i	0.751251	−	0.660017i	$-0.229451\pi$
$54$	2.53553	+	4.53553i	0.345042	+	0.617208i
$55$	17.3821			2.34381
$56$	1.00000			0.133631
$57$	−1.97318	−	11.5005i	−0.261354	−	1.52328i
$58$	−0.730537	−	0.730537i	−0.0959242	−	0.0959242i
$59$	5.98842	+	5.98842i	0.779626	+	0.779626i	0.979767	−	0.200141i	$-0.0641401\pi$
$59$	5.98842	+	5.98842i	0.779626	+	0.779626i	−0.200141	+	0.979767i	$0.564140\pi$
$60$	−1.14475	−	6.67210i	−0.147787	−	0.861364i
$61$	−15.2058			−1.94690			−0.973449	−	0.228905i	$-0.926486\pi$
$61$	−15.2058			−1.94690			−0.973449	+	0.228905i	$0.926486\pi$
$62$	0.828427			0.105210
$63$	−2.70711	−	1.29289i	−0.341063	−	0.162889i
$64$			1.00000i			0.125000i
$65$	−6.89318	+	12.2910i	−0.854994	+	1.52451i
$66$	6.28950	+	4.44735i	0.774184	+	0.547431i
$67$	8.70372	+	8.70372i	1.06333	+	1.06333i	0.997854	+	0.0654738i	$0.0208559\pi$
$67$	8.70372	+	8.70372i	1.06333	+	1.06333i	0.0654738	+	0.997854i	$0.479144\pi$
$68$		−	1.90842i		−	0.231430i
$69$	−6.44949	−	4.56048i	−0.776428	−	0.549017i
$70$	2.76367	+	2.76367i	0.330322	+	0.330322i
$71$	−6.49421	+	6.49421i	−0.770721	+	0.770721i	−0.978233	−	0.207512i	$-0.933464\pi$
$71$	−6.49421	+	6.49421i	−0.770721	+	0.770721i	0.207512	+	0.978233i	$0.433464\pi$
$72$	1.29289	−	2.70711i	0.152369	−	0.319036i
$73$	1.60103	−	1.60103i	0.187386	−	0.187386i	−0.607179	−	0.794565i	$-0.707699\pi$
$73$	1.60103	−	1.60103i	0.187386	−	0.187386i	0.794565	+	0.607179i	$0.207699\pi$
$74$			5.27578i			0.613297i
$75$	10.2758	−	14.5321i	1.18654	−	1.67803i
$76$	−4.76367	+	4.76367i	−0.546431	+	0.546431i
$77$	−4.44735			−0.506822
$78$	−5.63896	+	2.68368i	−0.638487	+	0.303867i
$79$	−4.35577			−0.490063			−0.245031	−	0.969515i	$-0.578798\pi$
$79$	−4.35577			−0.490063			−0.245031	+	0.969515i	$0.578798\pi$
$80$	−2.76367	+	2.76367i	−0.308988	+	0.308988i
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$		−	5.70372i		−	0.629870i
$83$	−0.908424	+	0.908424i	−0.0997125	+	0.0997125i	−0.755203	−	0.655491i	$-0.772462\pi$
$83$	−0.908424	+	0.908424i	−0.0997125	+	0.0997125i	0.655491	+	0.755203i	$0.272462\pi$
$84$	0.292893	+	1.70711i	0.0319573	+	0.186261i
$85$	5.27426	−	5.27426i	0.572074	−	0.572074i
$86$	2.22475	+	2.22475i	0.239901	+	0.239901i
$87$	1.03314	−	1.46107i	0.110764	−	0.156644i
$88$		−	4.44735i		−	0.474089i
$89$	−13.0595	−	13.0595i	−1.38430	−	1.38430i	−0.836811	−	0.547492i	$-0.815583\pi$
$89$	−13.0595	−	13.0595i	−1.38430	−	1.38430i	−0.547492	−	0.836811i	$-0.684417\pi$
$90$	11.0547	−	3.90842i	1.16527	−	0.411984i
$91$	1.76367	−	3.14475i	0.184883	−	0.329659i
$92$			4.56048i			0.475463i
$93$	0.242641	+	1.41421i	0.0251607	+	0.146647i
$94$	6.00000			0.618853
$95$	−26.3305			−2.70145
$96$	−1.70711	+	0.292893i	−0.174231	+	0.0298933i
$97$	5.41421	+	5.41421i	0.549730	+	0.549730i	0.926363	−	0.376633i	$-0.122918\pi$
$97$	5.41421	+	5.41421i	0.549730	+	0.549730i	−0.376633	+	0.926363i	$0.622918\pi$
$98$	−0.707107	−	0.707107i	−0.0714286	−	0.0714286i
$99$	−5.74995	+	12.0394i	−0.577891	+	1.21001i
$100$	−10.2758			−1.02758
$101$	4.19578			0.417496			0.208748	−	0.977969i	$-0.433061\pi$
$101$	4.19578			0.417496			0.208748	+	0.977969i	$0.433061\pi$
$102$	3.25788	−	0.558964i	0.322579	−	0.0553457i
$103$		−	2.55745i		−	0.251993i	−0.992031	−	0.125996i	$-0.959787\pi$
$103$		−	2.55745i		−	0.251993i	0.992031	−	0.125996i	$-0.0402128\pi$
$104$	3.14475	+	1.76367i	0.308368	+	0.172942i
$105$	−3.90842	+	5.52735i	−0.381423	+	0.539414i
$106$	−6.79529	−	6.79529i	−0.660017	−	0.660017i
$107$			0.828427i			0.0800871i	0.999198	+	0.0400435i	$0.0127497\pi$
$107$			0.828427i			0.0800871i	−0.999198	+	0.0400435i	$0.987250\pi$
$108$	5.00000	+	1.41421i	0.481125	+	0.136083i
$109$	−2.33573	−	2.33573i	−0.223723	−	0.223723i	0.586341	−	0.810064i	$-0.300568\pi$
$109$	−2.33573	−	2.33573i	−0.223723	−	0.223723i	−0.810064	+	0.586341i	$0.800568\pi$
$110$	12.2910	−	12.2910i	1.17190	−	1.17190i
$111$	−9.00631	+	1.54524i	−0.854841	+	0.146668i
$112$	0.707107	−	0.707107i	0.0668153	−	0.0668153i
$113$			4.48528i			0.421940i	0.977493	+	0.210970i	$0.0676622\pi$
$113$			4.48528i			0.421940i	−0.977493	+	0.210970i	$0.932338\pi$
$114$	−9.52735	−	6.73685i	−0.892318	−	0.630964i
$115$	−12.6037	+	12.6037i	−1.17530	+	1.17530i
$116$	−1.03314			−0.0959242
$117$	−6.23294	−	8.84028i	−0.576235	−	0.817284i
$118$	8.46891			0.779626
$119$	−1.34946	+	1.34946i	−0.123705	+	0.123705i
$120$	−5.52735	−	3.90842i	−0.504575	−	0.356789i
$121$			8.77892i			0.798083i
$122$	−10.7521	+	10.7521i	−0.973449	+	0.973449i
$123$	9.73685	−	1.67058i	0.877942	−	0.150631i
$124$	0.585786	−	0.585786i	0.0526052	−	0.0526052i
$125$	−14.5805	−	14.5805i	−1.30412	−	1.30412i
$126$	−2.82843	+	1.00000i	−0.251976	+	0.0890871i
$127$		−	6.03048i		−	0.535119i	−0.963541	−	0.267560i	$-0.913783\pi$
$127$		−	6.03048i		−	0.535119i	0.963541	−	0.267560i	$-0.0862172\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−3.14627	+	4.44949i	−0.277013	+	0.391756i
$130$	3.81685	+	13.5653i	0.334760	+	1.18975i
$131$		−	17.0926i		−	1.49339i	−0.665167	−	0.746695i	$-0.731640\pi$
$131$		−	17.0926i		−	1.49339i	0.665167	−	0.746695i	$-0.268360\pi$
$132$	7.59210	−	1.30260i	0.660807	−	0.113377i
$133$	6.73685			0.584159
$134$	12.3089			1.06333
$135$	9.90994	+	17.7268i	0.852912	+	1.52568i
$136$	−1.34946	−	1.34946i	−0.115715	−	0.115715i
$137$	10.8768	+	10.8768i	0.929268	+	0.929268i	0.997659	−	0.0683904i	$-0.0217864\pi$
$137$	10.8768	+	10.8768i	0.929268	+	0.929268i	−0.0683904	+	0.997659i	$0.521786\pi$
$138$	−7.78523	+	1.33573i	−0.662723	+	0.113705i
$139$	16.9884			1.44094			0.720470	−	0.693487i	$-0.243926\pi$
$139$	16.9884			1.44094			0.720470	+	0.693487i	$0.243926\pi$
$140$	3.90842			0.330322
$141$	1.75736	+	10.2426i	0.147996	+	0.862586i
$142$			9.18420i			0.770721i
$143$	−13.9858	−	7.84367i	−1.16955	−	0.655921i
$144$	−1.00000	−	2.82843i	−0.0833333	−	0.235702i
$145$	−2.85525	−	2.85525i	−0.237116	−	0.237116i
$146$		−	2.26420i		−	0.187386i
$147$	1.00000	−	1.41421i	0.0824786	−	0.116642i
$148$	3.73054	+	3.73054i	0.306648	+	0.306648i
$149$	−13.5020	+	13.5020i	−1.10613	+	1.10613i	−0.112476	+	0.993654i	$0.535878\pi$
$149$	−13.5020	+	13.5020i	−1.10613	+	1.10613i	−0.993654	+	0.112476i	$0.964122\pi$
$150$	−3.00971	−	17.5418i	−0.245741	−	1.43229i
$151$	−2.89318	+	2.89318i	−0.235444	+	0.235444i	−0.814960	−	0.579517i	$-0.803241\pi$
$151$	−2.89318	+	2.89318i	−0.235444	+	0.235444i	0.579517	+	0.814960i	$0.303241\pi$
$152$			6.73685i			0.546431i
$153$	1.90842	+	5.39784i	0.154287	+	0.436389i
$154$	−3.14475	+	3.14475i	−0.253411	+	0.253411i
$155$	3.23784			0.260070
$156$	−2.08970	+	5.88499i	−0.167310	+	0.471177i
$157$	1.63833			0.130753			0.0653766	−	0.997861i	$-0.479175\pi$
$157$	1.63833			0.130753			0.0653766	+	0.997861i	$0.479175\pi$
$158$	−3.08000	+	3.08000i	−0.245031	+	0.245031i
$159$	9.60999	−	13.5906i	0.762122	−	1.07780i
$160$			3.90842i			0.308988i
$161$	3.22475	−	3.22475i	0.254146	−	0.254146i
$162$	−0.949747	+	8.94975i	−0.0746192	+	0.703159i
$163$	6.64048	−	6.64048i	0.520122	−	0.520122i	−0.397486	−	0.917608i	$-0.630117\pi$
$163$	6.64048	−	6.64048i	0.520122	−	0.520122i	0.917608	+	0.397486i	$0.130117\pi$
$164$	−4.03314	−	4.03314i	−0.314935	−	0.314935i
$165$	24.5820	+	17.3821i	1.91371	+	1.35320i
$166$			1.28471i			0.0997125i
$167$	4.42946	+	4.42946i	0.342762	+	0.342762i	0.857405	−	0.514643i	$-0.172076\pi$
$167$	4.42946	+	4.42946i	0.342762	+	0.342762i	−0.514643	+	0.857405i	$0.672076\pi$
$168$	1.41421	+	1.00000i	0.109109	+	0.0771517i
$169$	11.0926	−	6.77892i	0.853279	−	0.521455i
$170$		−	7.45893i		−	0.572074i
$171$	8.71003	−	18.2374i	0.666073	−	1.39465i
$172$	3.14627			0.239901
$173$	22.0253			1.67455			0.837275	−	0.546783i	$-0.184148\pi$
$173$	22.0253			1.67455			0.837275	+	0.546783i	$0.184148\pi$
$174$	−0.302598	−	1.76367i	−0.0229399	−	0.133704i
$175$	7.26607	+	7.26607i	0.549263	+	0.549263i
$176$	−3.14475	−	3.14475i	−0.237045	−	0.237045i
$177$	2.48048	+	14.4573i	0.186445	+	1.08668i
$178$	−18.4689			−1.38430
$179$	9.46107			0.707154			0.353577	−	0.935405i	$-0.384965\pi$
$179$	9.46107			0.707154			0.353577	+	0.935405i	$0.384965\pi$
$180$	5.05317	−	10.5805i	0.376641	−	0.788625i
$181$		−	9.95314i		−	0.739811i	−0.929069	−	0.369905i	$-0.879390\pi$
$181$		−	9.95314i		−	0.739811i	0.929069	−	0.369905i	$-0.120610\pi$
$182$	−0.976570	−	3.47078i	−0.0723881	−	0.257271i
$183$	−21.5042	−	15.2058i	−1.58964	−	1.12404i
$184$	3.22475	+	3.22475i	0.237732	+	0.237732i
$185$			20.6200i			1.51601i
$186$	1.17157	+	0.828427i	0.0859039	+	0.0607432i
$187$	6.00152	+	6.00152i	0.438874	+	0.438874i
$188$	4.24264	−	4.24264i	0.309426	−	0.309426i
$189$	−2.53553	−	4.53553i	−0.184433	−	0.329912i
$190$	−18.6185	+	18.6185i	−1.35072	+	1.35072i
$191$		−	10.7205i		−	0.775706i	−0.921721	−	0.387853i	$-0.873217\pi$
$191$		−	10.7205i		−	0.775706i	0.921721	−	0.387853i	$-0.126783\pi$
$192$	−1.00000	+	1.41421i	−0.0721688	+	0.102062i
$193$	−13.1347	+	13.1347i	−0.945456	+	0.945456i	−0.998588	−	0.0531319i	$-0.983080\pi$
$193$	−13.1347	+	13.1347i	−0.945456	+	0.945456i	0.0531319	+	0.998588i	$0.483080\pi$
$194$	7.65685			0.549730
$195$	−22.0394	+	10.4889i	−1.57828	+	0.751129i
$196$	−1.00000			−0.0714286
$197$	−10.8968	+	10.8968i	−0.776368	+	0.776368i	−0.979211	−	0.202843i	$-0.934982\pi$
$197$	−10.8968	+	10.8968i	−0.776368	+	0.776368i	0.202843	+	0.979211i	$0.434982\pi$
$198$	4.44735	+	12.5790i	0.316059	+	0.893951i
$199$			19.5459i			1.38557i	0.721144	+	0.692785i	$0.243616\pi$
$199$			19.5459i			1.38557i	−0.721144	+	0.692785i	$0.756384\pi$
$200$	−7.26607	+	7.26607i	−0.513789	+	0.513789i
$201$	3.60520	+	21.0126i	0.254291	+	1.48212i
$202$	2.96686	−	2.96686i	0.208748	−	0.208748i
$203$	0.730537	+	0.730537i	0.0512737	+	0.0512737i
$204$	1.90842	−	2.69892i	0.133616	−	0.188962i
$205$		−	22.2925i		−	1.55698i
$206$	−1.80839	−	1.80839i	−0.125996	−	0.125996i
$207$	−4.56048	−	12.8990i	−0.316975	−	0.896542i
$208$	3.47078	−	0.976570i	0.240655	−	0.0677129i
$209$		−	29.9611i		−	2.07245i
$210$	1.14475	+	6.67210i	0.0789953	+	0.460418i
$211$	−21.6315			−1.48918			−0.744589	−	0.667524i	$-0.767354\pi$
$211$	−21.6315			−1.48918			−0.744589	+	0.667524i	$0.767354\pi$
$212$	−9.60999			−0.660017
$213$	−15.6784	+	2.68999i	−1.07427	+	0.184315i
$214$	0.585786	+	0.585786i	0.0400435	+	0.0400435i
$215$	8.69526	+	8.69526i	0.593012	+	0.593012i
$216$	4.53553	−	2.53553i	0.308604	−	0.172521i
$217$	−0.828427			−0.0562373
$218$	−3.30323			−0.223723
$219$	3.86523	−	0.663168i	0.261188	−	0.0448127i
$220$		−	17.3821i		−	1.17190i
$221$	−6.62372	+	1.86371i	−0.445560	+	0.125367i
$222$	−5.27578	+	7.46107i	−0.354087	+	0.500755i
$223$	−18.0148	−	18.0148i	−1.20636	−	1.20636i	−0.972198	−	0.234160i	$-0.924766\pi$
$223$	−18.0148	−	18.0148i	−1.20636	−	1.20636i	−0.234160	−	0.972198i	$-0.575234\pi$
$224$		−	1.00000i		−	0.0668153i
$225$	29.0643	−	10.2758i	1.93762	−	0.685052i
$226$	3.17157	+	3.17157i	0.210970	+	0.210970i
$227$	4.05469	−	4.05469i	0.269119	−	0.269119i	−0.559626	−	0.828745i	$-0.689055\pi$
$227$	4.05469	−	4.05469i	0.269119	−	0.269119i	0.828745	+	0.559626i	$0.189055\pi$
$228$	−11.5005	+	1.97318i	−0.761641	+	0.130677i
$229$	11.1842	−	11.1842i	0.739073	−	0.739073i	−0.233326	−	0.972399i	$-0.574961\pi$
$229$	11.1842	−	11.1842i	0.739073	−	0.739073i	0.972399	+	0.233326i	$0.0749609\pi$
$230$			17.8243i			1.17530i
$231$	−6.28950	−	4.44735i	−0.413819	−	0.292614i
$232$	−0.730537	+	0.730537i	−0.0479621	+	0.0479621i
$233$	−12.5389			−0.821452			−0.410726	−	0.911759i	$-0.634725\pi$
$233$	−12.5389			−0.821452			−0.410726	+	0.911759i	$0.634725\pi$
$234$	−10.6584	−	1.84367i	−0.696760	−	0.120524i
$235$	23.4505			1.52974
$236$	5.98842	−	5.98842i	0.389813	−	0.389813i
$237$	−6.15999	−	4.35577i	−0.400135	−	0.282938i
$238$			1.90842i			0.123705i
$239$	0.988420	−	0.988420i	0.0639356	−	0.0639356i	−0.674416	−	0.738352i	$-0.735605\pi$
$239$	0.988420	−	0.988420i	0.0639356	−	0.0639356i	0.738352	+	0.674416i	$0.235605\pi$
$240$	−6.67210	+	1.14475i	−0.430682	+	0.0738933i
$241$	17.4268	−	17.4268i	1.12256	−	1.12256i	0.131206	−	0.991355i	$-0.458115\pi$
$241$	17.4268	−	17.4268i	1.12256	−	1.12256i	0.991355	−	0.131206i	$-0.0418851\pi$
$242$	6.20763	+	6.20763i	0.399042	+	0.399042i
$243$	−15.5563	+	1.00000i	−0.997940	+	0.0641500i
$244$			15.2058i			0.973449i
$245$	−2.76367	−	2.76367i	−0.176565	−	0.176565i
$246$	5.70372	−	8.06627i	0.363656	−	0.514287i
$247$	21.1857	+	11.8816i	1.34801	+	0.756008i
$248$		−	0.828427i		−	0.0526052i
$249$	−2.19313	+	0.376281i	−0.138984	+	0.0238459i
$250$	−20.6200			−1.30412
$251$	19.6948			1.24312			0.621562	−	0.783365i	$-0.286498\pi$
$251$	19.6948			1.24312			0.621562	+	0.783365i	$0.286498\pi$
$252$	−1.29289	+	2.70711i	−0.0814446	+	0.170532i
$253$	−14.3416	−	14.3416i	−0.901647	−	0.901647i
$254$	−4.26420	−	4.26420i	−0.267560	−	0.267560i
$255$	12.7332	−	2.18467i	0.797383	−	0.136809i
$256$	1.00000			0.0625000
$257$	11.7231			0.731268			0.365634	−	0.930759i	$-0.380852\pi$
$257$	11.7231			0.731268			0.365634	+	0.930759i	$0.380852\pi$
$258$	0.921521	+	5.37102i	0.0573714	+	0.334385i
$259$		−	5.27578i		−	0.327821i
$260$	12.2910	+	6.89318i	0.762257	+	0.427497i
$261$	2.92215	−	1.03314i	0.180876	−	0.0639495i
$262$	−12.0863	−	12.0863i	−0.746695	−	0.746695i
$263$		−	10.8090i		−	0.666513i	−0.942836	−	0.333256i	$-0.891853\pi$
$263$		−	10.8090i		−	0.666513i	0.942836	−	0.333256i	$-0.108147\pi$
$264$	4.44735	−	6.28950i	0.273715	−	0.387092i
$265$	−26.5589	−	26.5589i	−1.63150	−	1.63150i
$266$	4.76367	−	4.76367i	0.292080	−	0.292080i
$267$	−5.40942	−	31.5284i	−0.331051	−	1.92951i
$268$	8.70372	−	8.70372i	0.531664	−	0.531664i
$269$		−	1.46107i		−	0.0890833i	−0.999008	−	0.0445416i	$-0.985817\pi$
$269$		−	1.46107i		−	0.0890833i	0.999008	−	0.0445416i	$-0.0141827\pi$
$270$	19.5421	+	5.52735i	1.18930	+	0.336384i
$271$	−7.90842	+	7.90842i	−0.480403	+	0.480403i	−0.905260	−	0.424858i	$-0.860324\pi$
$271$	−7.90842	+	7.90842i	−0.480403	+	0.480403i	0.424858	+	0.905260i	$0.360324\pi$
$272$	−1.90842			−0.115715
$273$	5.63896	−	2.68368i	0.341285	−	0.162423i
$274$	15.3821			0.929268
$275$	32.3148	−	32.3148i	1.94865	−	1.94865i
$276$	−4.56048	+	6.44949i	−0.274509	+	0.388214i
$277$		−	26.2663i		−	1.57819i	−0.614270	−	0.789096i	$-0.710549\pi$
$277$		−	26.2663i		−	1.57819i	0.614270	−	0.789096i	$-0.289451\pi$
$278$	12.0126	−	12.0126i	0.720470	−	0.720470i
$279$	−1.07107	+	2.24264i	−0.0641232	+	0.134263i
$280$	2.76367	−	2.76367i	0.165161	−	0.165161i
$281$	13.8363	+	13.8363i	0.825402	+	0.825402i	0.986877	−	0.161475i	$-0.0516251\pi$
$281$	13.8363	+	13.8363i	0.825402	+	0.825402i	−0.161475	+	0.986877i	$0.551625\pi$
$282$	8.48528	+	6.00000i	0.505291	+	0.357295i
$283$			22.6347i			1.34550i	0.739872	+	0.672748i	$0.234886\pi$
$283$			22.6347i			1.34550i	−0.739872	+	0.672748i	$0.765114\pi$
$284$	6.49421	+	6.49421i	0.385360	+	0.385360i
$285$	−37.2369	−	26.3305i	−2.20572	−	1.55968i
$286$	−15.4358	+	4.34315i	−0.912736	+	0.256816i
$287$			5.70372i			0.336680i
$288$	−2.70711	−	1.29289i	−0.159518	−	0.0761845i
$289$	−13.3579			−0.785760
$290$	−4.03793			−0.237116
$291$	2.24264	+	13.0711i	0.131466	+	0.766240i
$292$	−1.60103	−	1.60103i	−0.0936931	−	0.0936931i
$293$	1.39480	+	1.39480i	0.0814853	+	0.0814853i	0.746675	−	0.665189i	$-0.231649\pi$
$293$	1.39480	+	1.39480i	0.0814853	+	0.0814853i	−0.665189	+	0.746675i	$0.731649\pi$
$294$	−0.292893	−	1.70711i	−0.0170819	−	0.0995605i
$295$	33.1001			1.92716
$296$	5.27578			0.306648
$297$	−20.1711	+	11.2764i	−1.17045	+	0.654323i
$298$			19.0948i			1.10613i
$299$	15.8284	−	4.45363i	0.915382	−	0.257560i
$300$	−14.5321	−	10.2758i	−0.839014	−	0.593272i
$301$	−2.22475	−	2.22475i	−0.128232	−	0.128232i
$302$			4.09158i			0.235444i
$303$	5.93373	+	4.19578i	0.340884	+	0.241041i
$304$	4.76367	+	4.76367i	0.273215	+	0.273215i
$305$	−42.0237	+	42.0237i	−2.40627	+	2.40627i
$306$	5.16631	+	2.46739i	0.295338	+	0.141051i
$307$	24.0789	−	24.0789i	1.37426	−	1.37426i	0.520228	−	0.854028i	$-0.325847\pi$
$307$	24.0789	−	24.0789i	1.37426	−	1.37426i	0.854028	−	0.520228i	$-0.174153\pi$
$308$			4.44735i			0.253411i
$309$	2.55745	−	3.61678i	0.145488	−	0.205751i
$310$	2.28950	−	2.28950i	0.130035	−	0.130035i
$311$	10.6052			0.601366			0.300683	−	0.953724i	$-0.402785\pi$
$311$	10.6052			0.601366			0.300683	+	0.953724i	$0.402785\pi$
$312$	2.68368	+	5.63896i	0.151933	+	0.319243i
$313$	1.99697			0.112875			0.0564376	−	0.998406i	$-0.482026\pi$
$313$	1.99697			0.112875			0.0564376	+	0.998406i	$0.482026\pi$
$314$	1.15848	−	1.15848i	0.0653766	−	0.0653766i
$315$	−11.0547	+	3.90842i	−0.622861	+	0.220215i
$316$			4.35577i			0.245031i
$317$	12.7458	−	12.7458i	0.715874	−	0.715874i	−0.251883	−	0.967758i	$-0.581050\pi$
$317$	12.7458	−	12.7458i	0.715874	−	0.715874i	0.967758	+	0.251883i	$0.0810499\pi$
$318$	−2.81470	−	16.4053i	−0.157841	−	0.919963i
$319$	3.24895	−	3.24895i	0.181907	−	0.181907i
$320$	2.76367	+	2.76367i	0.154494	+	0.154494i
$321$	−0.828427	+	1.17157i	−0.0462383	+	0.0653908i
$322$		−	4.56048i		−	0.254146i
$323$	−9.09111	−	9.09111i	−0.505843	−	0.505843i
$324$	5.65685	+	7.00000i	0.314270	+	0.388889i
$325$	10.0350	+	35.6650i	0.556642	+	1.97834i
$326$		−	9.39105i		−	0.520122i
$327$	−0.967493	−	5.63896i	−0.0535025	−	0.311835i
$328$	−5.70372			−0.314935
$329$	−6.00000			−0.330791
$330$	29.6731	−	5.09111i	1.63345	−	0.280256i
$331$	−3.65206	−	3.65206i	−0.200735	−	0.200735i	0.599580	−	0.800315i	$-0.295334\pi$
$331$	−3.65206	−	3.65206i	−0.200735	−	0.200735i	−0.800315	+	0.599580i	$0.795334\pi$
$332$	0.908424	+	0.908424i	0.0498562	+	0.0498562i
$333$	−14.2821	−	6.82102i	−0.782654	−	0.373789i
$334$	6.26420			0.342762
$335$	48.1084			2.62845
$336$	1.70711	−	0.292893i	0.0931303	−	0.0159786i
$337$		−	16.5411i		−	0.901050i	−0.892764	−	0.450525i	$-0.851237\pi$
$337$		−	16.5411i		−	0.901050i	0.892764	−	0.450525i	$-0.148763\pi$
$338$	3.05025	−	12.6371i	0.165912	−	0.687367i
$339$	−4.48528	+	6.34315i	−0.243607	+	0.344512i
$340$	−5.27426	−	5.27426i	−0.286037	−	0.286037i
$341$			3.68430i			0.199516i
$342$	−6.73685	−	19.0547i	−0.364287	−	1.03036i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	2.22475	−	2.22475i	0.119950	−	0.119950i
$345$	−30.4280	+	5.22062i	−1.63819	+	0.281068i
$346$	15.5742	−	15.5742i	0.837275	−	0.837275i
$347$			0.159993i			0.00858889i	0.999991	+	0.00429445i	$0.00136697\pi$
$347$			0.159993i			0.00858889i	−0.999991	+	0.00429445i	$0.998633\pi$
$348$	−1.46107	−	1.03314i	−0.0783218	−	0.0553819i
$349$	−8.31784	+	8.31784i	−0.445244	+	0.445244i	−0.893770	−	0.448526i	$-0.851949\pi$
$349$	−8.31784	+	8.31784i	−0.445244	+	0.445244i	0.448526	+	0.893770i	$0.351949\pi$
$350$	10.2758			0.549263
$351$	0.0255762	−	18.7350i	0.00136515	−	0.999999i
$352$	−4.44735			−0.237045
$353$	2.00480	−	2.00480i	0.106705	−	0.106705i	−0.651739	−	0.758443i	$-0.725960\pi$
$353$	2.00480	−	2.00480i	0.106705	−	0.106705i	0.758443	+	0.651739i	$0.225960\pi$
$354$	11.9768	+	8.46891i	0.636562	+	0.450117i
$355$			35.8957i			1.90515i
$356$	−13.0595	+	13.0595i	−0.692151	+	0.692151i
$357$	−3.25788	+	0.558964i	−0.172425	+	0.0295835i
$358$	6.68999	−	6.68999i	0.353577	−	0.353577i
$359$	−0.0752002	−	0.0752002i	−0.00396892	−	0.00396892i	0.705120	−	0.709088i	$-0.250893\pi$
$359$	−0.0752002	−	0.0752002i	−0.00396892	−	0.00396892i	−0.709088	+	0.705120i	$0.750893\pi$
$360$	−3.90842	−	11.0547i	−0.205992	−	0.582633i
$361$			26.3852i			1.38869i
$362$	−7.03793	−	7.03793i	−0.369905	−	0.369905i
$363$	−8.77892	+	12.4153i	−0.460774	+	0.651632i
$364$	−3.14475	−	1.76367i	−0.164830	−	0.0924416i
$365$		−	8.84944i		−	0.463201i
$366$	−25.9578	+	4.45366i	−1.35684	+	0.232797i
$367$	24.2225			1.26441			0.632203	−	0.774803i	$-0.282151\pi$
$367$	24.2225			1.26441			0.632203	+	0.774803i	$0.282151\pi$
$368$	4.56048			0.237732
$369$	15.4406	+	7.37429i	0.803804	+	0.383890i
$370$	14.5805	+	14.5805i	0.758005	+	0.758005i
$371$	6.79529	+	6.79529i	0.352794	+	0.352794i
$372$	1.41421	−	0.242641i	0.0733236	−	0.0125803i
$373$	9.18420			0.475540			0.237770	−	0.971322i	$-0.423584\pi$
$373$	9.18420			0.475540			0.237770	+	0.971322i	$0.423584\pi$
$374$	8.48743			0.438874
$375$	−6.03945	−	35.2005i	−0.311876	−	1.81775i
$376$		−	6.00000i		−	0.309426i
$377$	1.00893	+	3.58579i	0.0519625	+	0.184677i
$378$	−5.00000	−	1.41421i	−0.257172	−	0.0727393i
$379$	−10.3353	−	10.3353i	−0.530887	−	0.530887i	0.389949	−	0.920836i	$-0.372492\pi$
$379$	−10.3353	−	10.3353i	−0.530887	−	0.530887i	−0.920836	+	0.389949i	$0.872492\pi$
$380$			26.3305i			1.35072i
$381$	6.03048	−	8.52839i	0.308951	−	0.436923i
$382$	−7.58052	−	7.58052i	−0.387853	−	0.387853i
$383$	−6.33573	+	6.33573i	−0.323741	+	0.323741i	−0.850200	−	0.526459i	$-0.823519\pi$
$383$	−6.33573	+	6.33573i	−0.323741	+	0.323741i	0.526459	+	0.850200i	$0.323519\pi$
$384$	0.292893	+	1.70711i	0.0149466	+	0.0871154i
$385$	−12.2910	+	12.2910i	−0.626408	+	0.626408i
$386$			18.5753i			0.945456i
$387$	−8.89899	+	3.14627i	−0.452361	+	0.159934i
$388$	5.41421	−	5.41421i	0.274865	−	0.274865i
$389$	21.0605			1.06781			0.533906	−	0.845544i	$-0.320724\pi$
$389$	21.0605			1.06781			0.533906	+	0.845544i	$0.320724\pi$
$390$	−8.16744	+	23.0010i	−0.413574	+	1.16470i
$391$	−8.70333			−0.440146
$392$	−0.707107	+	0.707107i	−0.0357143	+	0.0357143i
$393$	17.0926	−	24.1726i	0.862209	−	1.21935i
$394$			15.4105i			0.776368i
$395$	−12.0379	+	12.0379i	−0.605694	+	0.605694i
$396$	12.0394	+	5.74995i	0.605005	+	0.288946i
$397$	−8.87314	+	8.87314i	−0.445330	+	0.445330i	−0.893799	−	0.448468i	$-0.851970\pi$
$397$	−8.87314	+	8.87314i	−0.445330	+	0.445330i	0.448468	+	0.893799i	$0.351970\pi$
$398$	13.8210	+	13.8210i	0.692785	+	0.692785i
$399$	9.52735	+	6.73685i	0.476964	+	0.337264i
$400$			10.2758i			0.513789i
$401$	5.53109	+	5.53109i	0.276210	+	0.276210i	0.831594	−	0.555384i	$-0.187429\pi$
$401$	5.53109	+	5.53109i	0.276210	+	0.276210i	−0.555384	+	0.831594i	$0.687429\pi$
$402$	17.4074	+	12.3089i	0.868204	+	0.613913i
$403$	−2.60520	−	1.46107i	−0.129774	−	0.0727813i
$404$		−	4.19578i		−	0.208748i
$405$	−3.71202	+	34.9794i	−0.184452	+	1.73814i
$406$	1.03314			0.0512737
$407$	−23.4632			−1.16303
$408$	−0.558964	−	3.25788i	−0.0276729	−	0.161289i
$409$	−26.5053	−	26.5053i	−1.31060	−	1.31060i	−0.920970	−	0.389634i	$-0.872602\pi$
$409$	−26.5053	−	26.5053i	−1.31060	−	1.31060i	−0.389634	−	0.920970i	$-0.627398\pi$
$410$	−15.7632	−	15.7632i	−0.778489	−	0.778489i
$411$	4.50532	+	26.2589i	0.222231	+	1.29526i
$412$	−2.55745			−0.125996
$413$	−8.46891			−0.416728
$414$	−12.3457	−	5.89622i	−0.606759	−	0.289783i
$415$			5.02117i			0.246480i
$416$	1.76367	−	3.14475i	0.0864712	−	0.154184i
$417$	24.0253	+	16.9884i	1.17652	+	0.831927i
$418$	−21.1857	−	21.1857i	−1.03623	−	1.03623i
$419$			12.9326i			0.631800i	0.948792	+	0.315900i	$0.102306\pi$
$419$			12.9326i			0.631800i	−0.948792	+	0.315900i	$0.897694\pi$
$420$	5.52735	+	3.90842i	0.269707	+	0.190712i
$421$	20.0625	+	20.0625i	0.977788	+	0.977788i	0.999759	−	0.0219711i	$-0.00699417\pi$
$421$	20.0625	+	20.0625i	0.977788	+	0.977788i	−0.0219711	+	0.999759i	$0.506994\pi$
$422$	−15.2958	+	15.2958i	−0.744589	+	0.744589i
$423$	−7.75736	+	16.2426i	−0.377176	+	0.789744i
$424$	−6.79529	+	6.79529i	−0.330009	+	0.330009i
$425$		−	19.6105i		−	0.951251i
$426$	−9.18420	+	12.9884i	−0.444976	+	0.629291i
$427$	10.7521	−	10.7521i	0.520330	−	0.520330i
$428$	0.828427			0.0400435
$429$	−11.9352	−	25.0784i	−0.576239	−	1.21080i
$430$	12.2969			0.593012
$431$	23.5563	−	23.5563i	1.13467	−	1.13467i	0.145279	−	0.989391i	$-0.453592\pi$
$431$	23.5563	−	23.5563i	1.13467	−	1.13467i	0.989391	−	0.145279i	$-0.0464079\pi$
$432$	1.41421	−	5.00000i	0.0680414	−	0.240563i
$433$		−	14.0000i		−	0.672797i	−0.941720	−	0.336399i	$-0.890791\pi$
$433$		−	14.0000i		−	0.672797i	0.941720	−	0.336399i	$-0.109209\pi$
$434$	−0.585786	+	0.585786i	−0.0281186	+	0.0281186i
$435$	−1.18268	−	6.89318i	−0.0567053	−	0.330503i
$436$	−2.33573	+	2.33573i	−0.111861	+	0.111861i
$437$	21.7246	+	21.7246i	1.03923	+	1.03923i
$438$	2.26420	−	3.20206i	0.108188	−	0.153000i
$439$		−	35.4194i		−	1.69048i	−0.534391	−	0.845238i	$-0.679459\pi$
$439$		−	35.4194i		−	1.69048i	0.534391	−	0.845238i	$-0.320541\pi$
$440$	−12.2910	−	12.2910i	−0.585951	−	0.585951i
$441$	2.82843	−	1.00000i	0.134687	−	0.0476190i
$442$	−3.36584	+	6.00152i	−0.160096	+	0.285463i
$443$			28.5947i			1.35857i	0.733873	+	0.679287i	$0.237711\pi$
$443$			28.5947i			1.35857i	−0.733873	+	0.679287i	$0.762289\pi$
$444$	1.54524	+	9.00631i	0.0733338	+	0.427421i
$445$	−72.1843			−3.42186
$446$	−25.4767			−1.20636
$447$	−32.5968	+	5.59273i	−1.54178	+	0.264527i
$448$	−0.707107	−	0.707107i	−0.0334077	−	0.0334077i
$449$	−22.9169	−	22.9169i	−1.08151	−	1.08151i	−0.996368	−	0.0851461i	$-0.972864\pi$
$449$	−22.9169	−	22.9169i	−1.08151	−	1.08151i	−0.0851461	−	0.996368i	$-0.527136\pi$
$450$	13.2855	−	27.8176i	0.626284	−	1.31134i
$451$	25.3664			1.19446
$452$	4.48528			0.210970
$453$	−6.98476	+	1.19839i	−0.328173	+	0.0563055i
$454$		−	5.73420i		−	0.269119i
$455$	−3.81685	−	13.5653i	−0.178937	−	0.635950i
$456$	−6.73685	+	9.52735i	−0.315482	+	0.446159i
$457$	−0.0495117	−	0.0495117i	−0.00231606	−	0.00231606i	0.705948	−	0.708264i	$-0.250521\pi$
$457$	−0.0495117	−	0.0495117i	−0.00231606	−	0.00231606i	−0.708264	+	0.705948i	$0.750521\pi$
$458$		−	15.8168i		−	0.739073i
$459$	−2.69892	+	9.54212i	−0.125975	+	0.445388i
$460$	12.6037	+	12.6037i	0.587650	+	0.587650i
$461$	11.2668	−	11.2668i	0.524748	−	0.524748i	−0.394254	−	0.919002i	$-0.628997\pi$
$461$	11.2668	−	11.2668i	0.524748	−	0.524748i	0.919002	+	0.394254i	$0.128997\pi$
$462$	−7.59210	+	1.30260i	−0.353216	+	0.0606024i
$463$	−6.76367	+	6.76367i	−0.314335	+	0.314335i	−0.846586	−	0.532252i	$-0.821346\pi$
$463$	−6.76367	+	6.76367i	−0.314335	+	0.314335i	0.532252	+	0.846586i	$0.321346\pi$
$464$			1.03314i			0.0479621i
$465$	4.57900	+	3.23784i	0.212346	+	0.150151i
$466$	−8.86636	+	8.86636i	−0.410726	+	0.410726i
$467$	10.7011			0.495186			0.247593	−	0.968864i	$-0.420360\pi$
$467$	10.7011			0.495186			0.247593	+	0.968864i	$0.420360\pi$
$468$	−8.84028	+	6.23294i	−0.408642	+	0.288118i
$469$	−12.3089			−0.568373
$470$	16.5820	−	16.5820i	0.764872	−	0.764872i
$471$	2.31695	+	1.63833i	0.106760	+	0.0754904i
$472$		−	8.46891i		−	0.389813i
$473$	−9.89423	+	9.89423i	−0.454937	+	0.454937i
$474$	−7.43577	+	1.27578i	−0.341536	+	0.0585984i
$475$	−48.9504	+	48.9504i	−2.24600	+	2.24600i
$476$	1.34946	+	1.34946i	0.0618524	+	0.0618524i
$477$	27.1812	−	9.60999i	1.24454	−	0.440011i
$478$		−	1.39784i		−	0.0639356i
$479$	−6.55593	−	6.55593i	−0.299548	−	0.299548i	0.541289	−	0.840837i	$-0.317937\pi$
$479$	−6.55593	−	6.55593i	−0.299548	−	0.299548i	−0.840837	+	0.541289i	$0.817937\pi$
$480$	−3.90842	+	5.52735i	−0.178394	+	0.252288i
$481$	9.30474	−	16.5910i	0.424260	−	0.756485i
$482$		−	24.6453i		−	1.12256i
$483$	7.78523	−	1.33573i	0.354240	−	0.0607780i
$484$	8.77892			0.399042
$485$	29.9262			1.35888
$486$	−10.2929	+	11.7071i	−0.466895	+	0.531045i
$487$	19.5273	+	19.5273i	0.884869	+	0.884869i	0.994025	−	0.109156i	$-0.0348148\pi$
$487$	19.5273	+	19.5273i	0.884869	+	0.884869i	−0.109156	+	0.994025i	$0.534815\pi$
$488$	10.7521	+	10.7521i	0.486724	+	0.486724i
$489$	16.0315	−	2.75058i	0.724971	−	0.124385i
$490$	−3.90842			−0.176565
$491$	−25.9464			−1.17094			−0.585471	−	0.810693i	$-0.699091\pi$
$491$	−25.9464			−1.17094			−0.585471	+	0.810693i	$0.699091\pi$
$492$	−1.67058	−	9.73685i	−0.0753155	−	0.438971i
$493$		−	1.97166i		−	0.0887991i
$494$	23.3821	−	6.57900i	1.05201	−	0.296003i
$495$	17.3821	+	49.1641i	0.781268	+	2.20976i
$496$	−0.585786	−	0.585786i	−0.0263026	−	0.0263026i
$497$		−	9.18420i		−	0.411968i
$498$	−1.28471	+	1.81685i	−0.0575690	+	0.0814149i
$499$	−3.13629	−	3.13629i	−0.140400	−	0.140400i	0.633414	−	0.773813i	$-0.281653\pi$
$499$	−3.13629	−	3.13629i	−0.140400	−	0.140400i	−0.773813	+	0.633414i	$0.781653\pi$
$500$	−14.5805	+	14.5805i	−0.652061	+	0.652061i
$501$	1.83474	+	10.6937i	0.0819702	+	0.477757i
$502$	13.9263	−	13.9263i	0.621562	−	0.621562i
$503$		−	0.485281i		−	0.0216376i	−0.999941	−	0.0108188i	$-0.996556\pi$
$503$		−	0.485281i		−	0.0216376i	0.999941	−	0.0108188i	$-0.00344380\pi$
$504$	1.00000	+	2.82843i	0.0445435	+	0.125988i
$505$	11.5958	−	11.5958i	0.516005	−	0.516005i
$506$	−20.2821			−0.901647
$507$	22.4663	+	1.50579i	0.997761	+	0.0668745i
$508$	−6.03048			−0.267560
$509$	2.24791	−	2.24791i	0.0996367	−	0.0996367i	−0.655531	−	0.755168i	$-0.727555\pi$
$509$	2.24791	−	2.24791i	0.0996367	−	0.0996367i	0.755168	+	0.655531i	$0.227555\pi$
$510$	7.45893	−	10.5485i	0.330287	−	0.467096i
$511$			2.26420i			0.100162i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	30.5552	−	17.0815i	1.34905	−	0.754167i
$514$	8.28950	−	8.28950i	0.365634	−	0.365634i
$515$	−7.06795	−	7.06795i	−0.311451	−	0.311451i
$516$	4.44949	+	3.14627i	0.195878	+	0.138507i
$517$			26.6841i			1.17357i
$518$	−3.73054	−	3.73054i	−0.163910	−	0.163910i
$519$	31.1484	+	22.0253i	1.36726	+	0.966801i
$520$	13.5653	−	3.81685i	0.594877	−	0.167380i
$521$		−	33.7253i		−	1.47753i	−0.673963	−	0.738765i	$-0.735409\pi$
$521$		−	33.7253i		−	1.47753i	0.673963	−	0.738765i	$-0.264591\pi$
$522$	1.33573	−	2.79681i	0.0584635	−	0.122413i
$523$	−24.6937			−1.07978			−0.539890	−	0.841736i	$-0.681534\pi$
$523$	−24.6937			−1.07978			−0.539890	+	0.841736i	$0.681534\pi$
$524$	−17.0926			−0.746695
$525$	3.00971	+	17.5418i	0.131354	+	0.765589i
$526$	−7.64313	−	7.64313i	−0.333256	−	0.333256i
$527$	1.11793	+	1.11793i	0.0486977	+	0.0486977i
$528$	−1.30260	−	7.59210i	−0.0566883	−	0.330404i
$529$	−2.20201			−0.0957395
$530$	−37.5599			−1.63150
$531$	−10.9494	+	22.9262i	−0.475163	+	0.994914i
$532$		−	6.73685i		−	0.292080i
$533$	−10.0595	+	17.9368i	−0.435725	+	0.776927i
$534$	−26.1190	−	18.4689i	−1.13028	−	0.799228i
$535$	2.28950	+	2.28950i	0.0989838	+	0.0989838i
$536$		−	12.3089i		−	0.531664i
$537$	13.3800	+	9.46107i	0.577389	+	0.408276i
$538$	−1.03314	−	1.03314i	−0.0445416	−	0.0445416i
$539$	3.14475	−	3.14475i	0.135454	−	0.135454i
$540$	17.7268	−	9.90994i	0.762840	−	0.426456i
$541$	−14.7220	+	14.7220i	−0.632948	+	0.632948i	−0.948806	−	0.315858i	$-0.897708\pi$
$541$	−14.7220	+	14.7220i	−0.632948	+	0.632948i	0.315858	+	0.948806i	$0.397708\pi$
$542$			11.1842i			0.480403i
$543$	9.95314	−	14.0759i	0.427130	−	0.604053i
$544$	−1.34946	+	1.34946i	−0.0578576	+	0.0578576i
$545$	−12.9104			−0.553021
$546$	2.08970	−	5.88499i	0.0894310	−	0.251854i
$547$	−27.1210			−1.15961			−0.579804	−	0.814756i	$-0.696871\pi$
$547$	−27.1210			−1.15961			−0.579804	+	0.814756i	$0.696871\pi$
$548$	10.8768	−	10.8768i	0.464634	−	0.464634i
$549$	−15.2058	−	43.0084i	−0.648966	−	1.83555i
$550$		−	45.7000i		−	1.94865i
$551$	−4.92152	+	4.92152i	−0.209664	+	0.209664i
$552$	1.33573	+	7.78523i	0.0568526	+	0.331361i
$553$	3.08000	−	3.08000i	0.130975	−	0.130975i
$554$	−18.5731	−	18.5731i	−0.789096	−	0.789096i
$555$	−20.6200	+	29.1610i	−0.875269	+	1.23782i
$556$		−	16.9884i		−	0.720470i
$557$	6.66683	+	6.66683i	0.282483	+	0.282483i	0.834098	−	0.551616i	$-0.185988\pi$
$557$	6.66683	+	6.66683i	0.282483	+	0.282483i	−0.551616	+	0.834098i	$0.685988\pi$
$558$	0.828427	+	2.34315i	0.0350701	+	0.0991933i
$559$	−3.07255	−	10.9200i	−0.129955	−	0.461867i
$560$		−	3.90842i		−	0.165161i
$561$	2.48591	+	14.4889i	0.104955	+	0.611724i
$562$	19.5674			0.825402
$563$	−45.2526			−1.90717			−0.953585	−	0.301123i	$-0.902638\pi$
$563$	−45.2526			−1.90717			−0.953585	+	0.301123i	$0.902638\pi$
$564$	10.2426	−	1.75736i	0.431293	−	0.0739982i
$565$	12.3959	+	12.3959i	0.521497	+	0.521497i
$566$	16.0052	+	16.0052i	0.672748	+	0.672748i
$567$	0.949747	−	8.94975i	0.0398856	−	0.375854i
$568$	9.18420			0.385360
$569$	19.3704			0.812049			0.406024	−	0.913862i	$-0.366915\pi$
$569$	19.3704			0.812049			0.406024	+	0.913862i	$0.366915\pi$
$570$	−44.9489	+	7.71202i	−1.88270	+	0.323021i
$571$		−	9.90628i		−	0.414565i	−0.978281	−	0.207282i	$-0.933538\pi$
$571$		−	9.90628i		−	0.414565i	0.978281	−	0.207282i	$-0.0664619\pi$
$572$	−7.84367	+	13.9858i	−0.327960	+	0.584776i
$573$	10.7205	−	15.1610i	0.447854	−	0.633362i
$574$	4.03314	+	4.03314i	0.168340	+	0.168340i
$575$			46.8625i			1.95430i
$576$	−2.82843	+	1.00000i	−0.117851	+	0.0416667i
$577$	6.41526	+	6.41526i	0.267071	+	0.267071i	0.827919	−	0.560848i	$-0.189525\pi$
$577$	6.41526	+	6.41526i	0.267071	+	0.267071i	−0.560848	+	0.827919i	$0.689525\pi$
$578$	−9.44547	+	9.44547i	−0.392880	+	0.392880i
$579$	−31.7099	+	5.44057i	−1.31782	+	0.226102i
$580$	−2.85525	+	2.85525i	−0.118558	+	0.118558i
$581$		−	1.28471i		−	0.0532986i
$582$	10.8284	+	7.65685i	0.448853	+	0.317387i
$583$	30.2210	−	30.2210i	1.25163	−	1.25163i
$584$	−2.26420			−0.0936931
$585$	−41.6574	−	7.20584i	−1.72232	−	0.297925i
$586$	1.97255			0.0814853
$587$	−18.2474	+	18.2474i	−0.753152	+	0.753152i	−0.975066	−	0.221914i	$-0.928770\pi$
$587$	−18.2474	+	18.2474i	−0.753152	+	0.753152i	0.221914	+	0.975066i	$0.428770\pi$
$588$	−1.41421	−	1.00000i	−0.0583212	−	0.0412393i
$589$		−	5.58099i		−	0.229961i
$590$	23.4053	−	23.4053i	0.963580	−	0.963580i
$591$	−26.3073	+	4.51362i	−1.08214	+	0.185666i
$592$	3.73054	−	3.73054i	0.153324	−	0.153324i
$593$	13.2827	+	13.2827i	0.545456	+	0.545456i	0.925123	−	0.379667i	$-0.123962\pi$
$593$	13.2827	+	13.2827i	0.545456	+	0.545456i	−0.379667	+	0.925123i	$0.623962\pi$
$594$	−6.28950	+	22.2367i	−0.258061	+	0.912385i
$595$			7.45893i			0.305786i
$596$	13.5020	+	13.5020i	0.553065	+	0.553065i
$597$	−19.5459	+	27.6420i	−0.799959	+	1.13131i
$598$	8.04320	−	14.3416i	0.328911	−	0.586471i
$599$		−	1.41636i		−	0.0578709i	−0.999581	−	0.0289354i	$-0.990788\pi$
$599$		−	1.41636i		−	0.0578709i	0.999581	−	0.0289354i	$-0.00921172\pi$
$600$	−17.5418	+	3.00971i	−0.716143	+	0.122871i
$601$	−6.16529			−0.251488			−0.125744	−	0.992063i	$-0.540132\pi$
$601$	−6.16529			−0.251488			−0.125744	+	0.992063i	$0.540132\pi$
$602$	−3.14627			−0.128232
$603$	−15.9141	+	33.3215i	−0.648073	+	1.35696i
$604$	2.89318	+	2.89318i	0.117722	+	0.117722i
$605$	24.2621	+	24.2621i	0.986393	+	0.986393i
$606$	7.16264	−	1.22892i	0.290963	−	0.0499213i
$607$	12.4035			0.503443			0.251722	−	0.967800i	$-0.419003\pi$
$607$	12.4035			0.503443			0.251722	+	0.967800i	$0.419003\pi$
$608$	6.73685			0.273215
$609$	0.302598	+	1.76367i	0.0122619	+	0.0714676i
$610$			59.4305i			2.40627i
$611$	−18.8685	−	10.5820i	−0.763338	−	0.428103i
$612$	5.39784	−	1.90842i	0.218195	−	0.0771435i
$613$	7.56001	+	7.56001i	0.305346	+	0.305346i	0.843101	−	0.537755i	$-0.180727\pi$
$613$	7.56001	+	7.56001i	0.305346	+	0.305346i	−0.537755	+	0.843101i	$0.680727\pi$
$614$		−	34.0527i		−	1.37426i
$615$	22.2925	−	31.5264i	0.898922	−	1.27127i
$616$	3.14475	+	3.14475i	0.126706	+	0.126706i
$617$	−18.3475	+	18.3475i	−0.738641	+	0.738641i	−0.972315	−	0.233674i	$-0.924925\pi$
$617$	−18.3475	+	18.3475i	−0.738641	+	0.738641i	0.233674	+	0.972315i	$0.424925\pi$
$618$	−0.749059	−	4.36584i	−0.0301316	−	0.175620i
$619$	−1.94787	+	1.94787i	−0.0782916	+	0.0782916i	−0.745168	−	0.666877i	$-0.767631\pi$
$619$	−1.94787	+	1.94787i	−0.0782916	+	0.0782916i	0.666877	+	0.745168i	$0.267631\pi$
$620$		−	3.23784i		−	0.130035i
$621$	6.44949	−	22.8024i	0.258809	−	0.915029i
$622$	7.49901	−	7.49901i	0.300683	−	0.300683i
$623$	18.4689			0.739941
$624$	5.88499	+	2.08970i	0.235588	+	0.0836550i
$625$	−29.2127			−1.16851
$626$	1.41207	−	1.41207i	0.0564376	−	0.0564376i
$627$	29.9611	−	42.3714i	1.19653	−	1.69215i
$628$		−	1.63833i		−	0.0653766i
$629$	−7.11945	+	7.11945i	−0.283871	+	0.283871i
$630$	−5.05317	+	10.5805i	−0.201323	+	0.421538i
$631$	−16.4480	+	16.4480i	−0.654784	+	0.654784i	−0.954141	−	0.299357i	$-0.903228\pi$
$631$	−16.4480	+	16.4480i	−0.654784	+	0.654784i	0.299357	+	0.954141i	$0.403228\pi$
$632$	3.08000	+	3.08000i	0.122516	+	0.122516i
$633$	−30.5916	−	21.6315i	−1.21591	−	0.859777i
$634$		−	18.0253i		−	0.715874i
$635$	−16.6663	−	16.6663i	−0.661381	−	0.661381i
$636$	−13.5906	−	9.60999i	−0.538902	−	0.381061i
$637$	0.976570	+	3.47078i	0.0386931	+	0.137517i
$638$		−	4.59472i		−	0.181907i
$639$	−24.8626	−	11.8742i	−0.983550	−	0.469736i
$640$	3.90842			0.154494
$641$	8.16833			0.322630			0.161315	−	0.986903i	$-0.448427\pi$
$641$	8.16833			0.322630			0.161315	+	0.986903i	$0.448427\pi$
$642$	0.242641	+	1.41421i	0.00957626	+	0.0558146i
$643$	14.0015	+	14.0015i	0.552166	+	0.552166i	0.927065	−	0.374900i	$-0.122323\pi$
$643$	14.0015	+	14.0015i	0.552166	+	0.552166i	−0.374900	+	0.927065i	$0.622323\pi$
$644$	−3.22475	−	3.22475i	−0.127073	−	0.127073i
$645$	3.60169	+	20.9922i	0.141817	+	0.826567i
$646$	−12.8568			−0.505843
$647$	−28.9348			−1.13754			−0.568772	−	0.822495i	$-0.692581\pi$
$647$	−28.9348			−1.13754			−0.568772	+	0.822495i	$0.692581\pi$
$648$	8.94975	+	0.949747i	0.351579	+	0.0373096i
$649$			37.6642i			1.47845i
$650$	32.3148	+	18.1231i	1.26749	+	0.710847i
$651$	−1.17157	−	0.828427i	−0.0459176	−	0.0324686i
$652$	−6.64048	−	6.64048i	−0.260061	−	0.260061i
$653$			9.84590i			0.385300i	0.981268	+	0.192650i	$0.0617082\pi$
$653$			9.84590i			0.385300i	−0.981268	+	0.192650i	$0.938292\pi$
$654$	−4.67147	−	3.30323i	−0.182669	−	0.129166i
$655$	−47.2384	−	47.2384i	−1.84576	−	1.84576i
$656$	−4.03314	+	4.03314i	−0.157467	+	0.157467i
$657$	6.12942	+	2.92736i	0.239132	+	0.114207i
$658$	−4.24264	+	4.24264i	−0.165395	+	0.165395i
$659$			23.0137i			0.896485i	0.893912	+	0.448243i	$0.147950\pi$
$659$			23.0137i			0.896485i	−0.893912	+	0.448243i	$0.852050\pi$
$660$	17.3821	−	24.5820i	0.676598	−	0.956855i
$661$	−18.9237	+	18.9237i	−0.736047	+	0.736047i	−0.971810	−	0.235764i	$-0.924241\pi$
$661$	−18.9237	+	18.9237i	−0.736047	+	0.736047i	0.235764	+	0.971810i	$0.424241\pi$
$662$	−5.16479			−0.200735
$663$	−11.2311	−	3.98804i	−0.436178	−	0.154883i
$664$	1.28471			0.0498562
$665$	18.6185	−	18.6185i	0.721993	−	0.721993i
$666$	−14.9221	+	5.27578i	−0.578222	+	0.204432i
$667$			4.71160i			0.182434i
$668$	4.42946	−	4.42946i	0.171381	−	0.171381i
$669$	−7.46196	−	43.4915i	−0.288496	−	1.68148i
$670$	34.0178	−	34.0178i	1.31422	−	1.31422i
$671$	−47.8183	−	47.8183i	−1.84601	−	1.84601i
$672$	1.00000	−	1.41421i	0.0385758	−	0.0545545i
$673$		−	25.0189i		−	0.964406i	−0.876060	−	0.482203i	$-0.839837\pi$
$673$		−	25.0189i		−	0.964406i	0.876060	−	0.482203i	$-0.160163\pi$
$674$	−11.6963	−	11.6963i	−0.450525	−	0.450525i
$675$	51.3789	+	14.5321i	1.97757	+	0.559342i
$676$	−6.77892	−	11.0926i	−0.260728	−	0.426639i
$677$		−	5.91360i		−	0.227278i	−0.993522	−	0.113639i	$-0.963749\pi$
$677$		−	5.91360i		−	0.227278i	0.993522	−	0.113639i	$-0.0362508\pi$
$678$	1.31371	+	7.65685i	0.0504527	+	0.294060i
$679$	−7.65685			−0.293843
$680$	−7.45893			−0.286037
$681$	9.78889	−	1.67951i	0.375111	−	0.0643589i
$682$	2.60520	+	2.60520i	0.0997581	+	0.0997581i
$683$	13.4975	+	13.4975i	0.516467	+	0.516467i	0.916501	−	0.400033i	$-0.131002\pi$
$683$	13.4975	+	13.4975i	0.516467	+	0.516467i	−0.400033	+	0.916501i	$0.631002\pi$
$684$	−18.2374	−	8.71003i	−0.697323	−	0.333036i
$685$	60.1199			2.29706
$686$	1.00000			0.0381802
$687$	27.0010	−	4.63265i	1.03015	−	0.176747i
$688$		−	3.14627i		−	0.119950i
$689$	9.38483	+	33.3542i	0.357533	+	1.27069i
$690$	−17.8243	+	25.2074i	−0.678559	+	0.959628i
$691$	35.6768	+	35.6768i	1.35721	+	1.35721i	0.877339	+	0.479870i	$0.159316\pi$
$691$	35.6768	+	35.6768i	1.35721	+	1.35721i	0.479870	+	0.877339i	$0.340684\pi$
$692$		−	22.0253i		−	0.837275i
$693$	−4.44735	−	12.5790i	−0.168941	−	0.477837i
$694$	0.113132	+	0.113132i	0.00429445	+	0.00429445i
$695$	46.9504	−	46.9504i	1.78093	−	1.78093i
$696$	−1.76367	+	0.302598i	−0.0668519	+	0.0114700i
$697$	7.69693	−	7.69693i	0.291542	−	0.291542i
$698$			11.7632i			0.445244i
$699$	−17.7327	−	12.5389i	−0.670713	−	0.474266i
$700$	7.26607	−	7.26607i	0.274632	−	0.274632i
$701$	−48.3921			−1.82774			−0.913872	−	0.406002i	$-0.866923\pi$
$701$	−48.3921			−1.82774			−0.913872	+	0.406002i	$0.866923\pi$
$702$	−13.2295	−	13.2657i	−0.499317	−	0.500682i
$703$	35.5421			1.34050
$704$	−3.14475	+	3.14475i	−0.118522	+	0.118522i
$705$	33.1641	+	23.4505i	1.24903	+	0.883199i
$706$		−	2.83521i		−	0.106705i
$707$	−2.96686	+	2.96686i	−0.111580	+	0.111580i
$708$	14.4573	−	2.48048i	0.543340	−	0.0932223i
$709$	−12.0363	+	12.0363i	−0.452034	+	0.452034i	−0.896029	−	0.443995i	$-0.853561\pi$
$709$	−12.0363	+	12.0363i	−0.452034	+	0.452034i	0.443995	+	0.896029i	$0.353561\pi$
$710$	25.3821	+	25.3821i	0.952574	+	0.952574i
$711$	−4.35577	−	12.3200i	−0.163354	−	0.462036i
$712$			18.4689i			0.692151i
$713$	−2.67147	−	2.67147i	−0.100047	−	0.100047i
$714$	−1.90842	+	2.69892i	−0.0714210	+	0.101004i
$715$	−60.3295	+	16.9749i	−2.25620	+	0.634824i
$716$		−	9.46107i		−	0.353577i
$717$	2.38626	−	0.409417i	0.0891164	−	0.0152900i
$718$	−0.106349			−0.00396892
$719$	−21.2462			−0.792349			−0.396174	−	0.918175i	$-0.629662\pi$
$719$	−21.2462			−0.792349			−0.396174	+	0.918175i	$0.629662\pi$
$720$	−10.5805	−	5.05317i	−0.394313	−	0.188321i
$721$	1.80839	+	1.80839i	0.0673479	+	0.0673479i
$722$	18.6571	+	18.6571i	0.694346	+	0.694346i
$723$	42.0721	−	7.21843i	1.56468	−	0.268456i
$724$	−9.95314			−0.369905
$725$	−10.6163			−0.394278
$726$	2.57128	+	14.9865i	0.0954293	+	0.556203i
$727$			14.3879i			0.533616i	0.963750	+	0.266808i	$0.0859690\pi$
$727$			14.3879i			0.533616i	−0.963750	+	0.266808i	$0.914031\pi$
$728$	−3.47078	+	0.976570i	−0.128636	+	0.0361941i
$729$	−23.0000	−	14.1421i	−0.851852	−	0.523783i
$730$	−6.25750	−	6.25750i	−0.231600	−	0.231600i
$731$			6.00441i			0.222081i
$732$	−15.2058	+	21.5042i	−0.562021	+	0.794818i
$733$	23.1737	+	23.1737i	0.855939	+	0.855939i	0.990857	−	0.134918i	$-0.0430770\pi$
$733$	23.1737	+	23.1737i	0.855939	+	0.855939i	−0.134918	+	0.990857i	$0.543077\pi$
$734$	17.1279	−	17.1279i	0.632203	−	0.632203i
$735$	−1.14475	−	6.67210i	−0.0422248	−	0.246104i
$736$	3.22475	−	3.22475i	0.118866	−	0.118866i
$737$			54.7420i			2.01645i
$738$	16.1325	−	5.70372i	0.593847	−	0.209957i
$739$	−23.3795	+	23.3795i	−0.860028	+	0.860028i	−0.991341	−	0.131313i	$-0.958081\pi$
$739$	−23.3795	+	23.3795i	−0.860028	+	0.860028i	0.131313	+	0.991341i	$0.458081\pi$
$740$	20.6200			0.758005
$741$	18.0795	+	37.9888i	0.664168	+	1.39555i
$742$	9.60999			0.352794
$743$	−2.45998	+	2.45998i	−0.0902478	+	0.0902478i	−0.750789	−	0.660542i	$-0.770327\pi$
$743$	−2.45998	+	2.45998i	−0.0902478	+	0.0902478i	0.660542	+	0.750789i	$0.270327\pi$
$744$	0.828427	−	1.17157i	0.0303716	−	0.0429519i
$745$			74.6305i			2.73425i
$746$	6.49421	−	6.49421i	0.237770	−	0.237770i
$747$	−3.47783	−	1.66099i	−0.127247	−	0.0607723i
$748$	6.00152	−	6.00152i	0.219437	−	0.219437i
$749$	−0.585786	−	0.585786i	−0.0214042	−	0.0214042i
$750$	−29.1610	−	20.6200i	−1.06481	−	0.752935i
$751$			6.36840i			0.232386i	0.993227	+	0.116193i	$0.0370691\pi$
$751$			6.36840i			0.232386i	−0.993227	+	0.116193i	$0.962931\pi$
$752$	−4.24264	−	4.24264i	−0.154713	−	0.154713i
$753$	27.8526	+	19.6948i	1.01501	+	0.717718i
$754$	3.24895	+	1.82211i	0.118320	+	0.0663575i
$755$			15.9916i			0.581994i
$756$	−4.53553	+	2.53553i	−0.164956	+	0.0922165i
$757$	15.7327			0.571815			0.285908	−	0.958257i	$-0.407705\pi$
$757$	15.7327			0.571815			0.285908	+	0.958257i	$0.407705\pi$
$758$	−14.6163			−0.530887
$759$	−5.94048	−	34.6236i	−0.215626	−	1.25676i
$760$	18.6185	+	18.6185i	0.675362	+	0.675362i
$761$	−6.49311	−	6.49311i	−0.235375	−	0.235375i	0.579557	−	0.814932i	$-0.303226\pi$
$761$	−6.49311	−	6.49311i	−0.235375	−	0.235375i	−0.814932	+	0.579557i	$0.803226\pi$
$762$	−1.76629	−	10.2947i	−0.0639859	−	0.372937i
$763$	3.30323			0.119585
$764$	−10.7205			−0.387853
$765$	20.1921	+	9.64360i	0.730048	+	0.348665i
$766$			8.96008i			0.323741i
$767$	−26.6326	−	14.9364i	−0.961647	−	0.539321i
$768$	1.41421	+	1.00000i	0.0510310	+	0.0360844i
$769$	−19.6494	−	19.6494i	−0.708577	−	0.708577i	0.257659	−	0.966236i	$-0.417049\pi$
$769$	−19.6494	−	19.6494i	−0.708577	−	0.708577i	−0.966236	+	0.257659i	$0.917049\pi$
$770$			17.3821i			0.626408i
$771$	16.5790	+	11.7231i	0.597078	+	0.422198i
$772$	13.1347	+	13.1347i	0.472728	+	0.472728i
$773$	19.3248	−	19.3248i	0.695065	−	0.695065i	−0.268277	−	0.963342i	$-0.586454\pi$
$773$	19.3248	−	19.3248i	0.695065	−	0.695065i	0.963342	+	0.268277i	$0.0864541\pi$
$774$	−4.06779	+	8.51728i	−0.146214	+	0.306147i
$775$	6.01941	−	6.01941i	0.216224	−	0.216224i
$776$		−	7.65685i		−	0.274865i
$777$	5.27578	−	7.46107i	0.189267	−	0.267665i
$778$	14.8920	−	14.8920i	0.533906	−	0.533906i
$779$	−38.4251			−1.37672
$780$	10.4889	+	22.0394i	0.375564	+	0.789139i
$781$	−40.8453			−1.46156
$782$	−6.15418	+	6.15418i	−0.220073	+	0.220073i
$783$	5.16568	+	1.46107i	0.184606	+	0.0522145i
$784$			1.00000i			0.0357143i
$785$	4.52782	−	4.52782i	0.161605	−	0.161605i
$786$	−5.00631	−	29.1789i	−0.178569	−	1.04078i
$787$	−16.9637	+	16.9637i	−0.604692	+	0.604692i	−0.941554	−	0.336862i	$-0.890634\pi$
$787$	−16.9637	+	16.9637i	−0.604692	+	0.604692i	0.336862	+	0.941554i	$0.390634\pi$
$788$	10.8968	+	10.8968i	0.388184	+	0.388184i
$789$	10.8090	−	15.2863i	0.384811	−	0.544205i
$790$			17.0242i			0.605694i
$791$	−3.17157	−	3.17157i	−0.112768	−	0.112768i
$792$	12.5790	−	4.44735i	0.446975	−	0.158030i
$793$	52.7758	−	14.8495i	1.87412	−	0.527320i
$794$			12.5485i			0.445330i
$795$	−11.0010	−	64.1188i	−0.390167	−	2.27406i
$796$	19.5459			0.692785
$797$	2.12951			0.0754311			0.0377155	−	0.999289i	$-0.487992\pi$
$797$	2.12951			0.0754311			0.0377155	+	0.999289i	$0.487992\pi$
$798$	11.5005	−	1.97318i	0.407114	−	0.0698497i
$799$	8.09676	+	8.09676i	0.286443	+	0.286443i
$800$	7.26607	+	7.26607i	0.256894	+	0.256894i
$801$	23.8783	−	49.9973i	0.843699	−	1.76657i
$802$	7.82215			0.276210
$803$	10.0697			0.355351
$804$	21.0126	−	3.60520i	0.741058	−	0.127145i
$805$		−	17.8243i		−	0.628224i
$806$	−2.87529	+	0.809017i	−0.101278	+	0.0284964i
$807$	1.46107	−	2.06627i	0.0514323	−	0.0727362i
$808$	−2.96686	−	2.96686i	−0.104374	−	0.104374i
$809$		−	11.2452i		−	0.395359i	−0.980267	−	0.197680i	$-0.936659\pi$
$809$		−	11.2452i		−	0.395359i	0.980267	−	0.197680i	$-0.0633405\pi$
$810$	22.1094	+	27.3590i	0.776845	+	0.961296i
$811$	31.8048	+	31.8048i	1.11682	+	1.11682i	0.992206	+	0.124612i	$0.0397686\pi$
$811$	31.8048	+	31.8048i	1.11682	+	1.11682i	0.124612	+	0.992206i	$0.460231\pi$
$812$	0.730537	−	0.730537i	0.0256368	−	0.0256368i
$813$	−19.0926	+	3.27578i	−0.669608	+	0.114886i
$814$	−16.5910	+	16.5910i	−0.581514	+	0.581514i
$815$		−	36.7042i		−	1.28569i
$816$	−2.69892	−	1.90842i	−0.0944811	−	0.0668082i
$817$	14.9878	−	14.9878i	0.524356	−	0.524356i
$818$	−37.4842			−1.31060
$819$	10.6584	+	1.84367i	0.372434	+	0.0644230i
$820$	−22.2925			−0.778489
$821$	31.5206	−	31.5206i	1.10008	−	1.10008i	0.105674	−	0.994401i	$-0.466300\pi$
$821$	31.5206	−	31.5206i	1.10008	−	1.10008i	0.994401	−	0.105674i	$-0.0337001\pi$
$822$	21.7536	+	15.3821i	0.758744	+	0.536513i
$823$		−	23.9166i		−	0.833682i	−0.908980	−	0.416841i	$-0.863137\pi$
$823$		−	23.9166i		−	0.833682i	0.908980	−	0.416841i	$-0.136863\pi$
$824$	−1.80839	+	1.80839i	−0.0629982	+	0.0629982i
$825$	78.0147	−	13.3852i	2.71612	−	0.466013i
$826$	−5.98842	+	5.98842i	−0.208364	+	0.208364i
$827$	17.9805	+	17.9805i	0.625243	+	0.625243i	0.946867	−	0.321624i	$-0.104229\pi$
$827$	17.9805	+	17.9805i	0.625243	+	0.625243i	−0.321624	+	0.946867i	$0.604229\pi$
$828$	−12.8990	+	4.56048i	−0.448271	+	0.158488i
$829$		−	52.5291i		−	1.82441i	−0.409735	−	0.912205i	$-0.634379\pi$
$829$		−	52.5291i		−	1.82441i	0.409735	−	0.912205i	$-0.365621\pi$
$830$	3.55051	+	3.55051i	0.123240	+	0.123240i
$831$	26.2663	−	37.1462i	0.911169	−	1.28859i
$832$	−0.976570	−	3.47078i	−0.0338565	−	0.120328i
$833$		−	1.90842i		−	0.0661230i
$834$	29.0010	−	4.97579i	1.00422	−	0.172298i
$835$	24.4831			0.847274
$836$	−29.9611			−1.03623
$837$	−3.75736	+	2.10051i	−0.129873	+	0.0726041i
$838$	9.14475	+	9.14475i	0.315900	+	0.315900i
$839$	28.1615	+	28.1615i	0.972245	+	0.972245i	0.999625	−	0.0273805i	$-0.00871659\pi$
$839$	28.1615	+	28.1615i	0.972245	+	0.972245i	−0.0273805	+	0.999625i	$0.508717\pi$
$840$	6.67210	−	1.14475i	0.230209	−	0.0394977i
$841$	27.9326			0.963194
$842$	28.3727			0.977788
$843$	5.73117	+	33.4037i	0.197392	+	1.15048i
$844$			21.6315i			0.744589i
$845$	11.9217	−	49.3911i	0.410118	−	1.69911i
$846$	6.00000	+	16.9706i	0.206284	+	0.583460i
$847$	−6.20763	−	6.20763i	−0.213297	−	0.213297i
$848$			9.60999i			0.330009i
$849$	−22.6347	+	32.0104i	−0.776822	+	1.09859i
$850$	−13.8667	−	13.8667i	−0.475625	−	0.475625i
$851$	17.0130	−	17.0130i	0.583200	−	0.583200i
$852$	2.68999	+	15.6784i	0.0921575	+	0.537133i
$853$	3.07410	−	3.07410i	0.105255	−	0.105255i	−0.652518	−	0.757773i	$-0.726287\pi$
$853$	3.07410	−	3.07410i	0.105255	−	0.105255i	0.757773	+	0.652518i	$0.226287\pi$
$854$		−	15.2058i		−	0.520330i
$855$	−26.3305	−	74.4738i	−0.900483	−	2.54695i
$856$	0.585786	−	0.585786i	0.0200218	−	0.0200218i
$857$	33.6947			1.15099			0.575494	−	0.817806i	$-0.304810\pi$
$857$	33.6947			1.15099			0.575494	+	0.817806i	$0.304810\pi$
$858$	−26.1726	−	9.29363i	−0.893519	−	0.317279i
$859$	−53.7400			−1.83359			−0.916793	−	0.399362i	$-0.869232\pi$
$859$	−53.7400			−1.83359			−0.916793	+	0.399362i	$0.869232\pi$
$860$	8.69526	−	8.69526i	0.296506	−	0.296506i
$861$	−5.70372	+	8.06627i	−0.194382	+	0.274898i
$862$		−	33.3137i		−	1.13467i
$863$	15.3531	−	15.3531i	0.522626	−	0.522626i	−0.395737	−	0.918364i	$-0.629511\pi$
$863$	15.3531	−	15.3531i	0.522626	−	0.522626i	0.918364	+	0.395737i	$0.129511\pi$
$864$	−2.53553	−	4.53553i	−0.0862606	−	0.154302i
$865$	60.8706	−	60.8706i	2.06966	−	2.06966i
$866$	−9.89949	−	9.89949i	−0.336399	−	0.336399i
$867$	−18.8909	−	13.3579i	−0.641570	−	0.453659i
$868$			0.828427i			0.0281186i
$869$	−13.6978	−	13.6978i	−0.464667	−	0.464667i
$870$	−5.71050	−	4.03793i	−0.193604	−	0.136899i
$871$	−38.7085	−	21.7089i	−1.31159	−	0.735578i
$872$			3.30323i			0.111861i
$873$	−9.89949	+	20.7279i	−0.335047	+	0.701534i
$874$	30.7233			1.03923
$875$	20.6200			0.697082
$876$	−0.663168	−	3.86523i	−0.0224064	−	0.130594i
$877$	−34.2827	−	34.2827i	−1.15765	−	1.15765i	−0.984981	−	0.172664i	$-0.944762\pi$
$877$	−34.2827	−	34.2827i	−1.15765	−	1.15765i	−0.172664	−	0.984981i	$-0.555238\pi$
$878$	−25.0453	−	25.0453i	−0.845238	−	0.845238i
$879$	0.577746	+	3.36735i	0.0194869	+	0.113578i
$880$	−17.3821			−0.585951
$881$	−0.561963			−0.0189330			−0.00946651	−	0.999955i	$-0.503013\pi$
$881$	−0.561963			−0.0189330			−0.00946651	+	0.999955i	$0.503013\pi$
$882$	1.29289	−	2.70711i	0.0435340	−	0.0911530i
$883$		−	14.8210i		−	0.498766i	−0.968405	−	0.249383i	$-0.919772\pi$
$883$		−	14.8210i		−	0.498766i	0.968405	−	0.249383i	$-0.0802278\pi$
$884$	1.86371	+	6.62372i	0.0626833	+	0.222780i
$885$	46.8106	+	33.1001i	1.57352	+	1.11265i
$886$	20.2195	+	20.2195i	0.679287	+	0.679287i
$887$		−	9.05696i		−	0.304103i	−0.988373	−	0.152051i	$-0.951412\pi$
$887$		−	9.05696i		−	0.304103i	0.988373	−	0.152051i	$-0.0485879\pi$
$888$	7.46107	+	5.27578i	0.250377	+	0.177043i
$889$	4.26420	+	4.26420i	0.143017	+	0.143017i
$890$	−51.0420	+	51.0420i	−1.71093	+	1.71093i
$891$	−39.8027	−	4.22386i	−1.33344	−	0.141505i
$892$	−18.0148	+	18.0148i	−0.603179	+	0.603179i
$893$		−	40.4211i		−	1.35264i
$894$	−19.0948	+	27.0041i	−0.638625	+	0.903152i
$895$	26.1473	−	26.1473i	0.874008	−	0.874008i
$896$	−1.00000			−0.0334077
$897$	26.8384	+	9.53005i	0.896108	+	0.318199i
$898$	−32.4094			−1.08151
$899$	0.605197	−	0.605197i	0.0201844	−	0.0201844i
$900$	−10.2758	−	29.0643i	−0.342526	−	0.968809i
$901$		−	18.3399i		−	0.610992i
$902$	17.9368	−	17.9368i	0.597229	−	0.597229i
$903$	−0.921521	−	5.37102i	−0.0306663	−	0.178736i
$904$	3.17157	−	3.17157i	0.105485	−	0.105485i
$905$	−27.5072	−	27.5072i	−0.914371	−	0.914371i
$906$	−4.09158	+	5.78636i	−0.135934	+	0.192239i
$907$			17.9159i			0.594887i	0.954739	+	0.297443i	$0.0961339\pi$
$907$			17.9159i			0.594887i	−0.954739	+	0.297443i	$0.903866\pi$
$908$	−4.05469	−	4.05469i	−0.134560	−	0.134560i
$909$	4.19578	+	11.8675i	0.139165	+	0.393619i
$910$	−12.2910	−	6.89318i	−0.407443	−	0.228507i
$911$			22.3499i			0.740485i	0.928935	+	0.370242i	$0.120725\pi$
$911$			22.3499i			0.740485i	−0.928935	+	0.370242i	$0.879275\pi$
$912$	1.97318	+	11.5005i	0.0653385	+	0.380820i
$913$	−5.71353			−0.189090
$914$	−0.0700201			−0.00231606
$915$	−101.454	+	17.4068i	−3.35397	+	0.575451i
$916$	−11.1842	−	11.1842i	−0.369536	−	0.369536i
$917$	12.0863	+	12.0863i	0.399125	+	0.399125i
$918$	4.83887	+	8.65572i	0.159707	+	0.285681i
$919$	−27.8033			−0.917146			−0.458573	−	0.888657i	$-0.651639\pi$
$919$	−27.8033			−0.917146			−0.458573	+	0.888657i	$0.651639\pi$
$920$	17.8243			0.587650
$921$	58.1316	−	9.97381i	1.91550	−	0.328648i
$922$		−	15.9337i		−	0.524748i
$923$	16.1979	−	28.8820i	0.533161	−	0.950663i
$924$	−4.44735	+	6.28950i	−0.146307	+	0.206909i
$925$	38.3342	+	38.3342i	1.26042	+	1.26042i
$926$			9.56528i			0.314335i
$927$	7.23355	−	2.55745i	0.237581	−	0.0839976i
$928$	0.730537	+	0.730537i	0.0239811	+	0.0239811i
$929$	−34.4342	+	34.4342i	−1.12975	+	1.12975i	−0.139531	+	0.990218i	$0.544559\pi$
$929$	−34.4342	+	34.4342i	−1.12975	+	1.12975i	−0.990218	+	0.139531i	$0.955441\pi$
$930$	5.52735	−	0.948343i	0.181249	−	0.0310974i
$931$	−4.76367	+	4.76367i	−0.156123	+	0.156123i
$932$			12.5389i			0.410726i
$933$	14.9980	+	10.6052i	0.491013	+	0.347199i
$934$	7.56680	−	7.56680i	0.247593	−	0.247593i
$935$	33.1725			1.08486
$936$	−1.84367	+	10.6584i	−0.0602622	+	0.348380i
$937$	17.4981			0.571639			0.285819	−	0.958284i	$-0.407734\pi$
$937$	17.4981			0.571639			0.285819	+	0.958284i	$0.407734\pi$
$938$	−8.70372	+	8.70372i	−0.284186	+	0.284186i
$939$	2.82414	+	1.99697i	0.0921622	+	0.0651685i
$940$		−	23.4505i		−	0.764872i
$941$	−3.80422	+	3.80422i	−0.124014	+	0.124014i	−0.766390	−	0.642376i	$-0.777949\pi$
$941$	−3.80422	+	3.80422i	−0.124014	+	0.124014i	0.642376	+	0.766390i	$0.277949\pi$
$942$	2.79681	−	0.479857i	0.0911249	−	0.0156346i
$943$	−18.3930	+	18.3930i	−0.598960	+	0.598960i
$944$	−5.98842	−	5.98842i	−0.194906	−	0.194906i
$945$	−19.5421	−	5.52735i	−0.635705	−	0.179805i
$946$			13.9926i			0.454937i
$947$	−9.05532	−	9.05532i	−0.294258	−	0.294258i	0.544501	−	0.838760i	$-0.316719\pi$
$947$	−9.05532	−	9.05532i	−0.294258	−	0.294258i	−0.838760	+	0.544501i	$0.816719\pi$
$948$	−4.35577	+	6.15999i	−0.141469	+	0.200067i
$949$	−3.99330	+	7.12033i	−0.129628	+	0.231136i
$950$			69.2264i			2.24600i
$951$	30.7710	−	5.27947i	0.997819	−	0.171199i
$952$	1.90842			0.0618524
$953$	18.1106			0.586661			0.293331	−	0.956011i	$-0.405236\pi$
$953$	18.1106			0.586661			0.293331	+	0.956011i	$0.405236\pi$
$954$	12.4247	−	26.0153i	0.402264	−	0.842276i
$955$	−29.6279	−	29.6279i	−0.958736	−	0.958736i
$956$	−0.988420	−	0.988420i	−0.0319678	−	0.0319678i
$957$	7.84367	−	1.34576i	0.253550	−	0.0435023i
$958$	−9.27149			−0.299548
$959$	−15.3821			−0.496715
$960$	1.14475	+	6.67210i	0.0369467	+	0.215341i
$961$		−	30.3137i		−	0.977862i
$962$	−5.15216	−	18.3111i	−0.166112	−	0.590372i
$963$	−2.34315	+	0.828427i	−0.0755068	+	0.0266957i
$964$	−17.4268	−	17.4268i	−0.561281	−	0.561281i
$965$			72.6000i			2.33708i
$966$	4.56048	−	6.44949i	0.146731	−	0.207509i
$967$	−9.78788	−	9.78788i	−0.314757	−	0.314757i	0.531992	−	0.846749i	$-0.321444\pi$
$967$	−9.78788	−	9.78788i	−0.314757	−	0.314757i	−0.846749	+	0.531992i	$0.821444\pi$
$968$	6.20763	−	6.20763i	0.199521	−	0.199521i
$969$	−3.76566	−	21.9479i	−0.120970	−	0.705067i
$970$	21.1610	−	21.1610i	0.679440	−	0.679440i
$971$			40.1621i			1.28886i	0.764662	+	0.644431i	$0.222906\pi$
$971$			40.1621i			1.28886i	−0.764662	+	0.644431i	$0.777094\pi$
$972$	1.00000	+	15.5563i	0.0320750	+	0.498970i
$973$	−12.0126	+	12.0126i	−0.385107	+	0.385107i
$974$	27.6158			0.884869
$975$	−21.4733	+	60.4729i	−0.687696	+	1.93668i
$976$	15.2058			0.486724
$977$	−38.8716	+	38.8716i	−1.24361	+	1.24361i	−0.285120	+	0.958492i	$0.592033\pi$
$977$	−38.8716	+	38.8716i	−1.24361	+	1.24361i	−0.958492	+	0.285120i	$0.907967\pi$
$978$	9.39105	−	13.2810i	0.300293	−	0.424678i
$979$		−	82.1377i		−	2.62513i
$980$	−2.76367	+	2.76367i	−0.0882823	+	0.0882823i
$981$	4.27072	−	8.94219i	0.136354	−	0.285502i
$982$	−18.3468	+	18.3468i	−0.585471	+	0.585471i
$983$	−33.9969	−	33.9969i	−1.08433	−	1.08433i	−0.996100	−	0.0882321i	$-0.971878\pi$
$983$	−33.9969	−	33.9969i	−1.08433	−	1.08433i	−0.0882321	−	0.996100i	$-0.528122\pi$
$984$	−8.06627	−	5.70372i	−0.257143	−	0.181828i
$985$			60.2306i			1.91911i
$986$	−1.39417	−	1.39417i	−0.0443996	−	0.0443996i
$987$	−8.48528	−	6.00000i	−0.270089	−	0.190982i
$988$	11.8816	−	21.1857i	0.378004	−	0.674007i
$989$		−	14.3485i		−	0.456256i
$990$	47.0553	+	22.4732i	1.49551	+	0.714246i
$991$	37.1938			1.18150			0.590750	−	0.806855i	$-0.298832\pi$
$991$	37.1938			1.18150			0.590750	+	0.806855i	$0.298832\pi$
$992$	−0.828427			−0.0263026
$993$	−1.51273	−	8.81685i	−0.0480051	−	0.279794i
$994$	−6.49421	−	6.49421i	−0.205984	−	0.205984i
$995$	54.0184	+	54.0184i	1.71250	+	1.71250i
$996$	0.376281	+	2.19313i	0.0119229	+	0.0694920i
$997$	−11.3449			−0.359297			−0.179648	−	0.983731i	$-0.557496\pi$
$997$	−11.3449			−0.359297			−0.179648	+	0.983731i	$0.557496\pi$
$998$	−4.43539			−0.140400
$999$	−13.3769	−	23.9285i	−0.423227	−	0.757063i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.p.b.281.4	yes	8
3.2	odd	2		546.2.p.a.281.1	yes	8
13.5	odd	4		546.2.p.a.239.1	✓	8
39.5	even	4	inner	546.2.p.b.239.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.p.a.239.1	✓	8	13.5	odd	4
546.2.p.a.281.1	yes	8	3.2	odd	2
546.2.p.b.239.4	yes	8	39.5	even	4	inner
546.2.p.b.281.4	yes	8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.41421 + 1.00000i) q^{3} -1.00000i q^{4} +(2.76367 - 2.76367i) q^{5} +(1.70711 - 0.292893i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.41421 + 1.00000i) q^{3} -1.00000i q^{4} +(2.76367 - 2.76367i) q^{5} +(1.70711 - 0.292893i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} -3.90842i q^{10} +(3.14475 + 3.14475i) q^{11} +(1.00000 - 1.41421i) q^{12} +(-3.47078 + 0.976570i) q^{13} +1.00000i q^{14} +(6.67210 - 1.14475i) q^{15} -1.00000 q^{16} +1.90842 q^{17} +(2.70711 + 1.29289i) q^{18} +(-4.76367 - 4.76367i) q^{19} +(-2.76367 - 2.76367i) q^{20} +(-1.70711 + 0.292893i) q^{21} +4.44735 q^{22} -4.56048 q^{23} +(-0.292893 - 1.70711i) q^{24} -10.2758i q^{25} +(-1.76367 + 3.14475i) q^{26} +(-1.41421 + 5.00000i) q^{27} +(0.707107 + 0.707107i) q^{28} -1.03314i q^{29} +(3.90842 - 5.52735i) q^{30} +(0.585786 + 0.585786i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(1.30260 + 7.59210i) q^{33} +(1.34946 - 1.34946i) q^{34} +3.90842i q^{35} +(2.82843 - 1.00000i) q^{36} +(-3.73054 + 3.73054i) q^{37} -6.73685 q^{38} +(-5.88499 - 2.08970i) q^{39} -3.90842 q^{40} +(4.03314 - 4.03314i) q^{41} +(-1.00000 + 1.41421i) q^{42} +3.14627i q^{43} +(3.14475 - 3.14475i) q^{44} +(10.5805 + 5.05317i) q^{45} +(-3.22475 + 3.22475i) q^{46} +(4.24264 + 4.24264i) q^{47} +(-1.41421 - 1.00000i) q^{48} -1.00000i q^{49} +(-7.26607 - 7.26607i) q^{50} +(2.69892 + 1.90842i) q^{51} +(0.976570 + 3.47078i) q^{52} -9.60999i q^{53} +(2.53553 + 4.53553i) q^{54} +17.3821 q^{55} +1.00000 q^{56} +(-1.97318 - 11.5005i) q^{57} +(-0.730537 - 0.730537i) q^{58} +(5.98842 + 5.98842i) q^{59} +(-1.14475 - 6.67210i) q^{60} -15.2058 q^{61} +0.828427 q^{62} +(-2.70711 - 1.29289i) q^{63} +1.00000i q^{64} +(-6.89318 + 12.2910i) q^{65} +(6.28950 + 4.44735i) q^{66} +(8.70372 + 8.70372i) q^{67} -1.90842i q^{68} +(-6.44949 - 4.56048i) q^{69} +(2.76367 + 2.76367i) q^{70} +(-6.49421 + 6.49421i) q^{71} +(1.29289 - 2.70711i) q^{72} +(1.60103 - 1.60103i) q^{73} +5.27578i q^{74} +(10.2758 - 14.5321i) q^{75} +(-4.76367 + 4.76367i) q^{76} -4.44735 q^{77} +(-5.63896 + 2.68368i) q^{78} -4.35577 q^{79} +(-2.76367 + 2.76367i) q^{80} +(-7.00000 + 5.65685i) q^{81} -5.70372i q^{82} +(-0.908424 + 0.908424i) q^{83} +(0.292893 + 1.70711i) q^{84} +(5.27426 - 5.27426i) q^{85} +(2.22475 + 2.22475i) q^{86} +(1.03314 - 1.46107i) q^{87} -4.44735i q^{88} +(-13.0595 - 13.0595i) q^{89} +(11.0547 - 3.90842i) q^{90} +(1.76367 - 3.14475i) q^{91} +4.56048i q^{92} +(0.242641 + 1.41421i) q^{93} +6.00000 q^{94} -26.3305 q^{95} +(-1.70711 + 0.292893i) q^{96} +(5.41421 + 5.41421i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(-5.74995 + 12.0394i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{5} + 8 q^{6} + 8 q^{9}+O(q^{10}) \) 8 * q + 4 * q^5 + 8 * q^6 + 8 * q^9	\( 8 q + 4 q^{5} + 8 q^{6} + 8 q^{9} + 8 q^{11} + 8 q^{12} - 4 q^{13} - 8 q^{16} - 20 q^{17} + 16 q^{18} - 20 q^{19} - 4 q^{20} - 8 q^{21} + 12 q^{22} + 12 q^{23} - 8 q^{24} + 4 q^{26} - 4 q^{30} + 16 q^{31} + 4 q^{33} + 4 q^{34} - 24 q^{37} + 4 q^{38} - 12 q^{39} + 4 q^{40} + 20 q^{41} - 8 q^{42} + 8 q^{44} - 4 q^{45} + 4 q^{46} - 24 q^{50} + 8 q^{51} + 8 q^{52} - 8 q^{54} - 12 q^{55} + 8 q^{56} + 24 q^{57} + 8 q^{60} + 20 q^{61} - 16 q^{62} - 16 q^{63} - 28 q^{65} + 16 q^{66} + 24 q^{67} + 8 q^{69} + 4 q^{70} - 28 q^{71} + 16 q^{72} + 16 q^{73} + 36 q^{75} - 20 q^{76} - 12 q^{77} - 4 q^{78} + 24 q^{79} - 4 q^{80} - 56 q^{81} + 28 q^{83} + 8 q^{84} + 16 q^{85} - 12 q^{86} - 4 q^{87} + 16 q^{90} - 4 q^{91} - 32 q^{93} + 48 q^{94} - 92 q^{95} - 8 q^{96} + 32 q^{97} - 16 q^{99}+O(q^{100}) \) 8 * q + 4 * q^5 + 8 * q^6 + 8 * q^9 + 8 * q^11 + 8 * q^12 - 4 * q^13 - 8 * q^16 - 20 * q^17 + 16 * q^18 - 20 * q^19 - 4 * q^20 - 8 * q^21 + 12 * q^22 + 12 * q^23 - 8 * q^24 + 4 * q^26 - 4 * q^30 + 16 * q^31 + 4 * q^33 + 4 * q^34 - 24 * q^37 + 4 * q^38 - 12 * q^39 + 4 * q^40 + 20 * q^41 - 8 * q^42 + 8 * q^44 - 4 * q^45 + 4 * q^46 - 24 * q^50 + 8 * q^51 + 8 * q^52 - 8 * q^54 - 12 * q^55 + 8 * q^56 + 24 * q^57 + 8 * q^60 + 20 * q^61 - 16 * q^62 - 16 * q^63 - 28 * q^65 + 16 * q^66 + 24 * q^67 + 8 * q^69 + 4 * q^70 - 28 * q^71 + 16 * q^72 + 16 * q^73 + 36 * q^75 - 20 * q^76 - 12 * q^77 - 4 * q^78 + 24 * q^79 - 4 * q^80 - 56 * q^81 + 28 * q^83 + 8 * q^84 + 16 * q^85 - 12 * q^86 - 4 * q^87 + 16 * q^90 - 4 * q^91 - 32 * q^93 + 48 * q^94 - 92 * q^95 - 8 * q^96 + 32 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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