LMFDB - Embedded newform 546.2.p.b.281.2

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			281.2
Root			$3.15653i$ of defining polynomial
Character	$\chi$	$=$	546.281
Dual form			546.2.p.b.239.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.41421 + 1.00000i) q^{3} -1.00000i q^{4} +(2.23200 - 2.23200i) q^{5} +(0.292893 - 1.70711i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.00000 - 2.82843i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.41421 + 1.00000i) q^{3} -1.00000i q^{4} +(2.23200 - 2.23200i) q^{5} +(0.292893 - 1.70711i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.00000 - 2.82843i) q^{9} +3.15653i q^{10} +(-3.38853 - 3.38853i) q^{11} +(1.00000 + 1.41421i) q^{12} +(-1.52490 + 3.26721i) q^{13} +1.00000i q^{14} +(-0.924526 + 5.38853i) q^{15} -1.00000 q^{16} -5.15653 q^{17} +(1.29289 + 2.70711i) q^{18} +(-4.23200 - 4.23200i) q^{19} +(-2.23200 - 2.23200i) q^{20} +(-0.292893 + 1.70711i) q^{21} +4.79211 q^{22} -6.67033 q^{23} +(-1.70711 - 0.292893i) q^{24} -4.96368i q^{25} +(-1.23200 - 3.38853i) q^{26} +(1.41421 + 5.00000i) q^{27} +(-0.707107 - 0.707107i) q^{28} -4.20632i q^{29} +(-3.15653 - 4.46401i) q^{30} +(3.41421 + 3.41421i) q^{31} +(0.707107 - 0.707107i) q^{32} +(8.18065 + 1.40358i) q^{33} +(3.64622 - 3.64622i) q^{34} -3.15653i q^{35} +(-2.82843 - 1.00000i) q^{36} +(-0.0256791 + 0.0256791i) q^{37} +5.98496 q^{38} +(-1.11068 - 6.14544i) q^{39} +3.15653 q^{40} +(7.20632 - 7.20632i) q^{41} +(-1.00000 - 1.41421i) q^{42} +8.08455i q^{43} +(-3.38853 + 3.38853i) q^{44} +(-4.08106 - 8.54506i) q^{45} +(4.71664 - 4.71664i) q^{46} +(-4.24264 - 4.24264i) q^{47} +(1.41421 - 1.00000i) q^{48} -1.00000i q^{49} +(3.50985 + 3.50985i) q^{50} +(7.29244 - 5.15653i) q^{51} +(3.26721 + 1.52490i) q^{52} -2.87757i q^{53} +(-4.53553 - 2.53553i) q^{54} -15.1264 q^{55} +1.00000 q^{56} +(10.2170 + 1.75295i) q^{57} +(2.97432 + 2.97432i) q^{58} +(-2.48463 - 2.48463i) q^{59} +(5.38853 + 0.924526i) q^{60} +2.47115 q^{61} -4.82843 q^{62} +(-1.29289 - 2.70711i) q^{63} +1.00000i q^{64} +(3.88886 + 10.6960i) q^{65} +(-6.77707 + 4.79211i) q^{66} +(-7.19128 - 7.19128i) q^{67} +5.15653i q^{68} +(9.43328 - 6.67033i) q^{69} +(2.23200 + 2.23200i) q^{70} +(-2.25768 + 2.25768i) q^{71} +(2.70711 - 1.29289i) q^{72} +(8.14654 - 8.14654i) q^{73} -0.0363157i q^{74} +(4.96368 + 7.01971i) q^{75} +(-4.23200 + 4.23200i) q^{76} -4.79211 q^{77} +(5.13085 + 3.56011i) q^{78} +2.36442 q^{79} +(-2.23200 + 2.23200i) q^{80} +(-7.00000 - 5.65685i) q^{81} +10.1913i q^{82} +(6.15653 - 6.15653i) q^{83} +(1.70711 + 0.292893i) q^{84} +(-11.5094 + 11.5094i) q^{85} +(-5.71664 - 5.71664i) q^{86} +(4.20632 + 5.94864i) q^{87} -4.79211i q^{88} +(9.55570 + 9.55570i) q^{89} +(8.92802 + 3.15653i) q^{90} +(1.23200 + 3.38853i) q^{91} +6.67033i q^{92} +(-8.24264 - 1.41421i) q^{93} +6.00000 q^{94} -18.8917 q^{95} +(-0.292893 + 1.70711i) q^{96} +(2.58579 + 2.58579i) q^{97} +(0.707107 + 0.707107i) q^{98} +(-12.9728 + 6.19569i) 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
$5$	2.23200	−	2.23200i	0.998183	−	0.998183i	−0.00181579	−	0.999998i	$-0.500578\pi$
$5$	2.23200	−	2.23200i	0.998183	−	0.998183i	0.999998	+	0.00181579i	$0.000577983\pi$
$6$	0.292893	−	1.70711i	0.119573	−	0.696923i
$7$	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
$10$			3.15653i			0.998183i
$11$	−3.38853	−	3.38853i	−1.02168	−	1.02168i	−0.999760	−	0.0219219i	$-0.993021\pi$
$11$	−3.38853	−	3.38853i	−1.02168	−	1.02168i	−0.0219219	−	0.999760i	$-0.506979\pi$
$12$	1.00000	+	1.41421i	0.288675	+	0.408248i
$13$	−1.52490	+	3.26721i	−0.422930	+	0.906162i
$13$	−1.52490	+	3.26721i	−0.422930	+	0.906162i
$14$			1.00000i			0.267261i
$15$	−0.924526	+	5.38853i	−0.238712	+	1.39131i
$16$	−1.00000			−0.250000
$17$	−5.15653			−1.25064			−0.625321	−	0.780368i	$-0.715032\pi$
$17$	−5.15653			−1.25064			−0.625321	+	0.780368i	$0.715032\pi$
$18$	1.29289	+	2.70711i	0.304738	+	0.638071i
$19$	−4.23200	−	4.23200i	−0.970888	−	0.970888i	0.0286998	−	0.999588i	$-0.490863\pi$
$19$	−4.23200	−	4.23200i	−0.970888	−	0.970888i	−0.999588	+	0.0286998i	$0.990863\pi$
$20$	−2.23200	−	2.23200i	−0.499091	−	0.499091i
$21$	−0.292893	+	1.70711i	−0.0639145	+	0.372521i
$22$	4.79211			1.02168
$23$	−6.67033			−1.39086			−0.695430	−	0.718594i	$-0.744786\pi$
$23$	−6.67033			−1.39086			−0.695430	+	0.718594i	$0.744786\pi$
$24$	−1.70711	−	0.292893i	−0.348462	−	0.0597866i
$25$		−	4.96368i		−	0.992737i
$26$	−1.23200	−	3.38853i	−0.241616	−	0.664546i
$27$	1.41421	+	5.00000i	0.272166	+	0.962250i
$28$	−0.707107	−	0.707107i	−0.133631	−	0.133631i
$29$		−	4.20632i		−	0.781095i	−0.920583	−	0.390547i	$-0.872286\pi$
$29$		−	4.20632i		−	0.781095i	0.920583	−	0.390547i	$-0.127714\pi$
$30$	−3.15653	−	4.46401i	−0.576301	−	0.815013i
$31$	3.41421	+	3.41421i	0.613211	+	0.613211i	0.943781	−	0.330570i	$-0.107241\pi$
$31$	3.41421	+	3.41421i	0.613211	+	0.613211i	−0.330570	+	0.943781i	$0.607241\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	8.18065	+	1.40358i	1.42407	+	0.244331i
$34$	3.64622	−	3.64622i	0.625321	−	0.625321i
$35$		−	3.15653i		−	0.533551i
$36$	−2.82843	−	1.00000i	−0.471405	−	0.166667i
$37$	−0.0256791	+	0.0256791i	−0.00422161	+	0.00422161i	−0.709214	−	0.704993i	$-0.750950\pi$
$37$	−0.0256791	+	0.0256791i	−0.00422161	+	0.00422161i	0.704993	+	0.709214i	$0.250950\pi$
$38$	5.98496			0.970888
$39$	−1.11068	−	6.14544i	−0.177852	−	0.984057i
$40$	3.15653			0.499091
$41$	7.20632	−	7.20632i	1.12544	−	1.12544i	0.134529	−	0.990910i	$-0.457048\pi$
$41$	7.20632	−	7.20632i	1.12544	−	1.12544i	0.990910	−	0.134529i	$-0.0429522\pi$
$42$	−1.00000	−	1.41421i	−0.154303	−	0.218218i
$43$			8.08455i			1.23288i	0.787401	+	0.616441i	$0.211426\pi$
$43$			8.08455i			1.23288i	−0.787401	+	0.616441i	$0.788574\pi$
$44$	−3.38853	+	3.38853i	−0.510841	+	0.510841i
$45$	−4.08106	−	8.54506i	−0.608368	−	1.27382i
$46$	4.71664	−	4.71664i	0.695430	−	0.695430i
$47$	−4.24264	−	4.24264i	−0.618853	−	0.618853i	0.326384	−	0.945237i	$-0.394170\pi$
$47$	−4.24264	−	4.24264i	−0.618853	−	0.618853i	−0.945237	+	0.326384i	$0.894170\pi$
$48$	1.41421	−	1.00000i	0.204124	−	0.144338i
$49$		−	1.00000i		−	0.142857i
$50$	3.50985	+	3.50985i	0.496368	+	0.496368i
$51$	7.29244	−	5.15653i	1.02115	−	0.722059i
$52$	3.26721	+	1.52490i	0.453081	+	0.211465i
$53$		−	2.87757i		−	0.395265i	−0.980276	−	0.197633i	$-0.936675\pi$
$53$		−	2.87757i		−	0.395265i	0.980276	−	0.197633i	$-0.0633253\pi$
$54$	−4.53553	−	2.53553i	−0.617208	−	0.345042i
$55$	−15.1264			−2.03965
$56$	1.00000			0.133631
$57$	10.2170	+	1.75295i	1.35327	+	0.232184i
$58$	2.97432	+	2.97432i	0.390547	+	0.390547i
$59$	−2.48463	−	2.48463i	−0.323472	−	0.323472i	0.526626	−	0.850097i	$-0.323457\pi$
$59$	−2.48463	−	2.48463i	−0.323472	−	0.323472i	−0.850097	+	0.526626i	$0.823457\pi$
$60$	5.38853	+	0.924526i	0.695657	+	0.119356i
$61$	2.47115			0.316399			0.158199	−	0.987407i	$-0.449431\pi$
$61$	2.47115			0.316399			0.158199	+	0.987407i	$0.449431\pi$
$62$	−4.82843			−0.613211
$63$	−1.29289	−	2.70711i	−0.162889	−	0.341063i
$64$			1.00000i			0.125000i
$65$	3.88886	+	10.6960i	0.482354	+	1.32668i
$66$	−6.77707	+	4.79211i	−0.834200	+	0.589868i
$67$	−7.19128	−	7.19128i	−0.878555	−	0.878555i	0.114830	−	0.993385i	$-0.463368\pi$
$67$	−7.19128	−	7.19128i	−0.878555	−	0.878555i	−0.993385	+	0.114830i	$0.963368\pi$
$68$			5.15653i			0.625321i
$69$	9.43328	−	6.67033i	1.13563	−	0.803014i
$70$	2.23200	+	2.23200i	0.266776	+	0.266776i
$71$	−2.25768	+	2.25768i	−0.267938	+	0.267938i	−0.828269	−	0.560331i	$-0.810674\pi$
$71$	−2.25768	+	2.25768i	−0.267938	+	0.267938i	0.560331	+	0.828269i	$0.310674\pi$
$72$	2.70711	−	1.29289i	0.319036	−	0.152369i
$73$	8.14654	−	8.14654i	0.953481	−	0.953481i	−0.0454845	−	0.998965i	$-0.514483\pi$
$73$	8.14654	−	8.14654i	0.953481	−	0.953481i	0.998965	+	0.0454845i	$0.0144832\pi$
$74$		−	0.0363157i		−	0.00422161i
$75$	4.96368	+	7.01971i	0.573157	+	0.810566i
$76$	−4.23200	+	4.23200i	−0.485444	+	0.485444i
$77$	−4.79211			−0.546112
$78$	5.13085	+	3.56011i	0.580955	+	0.403103i
$79$	2.36442			0.266018			0.133009	−	0.991115i	$-0.457536\pi$
$79$	2.36442			0.266018			0.133009	+	0.991115i	$0.457536\pi$
$80$	−2.23200	+	2.23200i	−0.249546	+	0.249546i
$81$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$82$			10.1913i			1.12544i
$83$	6.15653	−	6.15653i	0.675767	−	0.675767i	−0.283272	−	0.959039i	$-0.591420\pi$
$83$	6.15653	−	6.15653i	0.675767	−	0.675767i	0.959039	+	0.283272i	$0.0914201\pi$
$84$	1.70711	+	0.292893i	0.186261	+	0.0319573i
$85$	−11.5094	+	11.5094i	−1.24837	+	1.24837i
$86$	−5.71664	−	5.71664i	−0.616441	−	0.616441i
$87$	4.20632	+	5.94864i	0.450965	+	0.637761i
$88$		−	4.79211i		−	0.510841i
$89$	9.55570	+	9.55570i	1.01290	+	1.01290i	0.999916	+	0.0129867i	$0.00413390\pi$
$89$	9.55570	+	9.55570i	1.01290	+	1.01290i	0.0129867	+	0.999916i	$0.495866\pi$
$90$	8.92802	+	3.15653i	0.941096	+	0.332728i
$91$	1.23200	+	3.38853i	0.129149	+	0.355215i
$92$			6.67033i			0.695430i
$93$	−8.24264	−	1.41421i	−0.854722	−	0.146647i
$94$	6.00000			0.618853
$95$	−18.8917			−1.93825
$96$	−0.292893	+	1.70711i	−0.0298933	+	0.174231i
$97$	2.58579	+	2.58579i	0.262547	+	0.262547i	0.826088	−	0.563541i	$-0.190561\pi$
$97$	2.58579	+	2.58579i	0.262547	+	0.262547i	−0.563541	+	0.826088i	$0.690561\pi$
$98$	0.707107	+	0.707107i	0.0714286	+	0.0714286i
$99$	−12.9728	+	6.19569i	−1.30381	+	0.622690i
$100$	−4.96368			−0.496368
$101$	0.291788			0.0290340			0.0145170	−	0.999895i	$-0.495379\pi$
$101$	0.291788			0.0290340			0.0145170	+	0.999895i	$0.495379\pi$
$102$	−1.51031	+	8.80275i	−0.149543	+	0.871602i
$103$			18.2758i			1.80077i	0.435093	+	0.900385i	$0.356715\pi$
$103$			18.2758i			1.80077i	−0.435093	+	0.900385i	$0.643285\pi$
$104$	−3.38853	+	1.23200i	−0.332273	+	0.120808i
$105$	3.15653	+	4.46401i	0.308046	+	0.435643i
$106$	2.03475	+	2.03475i	0.197633	+	0.197633i
$107$		−	4.82843i		−	0.466782i	−0.972383	−	0.233391i	$-0.925018\pi$
$107$		−	4.82843i		−	0.466782i	0.972383	−	0.233391i	$-0.0749821\pi$
$108$	5.00000	−	1.41421i	0.481125	−	0.136083i
$109$	−12.3870	−	12.3870i	−1.18646	−	1.18646i	−0.978040	−	0.208416i	$-0.933169\pi$
$109$	−12.3870	−	12.3870i	−1.18646	−	1.18646i	−0.208416	−	0.978040i	$-0.566831\pi$
$110$	10.6960	−	10.6960i	1.01982	−	1.01982i
$111$	0.0106366	−	0.0619948i	0.00100958	−	0.00588428i
$112$	−0.707107	+	0.707107i	−0.0668153	+	0.0668153i
$113$		−	12.4853i		−	1.17452i	−0.809400	−	0.587258i	$-0.800207\pi$
$113$		−	12.4853i		−	1.17452i	0.809400	−	0.587258i	$-0.199793\pi$
$114$	−8.46401	+	5.98496i	−0.792727	+	0.560543i
$115$	−14.8882	+	14.8882i	−1.38833	+	1.38833i
$116$	−4.20632			−0.390547
$117$	7.71618	+	7.58027i	0.713361	+	0.700797i
$118$	3.51380			0.323472
$119$	−3.64622	+	3.64622i	−0.334248	+	0.334248i
$120$	−4.46401	+	3.15653i	−0.407506	+	0.288150i
$121$			11.9643i			1.08767i
$122$	−1.74737	+	1.74737i	−0.158199	+	0.158199i
$123$	−2.98496	+	17.3976i	−0.269145	+	1.56869i
$124$	3.41421	−	3.41421i	0.306605	−	0.306605i
$125$	0.0810568	+	0.0810568i	0.00724994	+	0.00724994i
$126$	2.82843	+	1.00000i	0.251976	+	0.0890871i
$127$		−	13.4647i		−	1.19479i	−0.801945	−	0.597397i	$-0.796201\pi$
$127$		−	13.4647i		−	1.19479i	0.801945	−	0.597397i	$-0.203799\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−8.08455	−	11.4333i	−0.711805	−	1.00664i
$130$	−10.3131	−	4.81338i	−0.904515	−	0.422162i
$131$			2.34938i			0.205266i	0.994719	+	0.102633i	$0.0327267\pi$
$131$			2.34938i			0.205266i	−0.994719	+	0.102633i	$0.967273\pi$
$132$	1.40358	−	8.18065i	0.122166	−	0.712034i
$133$	−5.98496			−0.518962
$134$	10.1700			0.878555
$135$	14.3166	+	8.00349i	1.23217	+	0.688831i
$136$	−3.64622	−	3.64622i	−0.312661	−	0.312661i
$137$	12.1102	+	12.1102i	1.03465	+	1.03465i	0.999378	+	0.0352685i	$0.0112287\pi$
$137$	12.1102	+	12.1102i	1.03465	+	1.03465i	0.0352685	+	0.999378i	$0.488771\pi$
$138$	−1.95370	+	11.3870i	−0.166310	+	0.969323i
$139$	8.51537			0.722264			0.361132	−	0.932515i	$-0.382390\pi$
$139$	8.51537			0.722264			0.361132	+	0.932515i	$0.382390\pi$
$140$	−3.15653			−0.266776
$141$	10.2426	+	1.75736i	0.862586	+	0.147996i
$142$		−	3.19285i		−	0.267938i
$143$	16.2382	−	5.90390i	1.35791	−	0.493709i
$144$	−1.00000	+	2.82843i	−0.0833333	+	0.235702i
$145$	−9.38853	−	9.38853i	−0.779675	−	0.779675i
$146$			11.5209i			0.953481i
$147$	1.00000	+	1.41421i	0.0824786	+	0.116642i
$148$	0.0256791	+	0.0256791i	0.00211081	+	0.00211081i
$149$	−11.7201	+	11.7201i	−0.960150	+	0.960150i	−0.999236	−	0.0390856i	$-0.987555\pi$
$149$	−11.7201	+	11.7201i	−0.960150	+	0.960150i	0.0390856	+	0.999236i	$0.487555\pi$
$150$	−8.47354	−	1.45383i	−0.691862	−	0.118705i
$151$	7.88886	−	7.88886i	0.641986	−	0.641986i	−0.309057	−	0.951043i	$-0.600013\pi$
$151$	7.88886	−	7.88886i	0.641986	−	0.641986i	0.951043	+	0.309057i	$0.100013\pi$
$152$		−	5.98496i		−	0.485444i
$153$	−5.15653	+	14.5849i	−0.416881	+	1.17912i
$154$	3.38853	−	3.38853i	0.273056	−	0.273056i
$155$	15.2411			1.22419
$156$	−6.14544	+	1.11068i	−0.492029	+	0.0889259i
$157$	18.5676			1.48186			0.740929	−	0.671584i	$-0.234386\pi$
$157$	18.5676			1.48186			0.740929	+	0.671584i	$0.234386\pi$
$158$	−1.67190	+	1.67190i	−0.133009	+	0.133009i
$159$	2.87757	+	4.06950i	0.228206	+	0.322733i
$160$		−	3.15653i		−	0.249546i
$161$	−4.71664	+	4.71664i	−0.371723	+	0.371723i
$162$	8.94975	−	0.949747i	0.703159	−	0.0746192i
$163$	7.34223	−	7.34223i	0.575088	−	0.575088i	−0.358458	−	0.933546i	$-0.616697\pi$
$163$	7.34223	−	7.34223i	0.575088	−	0.575088i	0.933546	+	0.358458i	$0.116697\pi$
$164$	−7.20632	−	7.20632i	−0.562719	−	0.562719i
$165$	21.3920	−	15.1264i	1.66537	−	1.17759i
$166$			8.70665i			0.675767i
$167$	5.31811	+	5.31811i	0.411528	+	0.411528i	0.882271	−	0.470743i	$-0.156014\pi$
$167$	5.31811	+	5.31811i	0.411528	+	0.411528i	−0.470743	+	0.882271i	$0.656014\pi$
$168$	−1.41421	+	1.00000i	−0.109109	+	0.0771517i
$169$	−8.34938	−	9.96433i	−0.642260	−	0.766487i
$170$		−	16.2767i		−	1.24837i
$171$	−16.2019	+	7.73791i	−1.23899	+	0.591733i
$172$	8.08455			0.616441
$173$	−14.0425			−1.06764			−0.533818	−	0.845600i	$-0.679243\pi$
$173$	−14.0425			−1.06764			−0.533818	+	0.845600i	$0.679243\pi$
$174$	−7.18065	−	1.23200i	−0.544363	−	0.0933980i
$175$	−3.50985	−	3.50985i	−0.265320	−	0.265320i
$176$	3.38853	+	3.38853i	0.255420	+	0.255420i
$177$	5.99844	+	1.02917i	0.450870	+	0.0773571i
$178$	−13.5138			−1.01290
$179$	2.05136			0.153326			0.0766629	−	0.997057i	$-0.475573\pi$
$179$	2.05136			0.153326			0.0766629	+	0.997057i	$0.475573\pi$
$180$	−8.54506	+	4.08106i	−0.636912	+	0.304184i
$181$		−	14.5344i		−	1.08034i	−0.841557	−	0.540168i	$-0.818361\pi$
$181$		−	14.5344i		−	1.08034i	0.841557	−	0.540168i	$-0.181639\pi$
$182$	−3.26721	−	1.52490i	−0.242182	−	0.113033i
$183$	−3.49474	+	2.47115i	−0.258339	+	0.182673i
$184$	−4.71664	−	4.71664i	−0.347715	−	0.347715i
$185$			0.114632i			0.00842788i
$186$	6.82843	−	4.82843i	0.500685	−	0.354037i
$187$	17.4731	+	17.4731i	1.27776	+	1.27776i
$188$	−4.24264	+	4.24264i	−0.309426	+	0.309426i
$189$	4.53553	+	2.53553i	0.329912	+	0.184433i
$190$	13.3584	−	13.3584i	0.969124	−	0.969124i
$191$		−	10.0141i		−	0.724597i	−0.932062	−	0.362298i	$-0.881992\pi$
$191$		−	10.0141i		−	0.724597i	0.932062	−	0.362298i	$-0.118008\pi$
$192$	−1.00000	−	1.41421i	−0.0721688	−	0.102062i
$193$	−9.59991	+	9.59991i	−0.691017	+	0.691017i	−0.962456	−	0.271439i	$-0.912501\pi$
$193$	−9.59991	+	9.59991i	−0.691017	+	0.691017i	0.271439	+	0.962456i	$0.412501\pi$
$194$	−3.65685			−0.262547
$195$	−16.1957	−	11.2376i	−1.15980	−	0.804740i
$196$	−1.00000			−0.0714286
$197$	4.64116	−	4.64116i	0.330669	−	0.330669i	−0.522171	−	0.852841i	$-0.674878\pi$
$197$	4.64116	−	4.64116i	0.330669	−	0.330669i	0.852841	+	0.522171i	$0.174878\pi$
$198$	4.79211	−	13.5541i	0.340561	−	0.963251i
$199$		−	9.76046i		−	0.691901i	−0.938253	−	0.345950i	$-0.887557\pi$
$199$		−	9.76046i		−	0.691901i	0.938253	−	0.345950i	$-0.112443\pi$
$200$	3.50985	−	3.50985i	0.248184	−	0.248184i
$201$	17.3613	+	2.97873i	1.22457	+	0.210103i
$202$	−0.206325	+	0.206325i	−0.0145170	+	0.0145170i
$203$	−2.97432	−	2.97432i	−0.208756	−	0.208756i
$204$	−5.15653	−	7.29244i	−0.361029	−	0.510573i
$205$		−	32.1691i		−	2.24679i
$206$	−12.9230	−	12.9230i	−0.900385	−	0.900385i
$207$	−6.67033	+	18.8666i	−0.463620	+	1.31132i
$208$	1.52490	−	3.26721i	0.105733	−	0.226541i
$209$			28.6806i			1.98388i
$210$	−5.38853	−	0.924526i	−0.371844	−	0.0637984i
$211$	−9.59927			−0.660841			−0.330420	−	0.943834i	$-0.607191\pi$
$211$	−9.59927			−0.660841			−0.330420	+	0.943834i	$0.607191\pi$
$212$	−2.87757			−0.197633
$213$	0.935163	−	5.45053i	0.0640763	−	0.373464i
$214$	3.41421	+	3.41421i	0.233391	+	0.233391i
$215$	18.0447	+	18.0447i	1.23064	+	1.23064i
$216$	−2.53553	+	4.53553i	−0.172521	+	0.308604i
$217$	4.82843			0.327775
$218$	17.5178			1.18646
$219$	−3.37441	+	19.6675i	−0.228021	+	1.32901i
$220$			15.1264i			1.01982i
$221$	7.86318	−	16.8475i	0.528935	−	1.13328i
$222$	0.0363157	+	0.0513581i	0.00243735	+	0.00344693i
$223$	16.2467	+	16.2467i	1.08796	+	1.08796i	0.995739	+	0.0922180i	$0.0293957\pi$
$223$	16.2467	+	16.2467i	1.08796	+	1.08796i	0.0922180	+	0.995739i	$0.470604\pi$
$224$		−	1.00000i		−	0.0668153i
$225$	−14.0394	−	4.96368i	−0.935961	−	0.330912i
$226$	8.82843	+	8.82843i	0.587258	+	0.587258i
$227$	1.92802	−	1.92802i	0.127967	−	0.127967i	−0.640223	−	0.768189i	$-0.721158\pi$
$227$	1.92802	−	1.92802i	0.127967	−	0.127967i	0.768189	+	0.640223i	$0.221158\pi$
$228$	1.75295	−	10.2170i	0.116092	−	0.676635i
$229$	−1.19285	+	1.19285i	−0.0788255	+	0.0788255i	−0.745420	−	0.666595i	$-0.767751\pi$
$229$	−1.19285	+	1.19285i	−0.0788255	+	0.0788255i	0.666595	+	0.745420i	$0.267751\pi$
$230$		−	21.0551i		−	1.38833i
$231$	6.77707	−	4.79211i	0.445898	−	0.315298i
$232$	2.97432	−	2.97432i	0.195274	−	0.195274i
$233$	−19.9486			−1.30688			−0.653439	−	0.756979i	$-0.726675\pi$
$233$	−19.9486			−1.30688			−0.653439	+	0.756979i	$0.726675\pi$
$234$	−10.8162	+	0.0960992i	−0.707079	+	0.00628220i
$235$	−18.9392			−1.23546
$236$	−2.48463	+	2.48463i	−0.161736	+	0.161736i
$237$	−3.34379	+	2.36442i	−0.217203	+	0.153586i
$238$		−	5.15653i		−	0.334248i
$239$	−7.48463	+	7.48463i	−0.484141	+	0.484141i	−0.906451	−	0.422311i	$-0.861219\pi$
$239$	−7.48463	+	7.48463i	−0.484141	+	0.484141i	0.422311	+	0.906451i	$0.361219\pi$
$240$	0.924526	−	5.38853i	0.0596779	−	0.347828i
$241$	−3.43549	+	3.43549i	−0.221299	+	0.221299i	−0.809045	−	0.587746i	$-0.800015\pi$
$241$	−3.43549	+	3.43549i	−0.221299	+	0.221299i	0.587746	+	0.809045i	$0.300015\pi$
$242$	−8.46006	−	8.46006i	−0.543833	−	0.543833i
$243$	15.5563	+	1.00000i	0.997940	+	0.0641500i
$244$		−	2.47115i		−	0.158199i
$245$	−2.23200	−	2.23200i	−0.142598	−	0.142598i
$246$	−10.1913	−	14.4126i	−0.649772	−	0.918917i
$247$	20.2802	−	7.37349i	1.29040	−	0.469164i
$248$			4.82843i			0.306605i
$249$	−2.55012	+	14.8632i	−0.161607	+	0.941916i
$250$	−0.114632			−0.00724994
$251$	−8.93425			−0.563925			−0.281962	−	0.959425i	$-0.590985\pi$
$251$	−8.93425			−0.563925			−0.281962	+	0.959425i	$0.590985\pi$
$252$	−2.70711	+	1.29289i	−0.170532	+	0.0814446i
$253$	22.6027	+	22.6027i	1.42102	+	1.42102i
$254$	9.52095	+	9.52095i	0.597397	+	0.597397i
$255$	4.76735	−	27.7861i	0.298543	−	1.74004i
$256$	1.00000			0.0625000
$257$	6.75580			0.421415			0.210707	−	0.977549i	$-0.432423\pi$
$257$	6.75580			0.421415			0.210707	+	0.977549i	$0.432423\pi$
$258$	13.8012	+	2.36791i	0.859224	+	0.147420i
$259$			0.0363157i			0.00225655i
$260$	10.6960	−	3.88886i	0.663339	−	0.241177i
$261$	−11.8973	−	4.20632i	−0.736423	−	0.260365i
$262$	−1.66126	−	1.66126i	−0.102633	−	0.102633i
$263$			5.77551i			0.356133i	0.984018	+	0.178066i	$0.0569842\pi$
$263$			5.77551i			0.356133i	−0.984018	+	0.178066i	$0.943016\pi$
$264$	4.79211	+	6.77707i	0.294934	+	0.417100i
$265$	−6.42276	−	6.42276i	−0.394547	−	0.394547i
$266$	4.23200	−	4.23200i	0.259481	−	0.259481i
$267$	−23.0695	−	3.95810i	−1.41183	−	0.242232i
$268$	−7.19128	+	7.19128i	−0.439277	+	0.439277i
$269$			5.94864i			0.362695i	0.983419	+	0.181348i	$0.0580459\pi$
$269$			5.94864i			0.362695i	−0.983419	+	0.181348i	$0.941954\pi$
$270$	−15.7827	+	4.46401i	−0.960502	+	0.271671i
$271$	−0.843470	+	0.843470i	−0.0512371	+	0.0512371i	−0.732261	−	0.681024i	$-0.761535\pi$
$271$	−0.843470	+	0.843470i	−0.0512371	+	0.0512371i	0.681024	+	0.732261i	$0.261535\pi$
$272$	5.15653			0.312661
$273$	−5.13085	−	3.56011i	−0.310533	−	0.215467i
$274$	−17.1264			−1.03465
$275$	−16.8196	+	16.8196i	−1.01426	+	1.01426i
$276$	−6.67033	−	9.43328i	−0.401507	−	0.567816i
$277$			3.74634i			0.225096i	0.993646	+	0.112548i	$0.0359011\pi$
$277$			3.74634i			0.225096i	−0.993646	+	0.112548i	$0.964099\pi$
$278$	−6.02127	+	6.02127i	−0.361132	+	0.361132i
$279$	13.0711	−	6.24264i	0.782544	−	0.373737i
$280$	2.23200	−	2.23200i	0.133388	−	0.133388i
$281$	10.6340	+	10.6340i	0.634372	+	0.634372i	0.949162	−	0.314789i	$-0.101934\pi$
$281$	10.6340	+	10.6340i	0.634372	+	0.634372i	−0.314789	+	0.949162i	$0.601934\pi$
$282$	−8.48528	+	6.00000i	−0.505291	+	0.357295i
$283$		−	32.1320i		−	1.91005i	−0.296524	−	0.955025i	$-0.595827\pi$
$283$		−	32.1320i		−	1.91005i	0.296524	−	0.955025i	$-0.404173\pi$
$284$	2.25768	+	2.25768i	0.133969	+	0.133969i
$285$	26.7169	−	18.8917i	1.58257	−	1.11905i
$286$	−7.30748	+	15.6569i	−0.432100	+	0.925809i
$287$		−	10.1913i		−	0.601572i
$288$	−1.29289	−	2.70711i	−0.0761845	−	0.159518i
$289$	9.58981			0.564106
$290$	13.2774			0.779675
$291$	−6.24264	−	1.07107i	−0.365950	−	0.0627871i
$292$	−8.14654	−	8.14654i	−0.476740	−	0.476740i
$293$	−12.3613	−	12.3613i	−0.722154	−	0.722154i	0.246889	−	0.969044i	$-0.420592\pi$
$293$	−12.3613	−	12.3613i	−0.722154	−	0.722154i	−0.969044	+	0.246889i	$0.920592\pi$
$294$	−1.70711	−	0.292893i	−0.0995605	−	0.0170819i
$295$	−11.0914			−0.645768
$296$	−0.0363157			−0.00211081
$297$	12.1506	−	21.7348i	0.705047	−	1.26118i
$298$		−	16.5748i		−	0.960150i
$299$	10.1716	−	21.7934i	0.588237	−	1.26035i
$300$	7.01971	−	4.96368i	0.405283	−	0.286578i
$301$	5.71664	+	5.71664i	0.329502	+	0.329502i
$302$			11.1565i			0.641986i
$303$	−0.412650	+	0.291788i	−0.0237061	+	0.0167628i
$304$	4.23200	+	4.23200i	0.242722	+	0.242722i
$305$	5.51563	−	5.51563i	0.315824	−	0.315824i
$306$	−6.66684	−	13.9593i	−0.381118	−	0.797999i
$307$	12.3914	−	12.3914i	0.707213	−	0.707213i	−0.258735	−	0.965948i	$-0.583306\pi$
$307$	12.3914	−	12.3914i	0.707213	−	0.707213i	0.965948	+	0.258735i	$0.0833057\pi$
$308$			4.79211i			0.273056i
$309$	−18.2758	−	25.8459i	−1.03968	−	1.47032i
$310$	−10.7771	+	10.7771i	−0.612096	+	0.612096i
$311$	24.3613			1.38140			0.690701	−	0.723140i	$-0.257302\pi$
$311$	24.3613			1.38140			0.690701	+	0.723140i	$0.257302\pi$
$312$	3.56011	−	5.13085i	0.201551	−	0.290477i
$313$	−20.9462			−1.18395			−0.591974	−	0.805957i	$-0.701651\pi$
$313$	−20.9462			−1.18395			−0.591974	+	0.805957i	$0.701651\pi$
$314$	−13.1293	+	13.1293i	−0.740929	+	0.740929i
$315$	−8.92802	−	3.15653i	−0.503037	−	0.177850i
$316$		−	2.36442i		−	0.133009i
$317$	12.7580	−	12.7580i	0.716561	−	0.716561i	−0.251338	−	0.967899i	$-0.580871\pi$
$317$	12.7580	−	12.7580i	0.716561	−	0.716561i	0.967899	+	0.251338i	$0.0808707\pi$
$318$	−4.91233	−	0.842822i	−0.275470	−	0.0472631i
$319$	−14.2533	+	14.2533i	−0.798030	+	0.798030i
$320$	2.23200	+	2.23200i	0.124773	+	0.124773i
$321$	4.82843	+	6.82843i	0.269497	+	0.381126i
$322$		−	6.67033i		−	0.371723i
$323$	21.8225	+	21.8225i	1.21423	+	1.21423i
$324$	−5.65685	+	7.00000i	−0.314270	+	0.388889i
$325$	16.2174	+	7.56911i	0.899581	+	0.419859i
$326$			10.3835i			0.575088i
$327$	29.9048	+	5.13085i	1.65374	+	0.283737i
$328$	10.1913			0.562719
$329$	−6.00000			−0.330791
$330$	−4.43043	+	25.8225i	−0.243887	+	1.42148i
$331$	−12.8269	−	12.8269i	−0.705028	−	0.705028i	0.260457	−	0.965485i	$-0.416127\pi$
$331$	−12.8269	−	12.8269i	−0.705028	−	0.705028i	−0.965485	+	0.260457i	$0.916127\pi$
$332$	−6.15653	−	6.15653i	−0.337884	−	0.337884i
$333$	0.0469523	+	0.0983105i	0.00257297	+	0.00538738i
$334$	−7.52095			−0.411528
$335$	−32.1019			−1.75392
$336$	0.292893	−	1.70711i	0.0159786	−	0.0931303i
$337$		−	7.72325i		−	0.420712i	−0.977625	−	0.210356i	$-0.932538\pi$
$337$		−	7.72325i		−	0.420712i	0.977625	−	0.210356i	$-0.0674624\pi$
$338$	12.9497	+	1.14195i	0.704373	+	0.0621137i
$339$	12.4853	+	17.6569i	0.678107	+	0.958989i
$340$	11.5094	+	11.5094i	0.624185	+	0.624185i
$341$		−	23.1384i		−	1.25301i
$342$	5.98496	−	16.9280i	0.323629	−	0.915362i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−5.71664	+	5.71664i	−0.308220	+	0.308220i
$345$	6.16690	−	35.9433i	0.332015	−	1.93512i
$346$	9.92958	−	9.92958i	0.533818	−	0.533818i
$347$		−	2.65621i		−	0.142593i	−0.997455	−	0.0712963i	$-0.977286\pi$
$347$		−	2.65621i		−	0.142593i	0.997455	−	0.0712963i	$-0.0227136\pi$
$348$	5.94864	−	4.20632i	0.318881	−	0.225483i
$349$	−18.9130	+	18.9130i	−1.01239	+	1.01239i	−0.0124660	+	0.999922i	$0.503968\pi$
$349$	−18.9130	+	18.9130i	−1.01239	+	1.01239i	−0.999922	+	0.0124660i	$0.996032\pi$
$350$	4.96368			0.265320
$351$	−18.4926	−	3.00395i	−0.987062	−	0.160339i
$352$	−4.79211			−0.255420
$353$	−18.4837	+	18.4837i	−0.983789	+	0.983789i	−0.999871	−	0.0160816i	$-0.994881\pi$
$353$	−18.4837	+	18.4837i	−0.983789	+	0.983789i	0.0160816	+	0.999871i	$0.494881\pi$
$354$	−4.96927	+	3.51380i	−0.264114	+	0.186757i
$355$			10.0783i			0.534901i
$356$	9.55570	−	9.55570i	0.506451	−	0.506451i
$357$	1.51031	−	8.80275i	0.0799342	−	0.465891i
$358$	−1.45053	+	1.45053i	−0.0766629	+	0.0766629i
$359$	−19.1556	−	19.1556i	−1.01099	−	1.01099i	−0.999939	−	0.0110558i	$-0.996481\pi$
$359$	−19.1556	−	19.1556i	−1.01099	−	1.01099i	−0.0110558	−	0.999939i	$-0.503519\pi$
$360$	3.15653	−	8.92802i	0.166364	−	0.470548i
$361$			16.8197i			0.885248i
$362$	10.2774	+	10.2774i	0.540168	+	0.540168i
$363$	−11.9643	−	16.9201i	−0.627965	−	0.888076i
$364$	3.38853	−	1.23200i	0.177607	−	0.0645746i
$365$		−	36.3662i		−	1.90350i
$366$	0.723784	−	4.21853i	0.0378328	−	0.220506i
$367$	21.7343			1.13452			0.567259	−	0.823539i	$-0.308004\pi$
$367$	21.7343			1.13452			0.567259	+	0.823539i	$0.308004\pi$
$368$	6.67033			0.347715
$369$	−13.1762	−	27.5889i	−0.685928	−	1.43622i
$370$	−0.0810568	−	0.0810568i	−0.00421394	−	0.00421394i
$371$	−2.03475	−	2.03475i	−0.105639	−	0.105639i
$372$	−1.41421	+	8.24264i	−0.0733236	+	0.427361i
$373$	−3.19285			−0.165319			−0.0826597	−	0.996578i	$-0.526341\pi$
$373$	−3.19285			−0.165319			−0.0826597	+	0.996578i	$0.526341\pi$
$374$	−24.7107			−1.27776
$375$	−0.195688	−	0.0335748i	−0.0101053	−	0.00173380i
$376$		−	6.00000i		−	0.309426i
$377$	13.7430	+	6.41421i	0.707799	+	0.330349i
$378$	−5.00000	+	1.41421i	−0.257172	+	0.0727393i
$379$	17.5920	+	17.5920i	0.903641	+	0.903641i	0.995749	−	0.0921078i	$-0.0293604\pi$
$379$	17.5920	+	17.5920i	0.903641	+	0.903641i	−0.0921078	+	0.995749i	$0.529360\pi$
$380$			18.8917i			0.969124i
$381$	13.4647	+	19.0419i	0.689815	+	0.975546i
$382$	7.08106	+	7.08106i	0.362298	+	0.362298i
$383$	−16.3870	+	16.3870i	−0.837335	+	0.837335i	−0.988507	−	0.151172i	$-0.951695\pi$
$383$	−16.3870	+	16.3870i	−0.837335	+	0.837335i	0.151172	+	0.988507i	$0.451695\pi$
$384$	1.70711	+	0.292893i	0.0871154	+	0.0149466i
$385$	−10.6960	+	10.6960i	−0.545119	+	0.545119i
$386$		−	13.5763i		−	0.691017i
$387$	22.8666	+	8.08455i	1.16237	+	0.410961i
$388$	2.58579	−	2.58579i	0.131273	−	0.131273i
$389$	−28.0616			−1.42278			−0.711390	−	0.702797i	$-0.751934\pi$
$389$	−28.0616			−1.42278			−0.711390	+	0.702797i	$0.751934\pi$
$390$	19.3983	−	3.50591i	0.982269	−	0.177528i
$391$	34.3958			1.73947
$392$	0.707107	−	0.707107i	0.0357143	−	0.0357143i
$393$	−2.34938	−	3.32252i	−0.118510	−	0.167599i
$394$			6.56360i			0.330669i
$395$	5.27739	−	5.27739i	0.265534	−	0.265534i
$396$	6.19569	+	12.9728i	0.311345	+	0.651906i
$397$	−14.8625	+	14.8625i	−0.745929	+	0.745929i	−0.973712	−	0.227783i	$-0.926852\pi$
$397$	−14.8625	+	14.8625i	−0.745929	+	0.745929i	0.227783	+	0.973712i	$0.426852\pi$
$398$	6.90169	+	6.90169i	0.345950	+	0.345950i
$399$	8.46401	−	5.98496i	0.423730	−	0.299623i
$400$			4.96368i			0.248184i
$401$	10.4862	+	10.4862i	0.523656	+	0.523656i	0.918673	−	0.395018i	$-0.129262\pi$
$401$	10.4862	+	10.4862i	0.523656	+	0.523656i	−0.395018	+	0.918673i	$0.629262\pi$
$402$	−14.3826	+	10.1700i	−0.717337	+	0.507234i
$403$	−16.3613	+	5.94864i	−0.815014	+	0.296323i
$404$		−	0.291788i		−	0.0145170i
$405$	−28.2502	+	2.99791i	−1.40376	+	0.148967i
$406$	4.20632			0.208756
$407$	0.174029			0.00862629
$408$	8.80275	+	1.51031i	0.435801	+	0.0747716i
$409$	7.23667	+	7.23667i	0.357830	+	0.357830i	0.863013	−	0.505182i	$-0.168575\pi$
$409$	7.23667	+	7.23667i	0.357830	+	0.357830i	−0.505182	+	0.863013i	$0.668575\pi$
$410$	22.7470	+	22.7470i	1.12339	+	1.12339i
$411$	−29.2367	−	5.01622i	−1.44214	−	0.247432i
$412$	18.2758			0.900385
$413$	−3.51380			−0.172903
$414$	−8.62403	−	18.0573i	−0.423848	−	0.887468i
$415$		−	27.4828i		−	1.34908i
$416$	1.23200	+	3.38853i	0.0604040	+	0.166137i
$417$	−12.0425	+	8.51537i	−0.589726	+	0.416999i
$418$	−20.2802	−	20.2802i	−0.991939	−	0.991939i
$419$		−	3.69317i		−	0.180423i	−0.995923	−	0.0902116i	$-0.971246\pi$
$419$		−	3.69317i		−	0.180423i	0.995923	−	0.0902116i	$-0.0287543\pi$
$420$	4.46401	−	3.15653i	0.217821	−	0.154023i
$421$	20.3905	+	20.3905i	0.993770	+	0.993770i	0.999981	−	0.00621046i	$-0.00197686\pi$
$421$	20.3905	+	20.3905i	0.993770	+	0.993770i	−0.00621046	+	0.999981i	$0.501977\pi$
$422$	6.78771	−	6.78771i	0.330420	−	0.330420i
$423$	−16.2426	+	7.75736i	−0.789744	+	0.377176i
$424$	2.03475	−	2.03475i	0.0988163	−	0.0988163i
$425$			25.5954i			1.24156i
$426$	3.19285	+	4.51537i	0.154694	+	0.218770i
$427$	1.74737	−	1.74737i	0.0845612	−	0.0845612i
$428$	−4.82843			−0.233391
$429$	−17.0604	+	24.5876i	−0.823685	+	1.18710i
$430$	−25.5191			−1.23064
$431$	−7.55635	+	7.55635i	−0.363977	+	0.363977i	−0.865275	−	0.501298i	$-0.832856\pi$
$431$	−7.55635	+	7.55635i	−0.363977	+	0.363977i	0.501298	+	0.865275i	$0.332856\pi$
$432$	−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	$-0.109209\pi$
$434$	−3.41421	+	3.41421i	−0.163887	+	0.163887i
$435$	22.6659	+	3.88886i	1.08675	+	0.186456i
$436$	−12.3870	+	12.3870i	−0.593228	+	0.593228i
$437$	28.2289	+	28.2289i	1.35037	+	1.35037i
$438$	−11.5209	−	16.2931i	−0.550492	−	0.778514i
$439$		−	39.3066i		−	1.87600i	−0.346635	−	0.938000i	$-0.612676\pi$
$439$		−	39.3066i		−	1.87600i	0.346635	−	0.938000i	$-0.387324\pi$
$440$	−10.6960	−	10.6960i	−0.509912	−	0.509912i
$441$	−2.82843	−	1.00000i	−0.134687	−	0.0476190i
$442$	6.35287	+	17.4731i	0.302175	+	0.831110i
$443$			7.37075i			0.350195i	0.984551	+	0.175097i	$0.0560241\pi$
$443$			7.37075i			0.350195i	−0.984551	+	0.175097i	$0.943976\pi$
$444$	−0.0619948	−	0.0106366i	−0.00294214	−	0.000504792i
$445$	42.6567			2.02212
$446$	−22.9762			−1.08796
$447$	4.85464	−	28.2949i	0.229616	−	1.33830i
$448$	0.707107	+	0.707107i	0.0334077	+	0.0334077i
$449$	9.39255	+	9.39255i	0.443262	+	0.443262i	0.893107	−	0.449845i	$-0.148521\pi$
$449$	9.39255	+	9.39255i	0.443262	+	0.443262i	−0.449845	+	0.893107i	$0.648521\pi$
$450$	13.4372	−	6.41751i	0.633437	−	0.302525i
$451$	−48.8378			−2.29968
$452$	−12.4853			−0.587258
$453$	−3.26767	+	19.0454i	−0.153529	+	0.894830i
$454$			2.72663i			0.127967i
$455$	10.3131	+	4.81338i	0.483484	+	0.225655i
$456$	5.98496	+	8.46401i	0.280271	+	0.396363i
$457$	8.79276	+	8.79276i	0.411308	+	0.411308i	0.882194	−	0.470886i	$-0.156066\pi$
$457$	8.79276	+	8.79276i	0.411308	+	0.411308i	−0.470886	+	0.882194i	$0.656066\pi$
$458$		−	1.68694i		−	0.0788255i
$459$	−7.29244	−	25.7827i	−0.340382	−	1.20343i
$460$	14.8882	+	14.8882i	0.694166	+	0.694166i
$461$	19.2327	−	19.2327i	0.895754	−	0.895754i	−0.0993033	−	0.995057i	$-0.531661\pi$
$461$	19.2327	−	19.2327i	0.895754	−	0.895754i	0.995057	+	0.0993033i	$0.0316614\pi$
$462$	−1.40358	+	8.18065i	−0.0653003	+	0.380598i
$463$	−6.23200	+	6.23200i	−0.289626	+	0.289626i	−0.836932	−	0.547306i	$-0.815653\pi$
$463$	−6.23200	+	6.23200i	−0.289626	+	0.289626i	0.547306	+	0.836932i	$0.315653\pi$
$464$			4.20632i			0.195274i
$465$	−21.5541	+	15.2411i	−0.999549	+	0.706788i
$466$	14.1058	−	14.1058i	0.653439	−	0.653439i
$467$	−0.932952			−0.0431719			−0.0215859	−	0.999767i	$-0.506872\pi$
$467$	−0.932952			−0.0431719			−0.0215859	+	0.999767i	$0.506872\pi$
$468$	7.58027	−	7.71618i	0.350398	−	0.356681i
$469$	−10.1700			−0.469607
$470$	13.3920	−	13.3920i	0.617728	−	0.617728i
$471$	−26.2586	+	18.5676i	−1.20993	+	0.855551i
$472$		−	3.51380i		−	0.161736i
$473$	27.3948	−	27.3948i	1.25961	−	1.25961i
$474$	0.692522	−	4.03632i	0.0318086	−	0.185394i
$475$	−21.0063	+	21.0063i	−0.963837	+	0.963837i
$476$	3.64622	+	3.64622i	0.167124	+	0.167124i
$477$	−8.13901	−	2.87757i	−0.372660	−	0.131755i
$478$		−	10.5849i		−	0.484141i
$479$	25.7489	+	25.7489i	1.17650	+	1.17650i	0.980630	+	0.195867i	$0.0627522\pi$
$479$	25.7489	+	25.7489i	1.17650	+	1.17650i	0.195867	+	0.980630i	$0.437248\pi$
$480$	3.15653	+	4.46401i	0.144075	+	0.203753i
$481$	−0.0447411	−	0.123057i	−0.00204002	−	0.00561092i
$482$		−	4.85851i		−	0.221299i
$483$	1.95370	−	11.3870i	0.0888962	−	0.518125i
$484$	11.9643			0.543833
$485$	11.5430			0.524139
$486$	−11.7071	+	10.2929i	−0.531045	+	0.466895i
$487$	18.4640	+	18.4640i	0.836684	+	0.836684i	0.988421	−	0.151737i	$-0.0484866\pi$
$487$	18.4640	+	18.4640i	0.836684	+	0.836684i	−0.151737	+	0.988421i	$0.548487\pi$
$488$	1.74737	+	1.74737i	0.0790997	+	0.0790997i
$489$	−3.04125	+	17.7257i	−0.137530	+	0.801584i
$490$	3.15653			0.142598
$491$	−1.56608			−0.0706761			−0.0353380	−	0.999375i	$-0.511251\pi$
$491$	−1.56608			−0.0706761			−0.0353380	+	0.999375i	$0.511251\pi$
$492$	17.3976	+	2.98496i	0.784345	+	0.134572i
$493$			21.6900i			0.976870i
$494$	−9.12645	+	19.5541i	−0.410618	+	0.879782i
$495$	−15.1264	+	42.7840i	−0.679883	+	1.92300i
$496$	−3.41421	−	3.41421i	−0.153303	−	0.153303i
$497$			3.19285i			0.143219i
$498$	−8.70665	−	12.3131i	−0.390154	−	0.551761i
$499$	−21.8475	−	21.8475i	−0.978028	−	0.978028i	0.0217358	−	0.999764i	$-0.493081\pi$
$499$	−21.8475	−	21.8475i	−0.978028	−	0.978028i	−0.999764	+	0.0217358i	$0.993081\pi$
$500$	0.0810568	−	0.0810568i	0.00362497	−	0.00362497i
$501$	−12.8391	−	2.20284i	−0.573607	−	0.0984154i
$502$	6.31747	−	6.31747i	0.281962	−	0.281962i
$503$			16.4853i			0.735042i	0.930015	+	0.367521i	$0.119793\pi$
$503$			16.4853i			0.735042i	−0.930015	+	0.367521i	$0.880207\pi$
$504$	1.00000	−	2.82843i	0.0445435	−	0.125988i
$505$	0.651271	−	0.651271i	0.0289812	−	0.0289812i
$506$	−31.9650			−1.42102
$507$	21.7721	+	5.74232i	0.966934	+	0.255025i
$508$	−13.4647			−0.597397
$509$	11.2526	−	11.2526i	0.498764	−	0.498764i	−0.412289	−	0.911053i	$-0.635271\pi$
$509$	11.2526	−	11.2526i	0.498764	−	0.498764i	0.911053	+	0.412289i	$0.135271\pi$
$510$	16.2767	+	23.0188i	0.720746	+	1.01929i
$511$		−	11.5209i		−	0.509657i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	15.1751	−	27.1450i	0.669995	−	1.19848i
$514$	−4.77707	+	4.77707i	−0.210707	+	0.210707i
$515$	40.7917	+	40.7917i	1.79750	+	1.79750i
$516$	−11.4333	+	8.08455i	−0.503322	+	0.355902i
$517$			28.7527i			1.26454i
$518$	−0.0256791	−	0.0256791i	−0.00112827	−	0.00112827i
$519$	19.8592	−	14.0425i	0.871720	−	0.616399i
$520$	−4.81338	+	10.3131i	−0.211081	+	0.452258i
$521$		−	12.5304i		−	0.548967i	−0.961592	−	0.274484i	$-0.911493\pi$
$521$		−	12.5304i		−	0.548967i	0.961592	−	0.274484i	$-0.0885069\pi$
$522$	11.3870	−	5.43833i	0.498394	−	0.238029i
$523$	14.2148			0.621568			0.310784	−	0.950481i	$-0.399408\pi$
$523$	14.2148			0.621568			0.310784	+	0.950481i	$0.399408\pi$
$524$	2.34938			0.102633
$525$	8.47354	+	1.45383i	0.369816	+	0.0634503i
$526$	−4.08390	−	4.08390i	−0.178066	−	0.178066i
$527$	−17.6055	−	17.6055i	−0.766907	−	0.766907i
$528$	−8.18065	−	1.40358i	−0.356017	−	0.0610828i
$529$	21.4933			0.934493
$530$	9.08315			0.394547
$531$	−9.51224	+	4.54297i	−0.412796	+	0.197148i
$532$			5.98496i			0.259481i
$533$	12.5557	+	34.5335i	0.543848	+	1.49581i
$534$	19.1114	−	13.5138i	0.827031	−	0.584799i
$535$	−10.7771	−	10.7771i	−0.465933	−	0.465933i
$536$		−	10.1700i		−	0.439277i
$537$	−2.90106	+	2.05136i	−0.125190	+	0.0885226i
$538$	−4.20632	−	4.20632i	−0.181348	−	0.181348i
$539$	−3.38853	+	3.38853i	−0.145955	+	0.145955i
$540$	8.00349	−	14.3166i	0.344415	−	0.616086i
$541$	−25.4872	+	25.4872i	−1.09578	+	1.09578i	−0.100882	+	0.994898i	$0.532167\pi$
$541$	−25.4872	+	25.4872i	−1.09578	+	1.09578i	−0.994898	+	0.100882i	$0.967833\pi$
$542$		−	1.19285i		−	0.0512371i
$543$	14.5344	+	20.5548i	0.623732	+	0.882090i
$544$	−3.64622	+	3.64622i	−0.156330	+	0.156330i
$545$	−55.2955			−2.36860
$546$	6.14544	−	1.11068i	0.263000	−	0.0475329i
$547$	−31.3407			−1.34003			−0.670015	−	0.742348i	$-0.733712\pi$
$547$	−31.3407			−1.34003			−0.670015	+	0.742348i	$0.733712\pi$
$548$	12.1102	−	12.1102i	0.517323	−	0.517323i
$549$	2.47115	−	6.98948i	0.105466	−	0.298304i
$550$		−	23.7865i		−	1.01426i
$551$	−17.8012	+	17.8012i	−0.758356	+	0.758356i
$552$	11.3870	+	1.95370i	0.484662	+	0.0831548i
$553$	1.67190	−	1.67190i	0.0710963	−	0.0710963i
$554$	−2.64906	−	2.64906i	−0.112548	−	0.112548i
$555$	−0.114632	−	0.162114i	−0.00486584	−	0.00688134i
$556$		−	8.51537i		−	0.361132i
$557$	−18.4198	−	18.4198i	−0.780472	−	0.780472i	0.199439	−	0.979910i	$-0.436088\pi$
$557$	−18.4198	−	18.4198i	−0.780472	−	0.780472i	−0.979910	+	0.199439i	$0.936088\pi$
$558$	−4.82843	+	13.6569i	−0.204404	+	0.578141i
$559$	−26.4139	−	12.3281i	−1.11719	−	0.521423i
$560$			3.15653i			0.133388i
$561$	−42.1837	−	7.23759i	−1.78100	−	0.305571i
$562$	−15.0388			−0.634372
$563$	−22.9944			−0.969099			−0.484550	−	0.874764i	$-0.661016\pi$
$563$	−22.9944			−0.969099			−0.484550	+	0.874764i	$0.661016\pi$
$564$	1.75736	−	10.2426i	0.0739982	−	0.431293i
$565$	−27.8672	−	27.8672i	−1.17238	−	1.17238i
$566$	22.7208	+	22.7208i	0.955025	+	0.955025i
$567$	−8.94975	+	0.949747i	−0.375854	+	0.0398856i
$568$	−3.19285			−0.133969
$569$	44.0664			1.84736			0.923679	−	0.383166i	$-0.125166\pi$
$569$	44.0664			1.84736			0.923679	+	0.383166i	$0.125166\pi$
$570$	−5.53325	+	32.2502i	−0.231762	+	1.35081i
$571$		−	19.0689i		−	0.798007i	−0.916949	−	0.399003i	$-0.869356\pi$
$571$		−	19.0689i		−	0.798007i	0.916949	−	0.399003i	$-0.130644\pi$
$572$	−5.90390	−	16.2382i	−0.246854	−	0.678955i
$573$	10.0141	+	14.1621i	0.418346	+	0.591631i
$574$	7.20632	+	7.20632i	0.300786	+	0.300786i
$575$			33.1094i			1.38076i
$576$	2.82843	+	1.00000i	0.117851	+	0.0416667i
$577$	−22.9201	−	22.9201i	−0.954177	−	0.954177i	0.0448181	−	0.998995i	$-0.485729\pi$
$577$	−22.9201	−	22.9201i	−0.954177	−	0.954177i	−0.998995	+	0.0448181i	$0.985729\pi$
$578$	−6.78102	+	6.78102i	−0.282053	+	0.282053i
$579$	3.97641	−	23.1762i	0.165254	−	0.963172i
$580$	−9.38853	+	9.38853i	−0.389838	+	0.389838i
$581$		−	8.70665i		−	0.361213i
$582$	5.17157	−	3.65685i	0.214369	−	0.151581i
$583$	−9.75076	+	9.75076i	−0.403835	+	0.403835i
$584$	11.5209			0.476740
$585$	34.1417	−	0.303340i	1.41159	−	0.0125416i
$586$	17.4815			0.722154
$587$	10.7264	−	10.7264i	0.442724	−	0.442724i	−0.450202	−	0.892927i	$-0.648648\pi$
$587$	10.7264	−	10.7264i	0.442724	−	0.442724i	0.892927	+	0.450202i	$0.148648\pi$
$588$	1.41421	−	1.00000i	0.0583212	−	0.0412393i
$589$		−	28.8979i		−	1.19072i
$590$	7.84282	−	7.84282i	0.322884	−	0.322884i
$591$	−1.92243	+	11.2048i	−0.0790783	+	0.460902i
$592$	0.0256791	−	0.0256791i	0.00105540	−	0.00105540i
$593$	−28.7454	−	28.7454i	−1.18043	−	1.18043i	−0.979632	−	0.200801i	$-0.935646\pi$
$593$	−28.7454	−	28.7454i	−1.18043	−	1.18043i	−0.200801	−	0.979632i	$-0.564354\pi$
$594$	6.77707	+	23.9606i	0.278067	+	0.983114i
$595$			16.2767i			0.667281i
$596$	11.7201	+	11.7201i	0.480075	+	0.480075i
$597$	9.76046	+	13.8034i	0.399469	+	0.564935i
$598$	8.21788	+	22.6027i	0.336054	+	0.924291i
$599$			17.6396i			0.720735i	0.932811	+	0.360367i	$0.117349\pi$
$599$			17.6396i			0.720735i	−0.932811	+	0.360367i	$0.882651\pi$
$600$	−1.45383	+	8.47354i	−0.0593523	+	0.345931i
$601$	5.17287			0.211006			0.105503	−	0.994419i	$-0.466355\pi$
$601$	5.17287			0.211006			0.105503	+	0.994419i	$0.466355\pi$
$602$	−8.08455			−0.329502
$603$	−27.5313	+	13.1487i	−1.12116	+	0.535458i
$604$	−7.88886	−	7.88886i	−0.320993	−	0.320993i
$605$	26.7044	+	26.7044i	1.08569	+	1.08569i
$606$	0.0854626	−	0.498113i	0.00347168	−	0.0202344i
$607$	40.2727			1.63462			0.817309	−	0.576199i	$-0.195465\pi$
$607$	40.2727			1.63462			0.817309	+	0.576199i	$0.195465\pi$
$608$	−5.98496			−0.242722
$609$	7.18065	+	1.23200i	0.290974	+	0.0499233i
$610$			7.80028i			0.315824i
$611$	20.3312	−	7.39202i	0.822513	−	0.299049i
$612$	14.5849	+	5.15653i	0.589558	+	0.208440i
$613$	−28.3087	−	28.3087i	−1.14338	−	1.14338i	−0.987828	−	0.155547i	$-0.950286\pi$
$613$	−28.3087	−	28.3087i	−1.14338	−	1.14338i	−0.155547	−	0.987828i	$-0.549714\pi$
$614$			17.5241i			0.707213i
$615$	32.1691	+	45.4940i	1.29718	+	1.83449i
$616$	−3.38853	−	3.38853i	−0.136528	−	0.136528i
$617$	28.8059	−	28.8059i	1.15968	−	1.15968i	0.175136	−	0.984544i	$-0.443964\pi$
$617$	28.8059	−	28.8059i	1.15968	−	1.15968i	0.984544	−	0.175136i	$-0.0560364\pi$
$618$	31.1988	+	5.35287i	1.25500	+	0.215324i
$619$	10.9608	−	10.9608i	0.440553	−	0.440553i	−0.451645	−	0.892198i	$-0.649162\pi$
$619$	10.9608	−	10.9608i	0.440553	−	0.440553i	0.892198	+	0.451645i	$0.149162\pi$
$620$		−	15.2411i		−	0.612096i
$621$	−9.43328	−	33.3517i	−0.378544	−	1.33836i
$622$	−17.2260	+	17.2260i	−0.690701	+	0.690701i
$623$	13.5138			0.541419
$624$	1.11068	+	6.14544i	0.0444629	+	0.246014i
$625$	25.1803			1.00721
$626$	14.8112	−	14.8112i	0.591974	−	0.591974i
$627$	−28.6806	−	40.5605i	−1.14539	−	1.61983i
$628$		−	18.5676i		−	0.740929i
$629$	0.132415	−	0.132415i	0.00527973	−	0.00527973i
$630$	8.54506	−	4.08106i	0.340444	−	0.162593i
$631$	10.9064	−	10.9064i	0.434175	−	0.434175i	−0.455871	−	0.890046i	$-0.650672\pi$
$631$	10.9064	−	10.9064i	0.434175	−	0.434175i	0.890046	+	0.455871i	$0.150672\pi$
$632$	1.67190	+	1.67190i	0.0665045	+	0.0665045i
$633$	13.5754	−	9.59927i	0.539574	−	0.381537i
$634$			18.0425i			0.716561i
$635$	−30.0532	−	30.0532i	−1.19262	−	1.19262i
$636$	4.06950	−	2.87757i	0.161366	−	0.114103i
$637$	3.26721	+	1.52490i	0.129452	+	0.0604186i
$638$		−	20.1572i		−	0.798030i
$639$	4.12801	+	8.64338i	0.163302	+	0.341927i
$640$	−3.15653			−0.124773
$641$	19.7733			0.780998			0.390499	−	0.920603i	$-0.372302\pi$
$641$	19.7733			0.780998			0.390499	+	0.920603i	$0.372302\pi$
$642$	−8.24264	−	1.41421i	−0.325311	−	0.0558146i
$643$	25.4731	+	25.4731i	1.00456	+	1.00456i	0.999990	+	0.00457070i	$0.00145491\pi$
$643$	25.4731	+	25.4731i	1.00456	+	1.00456i	0.00457070	+	0.999990i	$0.498545\pi$
$644$	4.71664	+	4.71664i	0.185862	+	0.185862i
$645$	−43.5639	−	7.47438i	−1.71533	−	0.294303i
$646$	−30.8616			−1.21423
$647$	3.91856			0.154054			0.0770272	−	0.997029i	$-0.475457\pi$
$647$	3.91856			0.154054			0.0770272	+	0.997029i	$0.475457\pi$
$648$	−0.949747	−	8.94975i	−0.0373096	−	0.351579i
$649$			16.8385i			0.660970i
$650$	−16.8196	+	6.11528i	−0.659720	+	0.239861i
$651$	−6.82843	+	4.82843i	−0.267627	+	0.189241i
$652$	−7.34223	−	7.34223i	−0.287544	−	0.287544i
$653$			2.45301i			0.0959937i	0.998847	+	0.0479968i	$0.0152837\pi$
$653$			2.45301i			0.0959937i	−0.998847	+	0.0479968i	$0.984716\pi$
$654$	−24.7739	+	17.5178i	−0.968738	+	0.685001i
$655$	5.24382	+	5.24382i	0.204893	+	0.204893i
$656$	−7.20632	+	7.20632i	−0.281360	+	0.281360i
$657$	−14.8954	−	31.1884i	−0.581123	−	1.21678i
$658$	4.24264	−	4.24264i	0.165395	−	0.165395i
$659$		−	21.5272i		−	0.838580i	−0.907852	−	0.419290i	$-0.862279\pi$
$659$		−	21.5272i		−	0.838580i	0.907852	−	0.419290i	$-0.137721\pi$
$660$	−15.1264	−	21.3920i	−0.588796	−	0.832683i
$661$	10.4361	−	10.4361i	0.405919	−	0.405919i	−0.474394	−	0.880313i	$-0.657333\pi$
$661$	10.4361	−	10.4361i	0.405919	−	0.405919i	0.880313	+	0.474394i	$0.157333\pi$
$662$	18.1399			0.705028
$663$	5.72727	+	31.6891i	0.222429	+	1.23070i
$664$	8.70665			0.337884
$665$	−13.3584	+	13.3584i	−0.518018	+	0.518018i
$666$	−0.102716	−	0.0363157i	−0.00398018	−	0.00140720i
$667$			28.0576i			1.08639i
$668$	5.31811	−	5.31811i	0.205764	−	0.205764i
$669$	−39.2229	−	6.72959i	−1.51645	−	0.260181i
$670$	22.6995	−	22.6995i	0.876958	−	0.876958i
$671$	−8.37359	−	8.37359i	−0.323259	−	0.323259i
$672$	1.00000	+	1.41421i	0.0385758	+	0.0545545i
$673$			12.8064i			0.493651i	0.969060	+	0.246825i	$0.0793874\pi$
$673$			12.8064i			0.493651i	−0.969060	+	0.246825i	$0.920613\pi$
$674$	5.46117	+	5.46117i	0.210356	+	0.210356i
$675$	24.8184	−	7.01971i	0.955261	−	0.270189i
$676$	−9.96433	+	8.34938i	−0.383244	+	0.321130i
$677$		−	5.56424i		−	0.213851i	−0.994267	−	0.106926i	$-0.965899\pi$
$677$		−	5.56424i		−	0.213851i	0.994267	−	0.106926i	$-0.0341007\pi$
$678$	−21.3137	−	3.65685i	−0.818548	−	0.140441i
$679$	3.65685			0.140337
$680$	−16.2767			−0.624185
$681$	−0.798610	+	4.65464i	−0.0306028	+	0.178366i
$682$	16.3613	+	16.3613i	0.626506	+	0.626506i
$683$	−22.6991	−	22.6991i	−0.868558	−	0.868558i	0.123755	−	0.992313i	$-0.460506\pi$
$683$	−22.6991	−	22.6991i	−0.868558	−	0.868558i	−0.992313	+	0.123755i	$0.960506\pi$
$684$	7.73791	+	16.2019i	0.295866	+	0.619496i
$685$	54.0601			2.06553
$686$	1.00000			0.0381802
$687$	0.494093	−	2.87979i	0.0188508	−	0.109871i
$688$		−	8.08455i		−	0.308220i
$689$	9.40165	+	4.38800i	0.358174	+	0.167170i
$690$	21.0551	+	29.7764i	0.801554	+	1.13357i
$691$	−3.18274	−	3.18274i	−0.121077	−	0.121077i	0.643972	−	0.765049i	$-0.277285\pi$
$691$	−3.18274	−	3.18274i	−0.121077	−	0.121077i	−0.765049	+	0.643972i	$0.777285\pi$
$692$			14.0425i			0.533818i
$693$	−4.79211	+	13.5541i	−0.182037	+	0.514879i
$694$	1.87822	+	1.87822i	0.0712963	+	0.0712963i
$695$	19.0063	−	19.0063i	0.720951	−	0.720951i
$696$	−1.23200	+	7.18065i	−0.0466990	+	0.272182i
$697$	−37.1596	+	37.1596i	−1.40752	+	1.40752i
$698$		−	26.7470i		−	1.01239i
$699$	28.2116	−	19.9486i	1.06706	−	0.754527i
$700$	−3.50985	+	3.50985i	−0.132660	+	0.132660i
$701$	−2.11061			−0.0797167			−0.0398584	−	0.999205i	$-0.512691\pi$
$701$	−2.11061			−0.0797167			−0.0398584	+	0.999205i	$0.512691\pi$
$702$	15.2004	−	10.9521i	0.573700	−	0.413362i
$703$	0.217348			0.00819743
$704$	3.38853	−	3.38853i	0.127710	−	0.127710i
$705$	26.7840	−	18.9392i	1.00875	−	0.713291i
$706$		−	26.1399i		−	0.983789i
$707$	0.206325	−	0.206325i	0.00775965	−	0.00775965i
$708$	1.02917	−	5.99844i	0.0386785	−	0.225435i
$709$	27.5250	−	27.5250i	1.03372	−	1.03372i	0.0343107	−	0.999411i	$-0.489076\pi$
$709$	27.5250	−	27.5250i	1.03372	−	1.03372i	0.999411	−	0.0343107i	$-0.0109236\pi$
$710$	−7.12645	−	7.12645i	−0.267451	−	0.267451i
$711$	2.36442	−	6.68759i	0.0886726	−	0.250804i
$712$			13.5138i			0.506451i
$713$	−22.7739	−	22.7739i	−0.852891	−	0.852891i
$714$	5.15653	+	7.29244i	0.192978	+	0.272913i
$715$	23.0663	−	49.4213i	0.862630	−	1.84825i
$716$		−	2.05136i		−	0.0766629i
$717$	3.10024	−	18.0695i	0.115780	−	0.674818i
$718$	27.0901			1.01099
$719$	−47.6706			−1.77781			−0.888906	−	0.458089i	$-0.848534\pi$
$719$	−47.6706			−1.77781			−0.888906	+	0.458089i	$0.848534\pi$
$720$	4.08106	+	8.54506i	0.152092	+	0.318456i
$721$	12.9230	+	12.9230i	0.481276	+	0.481276i
$722$	−11.8933	−	11.8933i	−0.442624	−	0.442624i
$723$	1.42303	−	8.29400i	0.0529229	−	0.308457i
$724$	−14.5344			−0.540168
$725$	−20.8789			−0.775422
$726$	20.4244	+	3.50427i	0.758020	+	0.130056i
$727$			37.3478i			1.38515i	0.721344	+	0.692577i	$0.243525\pi$
$727$			37.3478i			1.38515i	−0.721344	+	0.692577i	$0.756475\pi$
$728$	−1.52490	+	3.26721i	−0.0565165	+	0.121091i
$729$	−23.0000	+	14.1421i	−0.851852	+	0.523783i
$730$	25.7148	+	25.7148i	0.951748	+	0.951748i
$731$		−	41.6882i		−	1.54189i
$732$	2.47115	+	3.49474i	0.0913365	+	0.129169i
$733$	−24.1834	−	24.1834i	−0.893234	−	0.893234i	0.101592	−	0.994826i	$-0.467606\pi$
$733$	−24.1834	−	24.1834i	−0.893234	−	0.893234i	−0.994826	+	0.101592i	$0.967606\pi$
$734$	−15.3684	+	15.3684i	−0.567259	+	0.567259i
$735$	5.38853	+	0.924526i	0.198759	+	0.0341017i
$736$	−4.71664	+	4.71664i	−0.173858	+	0.173858i
$737$			48.7358i			1.79521i
$738$	28.8253	+	10.1913i	1.06107	+	0.375146i
$739$	4.86811	−	4.86811i	0.179076	−	0.179076i	−0.611877	−	0.790953i	$-0.709585\pi$
$739$	4.86811	−	4.86811i	0.179076	−	0.179076i	0.790953	+	0.611877i	$0.209585\pi$
$740$	0.114632			0.00421394
$741$	−21.3071	+	30.7079i	−0.782736	+	1.12808i
$742$	2.87757			0.105639
$743$	15.2292	−	15.2292i	0.558704	−	0.558704i	−0.370235	−	0.928938i	$-0.620723\pi$
$743$	15.2292	−	15.2292i	0.558704	−	0.558704i	0.928938	+	0.370235i	$0.120723\pi$
$744$	−4.82843	−	6.82843i	−0.177019	−	0.250342i
$745$			52.3187i			1.91681i
$746$	2.25768	−	2.25768i	0.0826597	−	0.0826597i
$747$	−11.2568	−	23.5698i	−0.411864	−	0.862375i
$748$	17.4731	−	17.4731i	0.638879	−	0.638879i
$749$	−3.41421	−	3.41421i	−0.124753	−	0.124753i
$750$	0.162114	−	0.114632i	0.00591955	−	0.00418575i
$751$		−	18.3857i		−	0.670903i	−0.942057	−	0.335452i	$-0.891111\pi$
$751$		−	18.3857i		−	0.670903i	0.942057	−	0.335452i	$-0.108889\pi$
$752$	4.24264	+	4.24264i	0.154713	+	0.154713i
$753$	12.6349	−	8.93425i	0.460443	−	0.325582i
$754$	−14.2533	+	5.18221i	−0.519074	+	0.188725i
$755$		−	35.2159i		−	1.28164i
$756$	2.53553	−	4.53553i	0.0922165	−	0.164956i
$757$	−30.2116			−1.09806			−0.549030	−	0.835802i	$-0.685003\pi$
$757$	−30.2116			−1.09806			−0.549030	+	0.835802i	$0.685003\pi$
$758$	−24.8789			−0.903641
$759$	−54.5676	−	9.36233i	−1.98068	−	0.339831i
$760$	−13.3584	−	13.3584i	−0.484562	−	0.484562i
$761$	8.02284	+	8.02284i	0.290828	+	0.290828i	0.837407	−	0.546580i	$-0.184070\pi$
$761$	8.02284	+	8.02284i	0.290828	+	0.290828i	−0.546580	+	0.837407i	$0.684070\pi$
$762$	−22.9856	−	3.94371i	−0.832681	−	0.142865i
$763$	−17.5178			−0.634188
$764$	−10.0141			−0.362298
$765$	21.0441	+	44.0629i	0.760851	+	1.59310i
$766$		−	23.1747i		−	0.837335i
$767$	11.9066	−	4.32902i	0.429924	−	0.156312i
$768$	−1.41421	+	1.00000i	−0.0510310	+	0.0360844i
$769$	−7.07326	−	7.07326i	−0.255068	−	0.255068i	0.567976	−	0.823045i	$-0.307726\pi$
$769$	−7.07326	−	7.07326i	−0.255068	−	0.255068i	−0.823045	+	0.567976i	$0.807726\pi$
$770$		−	15.1264i		−	0.545119i
$771$	−9.55414	+	6.75580i	−0.344084	+	0.243304i
$772$	9.59991	+	9.59991i	0.345508	+	0.345508i
$773$	−32.8081	+	32.8081i	−1.18002	+	1.18002i	−0.200287	+	0.979737i	$0.564187\pi$
$773$	−32.8081	+	32.8081i	−1.18002	+	1.18002i	−0.979737	+	0.200287i	$0.935813\pi$
$774$	−21.8857	+	10.4525i	−0.786666	+	0.375706i
$775$	16.9471	−	16.9471i	0.608757	−	0.608757i
$776$			3.65685i			0.131273i
$777$	−0.0363157	−	0.0513581i	−0.00130282	−	0.00184246i
$778$	19.8426	−	19.8426i	0.711390	−	0.711390i
$779$	−60.9944			−2.18535
$780$	−11.2376	+	16.1957i	−0.402370	+	0.579899i
$781$	15.3005			0.547494
$782$	−24.3215	+	24.3215i	−0.869735	+	0.869735i
$783$	21.0316	−	5.94864i	0.751609	−	0.212587i
$784$			1.00000i			0.0357143i
$785$	41.4430	−	41.4430i	1.47916	−	1.47916i
$786$	4.01064	+	0.688116i	0.143055	+	0.0245443i
$787$	19.9270	−	19.9270i	0.710320	−	0.710320i	−0.256282	−	0.966602i	$-0.582498\pi$
$787$	19.9270	−	19.9270i	0.710320	−	0.710320i	0.966602	+	0.256282i	$0.0824975\pi$
$788$	−4.64116	−	4.64116i	−0.165335	−	0.165335i
$789$	−5.77551	−	8.16780i	−0.205613	−	0.290781i
$790$			7.46336i			0.265534i
$791$	−8.82843	−	8.82843i	−0.313903	−	0.313903i
$792$	−13.5541	−	4.79211i	−0.481625	−	0.170280i
$793$	−3.76826	+	8.07379i	−0.133815	+	0.286709i
$794$		−	21.0188i		−	0.745929i
$795$	15.5059	+	2.66039i	0.549938	+	0.0943544i
$796$	−9.76046			−0.345950
$797$	−8.12086			−0.287656			−0.143828	−	0.989603i	$-0.545941\pi$
$797$	−8.12086			−0.287656			−0.143828	+	0.989603i	$0.545941\pi$
$798$	−1.75295	+	10.2170i	−0.0620539	+	0.361677i
$799$	21.8773	+	21.8773i	0.773963	+	0.773963i
$800$	−3.50985	−	3.50985i	−0.124092	−	0.124092i
$801$	36.5833	−	17.4719i	1.29261	−	0.617339i
$802$	−14.8297			−0.523656
$803$	−55.2097			−1.94831
$804$	2.97873	−	17.3613i	0.105052	−	0.612286i
$805$			21.0551i			0.742095i
$806$	7.36286	−	15.7755i	0.259346	−	0.555668i
$807$	−5.94864	−	8.41265i	−0.209402	−	0.296139i
$808$	0.206325	+	0.206325i	0.00725849	+	0.00725849i
$809$		−	13.7365i		−	0.482948i	−0.970407	−	0.241474i	$-0.922369\pi$
$809$		−	13.7365i		−	0.482948i	0.970407	−	0.241474i	$-0.0776309\pi$
$810$	17.8560	−	22.0957i	0.627397	−	0.776364i
$811$	−28.7767	−	28.7767i	−1.01049	−	1.01049i	−0.999944	−	0.0105416i	$-0.996644\pi$
$811$	−28.7767	−	28.7767i	−1.01049	−	1.01049i	−0.0105416	−	0.999944i	$-0.503356\pi$
$812$	−2.97432	+	2.97432i	−0.104378	+	0.104378i
$813$	0.349377	−	2.03632i	0.0122532	−	0.0714167i
$814$	−0.123057	+	0.123057i	−0.00431315	+	0.00431315i
$815$		−	32.7758i		−	1.14809i
$816$	−7.29244	+	5.15653i	−0.255286	+	0.180515i
$817$	34.2138	−	34.2138i	1.19699	−	1.19699i
$818$	−10.2342			−0.357830
$819$	10.8162	−	0.0960992i	0.377950	−	0.00335798i
$820$	−32.1691			−1.12339
$821$	1.49566	−	1.49566i	0.0521988	−	0.0521988i	−0.680526	−	0.732724i	$-0.738248\pi$
$821$	1.49566	−	1.49566i	0.0521988	−	0.0521988i	0.732724	+	0.680526i	$0.238248\pi$
$822$	24.2205	−	17.1264i	0.844785	−	0.597353i
$823$		−	46.5104i		−	1.62125i	−0.585565	−	0.810625i	$-0.699127\pi$
$823$		−	46.5104i		−	1.62125i	0.585565	−	0.810625i	$-0.300873\pi$
$824$	−12.9230	+	12.9230i	−0.450193	+	0.450193i
$825$	6.96691	−	40.6061i	0.242557	−	1.41372i
$826$	2.48463	−	2.48463i	0.0864515	−	0.0864515i
$827$	−3.72157	−	3.72157i	−0.129412	−	0.129412i	0.639434	−	0.768846i	$-0.279169\pi$
$827$	−3.72157	−	3.72157i	−0.129412	−	0.129412i	−0.768846	+	0.639434i	$0.779169\pi$
$828$	18.8666	+	6.67033i	0.655658	+	0.231810i
$829$			28.7523i			0.998609i	0.866427	+	0.499304i	$0.166411\pi$
$829$			28.7523i			0.998609i	−0.866427	+	0.499304i	$0.833589\pi$
$830$	19.4333	+	19.4333i	0.674539	+	0.674539i
$831$	−3.74634	−	5.29812i	−0.129959	−	0.183790i
$832$	−3.26721	−	1.52490i	−0.113270	−	0.0528663i
$833$			5.15653i			0.178663i
$834$	2.49409	−	14.5366i	0.0863634	−	0.503363i
$835$	23.7401			0.821560
$836$	28.6806			0.991939
$837$	−12.2426	+	21.8995i	−0.423168	+	0.756957i
$838$	2.61147	+	2.61147i	0.0902116	+	0.0902116i
$839$	10.8049	+	10.8049i	0.373028	+	0.373028i	0.868579	−	0.495551i	$-0.165034\pi$
$839$	10.8049	+	10.8049i	0.373028	+	0.373028i	−0.495551	+	0.868579i	$0.665034\pi$
$840$	−0.924526	+	5.38853i	−0.0318992	+	0.185922i
$841$	11.3068			0.389891
$842$	−28.8365			−0.993770
$843$	−25.6728	−	4.40475i	−0.884218	−	0.151708i
$844$			9.59927i			0.330420i
$845$	−40.8763	−	3.60459i	−1.40619	−	0.124002i
$846$	6.00000	−	16.9706i	0.206284	−	0.583460i
$847$	8.46006	+	8.46006i	0.290691	+	0.290691i
$848$			2.87757i			0.0988163i
$849$	32.1320	+	45.4416i	1.10277	+	1.55955i
$850$	−18.0987	−	18.0987i	−0.620779	−	0.620779i
$851$	0.171288	−	0.171288i	0.00587168	−	0.00587168i
$852$	−5.45053	−	0.935163i	−0.186732	−	0.0320382i
$853$	11.8751	−	11.8751i	0.406595	−	0.406595i	−0.473954	−	0.880550i	$-0.657174\pi$
$853$	11.8751	−	11.8751i	0.406595	−	0.406595i	0.880550	+	0.473954i	$0.157174\pi$
$854$			2.47115i			0.0845612i
$855$	−18.8917	+	53.4338i	−0.646083	+	1.82740i
$856$	3.41421	−	3.41421i	0.116695	−	0.116695i
$857$	20.3032			0.693544			0.346772	−	0.937950i	$-0.387278\pi$
$857$	20.3032			0.693544			0.346772	+	0.937950i	$0.387278\pi$
$858$	−5.32252	−	29.4496i	−0.181708	−	1.00539i
$859$	1.71625			0.0585577			0.0292789	−	0.999571i	$-0.490679\pi$
$859$	1.71625			0.0585577			0.0292789	+	0.999571i	$0.490679\pi$
$860$	18.0447	−	18.0447i	0.615321	−	0.615321i
$861$	10.1913	+	14.4126i	0.347318	+	0.491182i
$862$		−	10.6863i		−	0.363977i
$863$	12.8939	−	12.8939i	0.438914	−	0.438914i	−0.452733	−	0.891646i	$-0.649551\pi$
$863$	12.8939	−	12.8939i	0.438914	−	0.438914i	0.891646	+	0.452733i	$0.149551\pi$
$864$	4.53553	+	2.53553i	0.154302	+	0.0862606i
$865$	−31.3430	+	31.3430i	−1.06569	+	1.06569i
$866$	9.89949	+	9.89949i	0.336399	+	0.336399i
$867$	−13.5620	+	9.58981i	−0.460591	+	0.325687i
$868$		−	4.82843i		−	0.163887i
$869$	−8.01192	−	8.01192i	−0.271786	−	0.271786i
$870$	−18.7771	+	13.2774i	−0.636602	+	0.450146i
$871$	34.4614	−	12.5295i	1.16768	−	0.424546i
$872$		−	17.5178i		−	0.593228i
$873$	9.89949	−	4.72792i	0.335047	−	0.160016i
$874$	−39.9217			−1.35037
$875$	0.114632			0.00387526
$876$	19.6675	+	3.37441i	0.664503	+	0.114011i
$877$	7.74542	+	7.74542i	0.261544	+	0.261544i	0.825681	−	0.564137i	$-0.190791\pi$
$877$	7.74542	+	7.74542i	0.261544	+	0.261544i	−0.564137	+	0.825681i	$0.690791\pi$
$878$	27.7939	+	27.7939i	0.938000	+	0.938000i
$879$	29.8428	+	5.12021i	1.00657	+	0.172701i
$880$	15.1264			0.509912
$881$	−40.1553			−1.35287			−0.676434	−	0.736503i	$-0.736476\pi$
$881$	−40.1553			−1.35287			−0.676434	+	0.736503i	$0.736476\pi$
$882$	2.70711	−	1.29289i	0.0911530	−	0.0435340i
$883$		−	33.9136i		−	1.14128i	−0.821199	−	0.570642i	$-0.806694\pi$
$883$		−	33.9136i		−	1.14128i	0.821199	−	0.570642i	$-0.193306\pi$
$884$	−16.8475	−	7.86318i	−0.566642	−	0.264467i
$885$	15.6856	−	11.0914i	0.527267	−	0.372834i
$886$	−5.21191	−	5.21191i	−0.175097	−	0.175097i
$887$			24.5348i			0.823798i	0.911229	+	0.411899i	$0.135134\pi$
$887$			24.5348i			0.823798i	−0.911229	+	0.411899i	$0.864866\pi$
$888$	0.0513581	−	0.0363157i	0.00172347	−	0.00121867i
$889$	−9.52095	−	9.52095i	−0.319322	−	0.319322i
$890$	−30.1629	+	30.1629i	−1.01106	+	1.01106i
$891$	4.55130	+	42.8882i	0.152474	+	1.43681i
$892$	16.2467	−	16.2467i	0.543978	−	0.543978i
$893$			35.9097i			1.20167i
$894$	16.5748	+	23.4403i	0.554343	+	0.783959i
$895$	4.57864	−	4.57864i	0.153047	−	0.153047i
$896$	−1.00000			−0.0334077
$897$	7.40863	+	40.9921i	0.247367	+	1.36869i
$898$	−13.2831			−0.443262
$899$	14.3613	−	14.3613i	0.478976	−	0.478976i
$900$	−4.96368	+	14.0394i	−0.165456	+	0.467981i
$901$			14.8383i			0.494335i
$902$	34.5335	−	34.5335i	1.14984	−	1.14984i
$903$	−13.8012	−	2.36791i	−0.459275	−	0.0787991i
$904$	8.82843	−	8.82843i	0.293629	−	0.293629i
$905$	−32.4409	−	32.4409i	−1.07837	−	1.07837i
$906$	−11.1565	−	15.7777i	−0.370651	−	0.524180i
$907$		−	13.8986i		−	0.461495i	−0.973014	−	0.230747i	$-0.925883\pi$
$907$		−	13.8986i		−	0.461495i	0.973014	−	0.230747i	$-0.0741171\pi$
$908$	−1.92802	−	1.92802i	−0.0639835	−	0.0639835i
$909$	0.291788	−	0.825300i	0.00967798	−	0.0273735i
$910$	−10.6960	+	3.88886i	−0.354569	+	0.128914i
$911$			25.8388i			0.856077i	0.903761	+	0.428038i	$0.140795\pi$
$911$			25.8388i			0.856077i	−0.903761	+	0.428038i	$0.859205\pi$
$912$	−10.2170	−	1.75295i	−0.338317	−	0.0580461i
$913$	−41.7232			−1.38084
$914$	−12.4348			−0.411308
$915$	−2.28465	+	13.3159i	−0.0755281	+	0.440210i
$916$	1.19285	+	1.19285i	0.0394127	+	0.0394127i
$917$	1.66126	+	1.66126i	0.0548596	+	0.0548596i
$918$	23.3876	+	13.0746i	0.771906	+	0.431525i
$919$	44.2498			1.45967			0.729833	−	0.683626i	$-0.239598\pi$
$919$	44.2498			1.45967			0.729833	+	0.683626i	$0.239598\pi$
$920$	−21.0551			−0.694166
$921$	−5.13268	+	29.9154i	−0.169127	+	0.985747i
$922$			27.1991i			0.895754i
$923$	−3.93360	−	10.8191i	−0.129476	−	0.356114i
$924$	−4.79211	−	6.77707i	−0.157649	−	0.222949i
$925$	0.127463	+	0.127463i	0.00419095	+	0.00419095i
$926$		−	8.81338i		−	0.289626i
$927$	51.6919	+	18.2758i	1.69778	+	0.600257i
$928$	−2.97432	−	2.97432i	−0.0976369	−	0.0976369i
$929$	−4.05990	+	4.05990i	−0.133201	+	0.133201i	−0.770564	−	0.637363i	$-0.780025\pi$
$929$	−4.05990	+	4.05990i	−0.133201	+	0.133201i	0.637363	+	0.770564i	$0.280025\pi$
$930$	4.46401	−	26.0181i	0.146381	−	0.853169i
$931$	−4.23200	+	4.23200i	−0.138698	+	0.138698i
$932$			19.9486i			0.653439i
$933$	−34.4521	+	24.3613i	−1.12791	+	0.797553i
$934$	0.659697	−	0.659697i	0.0215859	−	0.0215859i
$935$	78.0000			2.55087
$936$	0.0960992	+	10.8162i	0.00314110	+	0.353539i
$937$	−46.3976			−1.51574			−0.757872	−	0.652404i	$-0.773761\pi$
$937$	−46.3976			−1.51574			−0.757872	+	0.652404i	$0.773761\pi$
$938$	7.19128	−	7.19128i	0.234804	−	0.234804i
$939$	29.6223	−	20.9462i	0.966689	−	0.683552i
$940$			18.9392i			0.617728i
$941$	−7.70821	+	7.70821i	−0.251281	+	0.251281i	−0.821496	−	0.570215i	$-0.806860\pi$
$941$	−7.70821	+	7.70821i	−0.251281	+	0.251281i	0.570215	+	0.821496i	$0.306860\pi$
$942$	5.43833	−	31.6969i	0.177190	−	1.03274i
$943$	−48.0686	+	48.0686i	−1.56533	+	1.56533i
$944$	2.48463	+	2.48463i	0.0808679	+	0.0808679i
$945$	15.7827	−	4.46401i	0.513410	−	0.145214i
$946$			38.7420i			1.25961i
$947$	20.7705	+	20.7705i	0.674949	+	0.674949i	0.958853	−	0.283904i	$-0.0916296\pi$
$947$	20.7705	+	20.7705i	0.674949	+	0.674949i	−0.283904	+	0.958853i	$0.591630\pi$
$948$	2.36442	+	3.34379i	0.0767928	+	0.108601i
$949$	14.1939	+	39.0391i	0.460752	+	1.26726i
$950$		−	29.7074i		−	0.963837i
$951$	−5.28454	+	30.8006i	−0.171363	+	0.998776i
$952$	−5.15653			−0.167124
$953$	−41.5409			−1.34564			−0.672821	−	0.739805i	$-0.734918\pi$
$953$	−41.5409			−1.34564			−0.672821	+	0.739805i	$0.734918\pi$
$954$	7.78990	−	3.72040i	0.252207	−	0.120452i
$955$	−22.3516	−	22.3516i	−0.723280	−	0.723280i
$956$	7.48463	+	7.48463i	0.242070	+	0.242070i
$957$	5.90390	−	34.4105i	0.190846	−	1.11233i
$958$	−36.4145			−1.17650
$959$	17.1264			0.553042
$960$	−5.38853	−	0.924526i	−0.173914	−	0.0298390i
$961$		−	7.68629i		−	0.247945i
$962$	0.118651	+	0.0553777i	0.00382547	+	0.00178545i
$963$	−13.6569	−	4.82843i	−0.440086	−	0.155594i
$964$	3.43549	+	3.43549i	0.110650	+	0.110650i
$965$			42.8541i			1.37952i
$966$	6.67033	+	9.43328i	0.214614	+	0.303511i
$967$	0.304635	+	0.304635i	0.00979642	+	0.00979642i	0.711988	−	0.702192i	$-0.247795\pi$
$967$	0.304635	+	0.304635i	0.00979642	+	0.00979642i	−0.702192	+	0.711988i	$0.747795\pi$
$968$	−8.46006	+	8.46006i	−0.271917	+	0.271917i
$969$	−52.6841	−	9.03916i	−1.69246	−	0.290380i
$970$	−8.16211	+	8.16211i	−0.262070	+	0.262070i
$971$		−	15.6680i		−	0.502811i	−0.967882	−	0.251405i	$-0.919107\pi$
$971$		−	15.6680i		−	0.502811i	0.967882	−	0.251405i	$-0.0808927\pi$
$972$	1.00000	−	15.5563i	0.0320750	−	0.498970i
$973$	6.02127	−	6.02127i	0.193033	−	0.193033i
$974$	−26.1121			−0.836684
$975$	−30.5040	+	5.51308i	−0.976910	+	0.176560i
$976$	−2.47115			−0.0790997
$977$	3.39698	−	3.39698i	0.108679	−	0.108679i	−0.650676	−	0.759355i	$-0.725515\pi$
$977$	3.39698	−	3.39698i	0.108679	−	0.108679i	0.759355	+	0.650676i	$0.225515\pi$
$978$	−10.3835	−	14.6845i	−0.332027	−	0.469557i
$979$		−	64.7596i		−	2.06973i
$980$	−2.23200	+	2.23200i	−0.0712988	+	0.0712988i
$981$	−47.4226	+	22.6487i	−1.51409	+	0.723116i
$982$	1.10738	−	1.10738i	0.0353380	−	0.0353380i
$983$	−0.279343	−	0.279343i	−0.00890965	−	0.00890965i	0.702638	−	0.711548i	$-0.252005\pi$
$983$	−0.279343	−	0.279343i	−0.00890965	−	0.00890965i	−0.711548	+	0.702638i	$0.752005\pi$
$984$	−14.4126	+	10.1913i	−0.459459	+	0.324886i
$985$		−	20.7182i		−	0.660137i
$986$	−15.3372	−	15.3372i	−0.488435	−	0.488435i
$987$	8.48528	−	6.00000i	0.270089	−	0.190982i
$988$	−7.37349	−	20.2802i	−0.234582	−	0.645200i
$989$		−	53.9266i		−	1.71477i
$990$	−19.5569	−	40.9489i	−0.621558	−	1.30144i
$991$	−16.1603			−0.513348			−0.256674	−	0.966498i	$-0.582627\pi$
$991$	−16.1603			−0.513348			−0.256674	+	0.966498i	$0.582627\pi$
$992$	4.82843			0.153303
$993$	30.9668	+	5.31306i	0.982701	+	0.168605i
$994$	−2.25768	−	2.25768i	−0.0716094	−	0.0716094i
$995$	−21.7854	−	21.7854i	−0.690643	−	0.690643i
$996$	14.8632	+	2.55012i	0.470958	+	0.0808036i
$997$	20.7730			0.657888			0.328944	−	0.944349i	$-0.393307\pi$
$997$	20.7730			0.657888			0.328944	+	0.944349i	$0.393307\pi$
$998$	30.8970			0.978028
$999$	−0.164711	−	0.0920797i	−0.00521123	−	0.00291327i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.p.b.281.2	yes	8
3.2	odd	2		546.2.p.a.281.3	yes	8
13.5	odd	4		546.2.p.a.239.3	✓	8
39.5	even	4	inner	546.2.p.b.239.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.p.a.239.3	✓	8	13.5	odd	4
546.2.p.a.281.3	yes	8	3.2	odd	2
546.2.p.b.239.2	yes	8	39.5	even	4	inner
546.2.p.b.281.2	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.41421 + 1.00000i) q^{3} -1.00000i q^{4} +(2.23200 - 2.23200i) q^{5} +(0.292893 - 1.70711i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.00000 - 2.82843i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.41421 + 1.00000i) q^{3} -1.00000i q^{4} +(2.23200 - 2.23200i) q^{5} +(0.292893 - 1.70711i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.00000 - 2.82843i) q^{9} +3.15653i q^{10} +(-3.38853 - 3.38853i) q^{11} +(1.00000 + 1.41421i) q^{12} +(-1.52490 + 3.26721i) q^{13} +1.00000i q^{14} +(-0.924526 + 5.38853i) q^{15} -1.00000 q^{16} -5.15653 q^{17} +(1.29289 + 2.70711i) q^{18} +(-4.23200 - 4.23200i) q^{19} +(-2.23200 - 2.23200i) q^{20} +(-0.292893 + 1.70711i) q^{21} +4.79211 q^{22} -6.67033 q^{23} +(-1.70711 - 0.292893i) q^{24} -4.96368i q^{25} +(-1.23200 - 3.38853i) q^{26} +(1.41421 + 5.00000i) q^{27} +(-0.707107 - 0.707107i) q^{28} -4.20632i q^{29} +(-3.15653 - 4.46401i) q^{30} +(3.41421 + 3.41421i) q^{31} +(0.707107 - 0.707107i) q^{32} +(8.18065 + 1.40358i) q^{33} +(3.64622 - 3.64622i) q^{34} -3.15653i q^{35} +(-2.82843 - 1.00000i) q^{36} +(-0.0256791 + 0.0256791i) q^{37} +5.98496 q^{38} +(-1.11068 - 6.14544i) q^{39} +3.15653 q^{40} +(7.20632 - 7.20632i) q^{41} +(-1.00000 - 1.41421i) q^{42} +8.08455i q^{43} +(-3.38853 + 3.38853i) q^{44} +(-4.08106 - 8.54506i) q^{45} +(4.71664 - 4.71664i) q^{46} +(-4.24264 - 4.24264i) q^{47} +(1.41421 - 1.00000i) q^{48} -1.00000i q^{49} +(3.50985 + 3.50985i) q^{50} +(7.29244 - 5.15653i) q^{51} +(3.26721 + 1.52490i) q^{52} -2.87757i q^{53} +(-4.53553 - 2.53553i) q^{54} -15.1264 q^{55} +1.00000 q^{56} +(10.2170 + 1.75295i) q^{57} +(2.97432 + 2.97432i) q^{58} +(-2.48463 - 2.48463i) q^{59} +(5.38853 + 0.924526i) q^{60} +2.47115 q^{61} -4.82843 q^{62} +(-1.29289 - 2.70711i) q^{63} +1.00000i q^{64} +(3.88886 + 10.6960i) q^{65} +(-6.77707 + 4.79211i) q^{66} +(-7.19128 - 7.19128i) q^{67} +5.15653i q^{68} +(9.43328 - 6.67033i) q^{69} +(2.23200 + 2.23200i) q^{70} +(-2.25768 + 2.25768i) q^{71} +(2.70711 - 1.29289i) q^{72} +(8.14654 - 8.14654i) q^{73} -0.0363157i q^{74} +(4.96368 + 7.01971i) q^{75} +(-4.23200 + 4.23200i) q^{76} -4.79211 q^{77} +(5.13085 + 3.56011i) q^{78} +2.36442 q^{79} +(-2.23200 + 2.23200i) q^{80} +(-7.00000 - 5.65685i) q^{81} +10.1913i q^{82} +(6.15653 - 6.15653i) q^{83} +(1.70711 + 0.292893i) q^{84} +(-11.5094 + 11.5094i) q^{85} +(-5.71664 - 5.71664i) q^{86} +(4.20632 + 5.94864i) q^{87} -4.79211i q^{88} +(9.55570 + 9.55570i) q^{89} +(8.92802 + 3.15653i) q^{90} +(1.23200 + 3.38853i) q^{91} +6.67033i q^{92} +(-8.24264 - 1.41421i) q^{93} +6.00000 q^{94} -18.8917 q^{95} +(-0.292893 + 1.70711i) q^{96} +(2.58579 + 2.58579i) q^{97} +(0.707107 + 0.707107i) q^{98} +(-12.9728 + 6.19569i) 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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