LMFDB - Embedded newform 546.2.p.a.281.3

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			281.3
Root			$-0.742317i$ of defining polynomial
Character	$\chi$	$=$	546.281
Dual form			546.2.p.a.239.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-1.41421 - 1.00000i) q^{3} -1.00000i q^{4} +(-2.23200 + 2.23200i) q^{5} +(-1.70711 + 0.292893i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.41421 - 1.00000i) q^{3} -1.00000i q^{4} +(-2.23200 + 2.23200i) 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} +3.15653i q^{10} +(3.38853 + 3.38853i) q^{11} +(-1.00000 + 1.41421i) q^{12} +(-1.52490 + 3.26721i) q^{13} -1.00000i q^{14} +(5.38853 - 0.924526i) q^{15} -1.00000 q^{16} +5.15653 q^{17} +(2.70711 + 1.29289i) q^{18} +(-4.23200 - 4.23200i) q^{19} +(2.23200 + 2.23200i) q^{20} +(-1.70711 + 0.292893i) q^{21} +4.79211 q^{22} +6.67033 q^{23} +(0.292893 + 1.70711i) 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} +(-1.40358 - 8.18065i) 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} +(5.42374 - 3.09564i) 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} +(-8.54506 - 4.08106i) 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} +(-2.53553 - 4.53553i) q^{54} -15.1264 q^{55} -1.00000 q^{56} +(1.75295 + 10.2170i) q^{57} +(2.97432 + 2.97432i) q^{58} +(2.48463 + 2.48463i) q^{59} +(-0.924526 - 5.38853i) q^{60} +2.47115 q^{61} +4.82843 q^{62} +(2.70711 + 1.29289i) 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} +(1.29289 - 2.70711i) 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} +(1.64622 - 6.02412i) 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} +(0.292893 + 1.70711i) 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} +(-1.41421 - 8.24264i) q^{93} +6.00000 q^{94} +18.8917 q^{95} +(1.70711 - 0.292893i) q^{96} +(2.58579 + 2.58579i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(-6.19569 + 12.9728i) 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^{15} - 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} - 20 q^{33} + 4 q^{34} - 24 q^{37} - 4 q^{38} + 4 q^{39} + 4 q^{40} - 20 q^{41} - 8 q^{42} - 8 q^{44} - 12 q^{45} + 4 q^{46} + 24 q^{50} - 8 q^{51} + 8 q^{52} + 8 q^{54} - 12 q^{55} - 8 q^{56} - 16 q^{57} + 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} - 12 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} + 48 q^{94} + 92 q^{95} + 8 q^{96} + 32 q^{97} - 32 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^15 - 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 - 20 * q^33 + 4 * q^34 - 24 * q^37 - 4 * q^38 + 4 * q^39 + 4 * q^40 - 20 * q^41 - 8 * q^42 - 8 * q^44 - 12 * q^45 + 4 * q^46 + 24 * q^50 - 8 * q^51 + 8 * q^52 + 8 * q^54 - 12 * q^55 - 8 * q^56 - 16 * q^57 + 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 - 12 * 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 + 48 * q^94 + 92 * q^95 + 8 * q^96 + 32 * q^97 - 32 * 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	−0.999998	−	0.00181579i	$-0.999422\pi$
$5$	−2.23200	+	2.23200i	−0.998183	+	0.998183i	0.00181579	+	0.999998i	$0.499422\pi$
$6$	−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
$10$			3.15653i			0.998183i
$11$	3.38853	+	3.38853i	1.02168	+	1.02168i	0.999760	+	0.0219219i	$0.00697852\pi$
$11$	3.38853	+	3.38853i	1.02168	+	1.02168i	0.0219219	+	0.999760i	$0.493021\pi$
$12$	−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
$15$	5.38853	−	0.924526i	1.39131	−	0.238712i
$16$	−1.00000			−0.250000
$17$	5.15653			1.25064			0.625321	−	0.780368i	$-0.284968\pi$
$17$	5.15653			1.25064			0.625321	+	0.780368i	$0.284968\pi$
$18$	2.70711	+	1.29289i	0.638071	+	0.304738i
$19$	−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
$21$	−1.70711	+	0.292893i	−0.372521	+	0.0639145i
$22$	4.79211			1.02168
$23$	6.67033			1.39086			0.695430	−	0.718594i	$-0.255214\pi$
$23$	6.67033			1.39086			0.695430	+	0.718594i	$0.255214\pi$
$24$	0.292893	+	1.70711i	0.0597866	+	0.348462i
$25$		−	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	$0.127714\pi$
$29$			4.20632i			0.781095i	−0.920583	+	0.390547i	$0.872286\pi$
$30$	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
$33$	−1.40358	−	8.18065i	−0.244331	−	1.42407i
$34$	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
$39$	5.42374	−	3.09564i	0.868494	−	0.495699i
$40$	3.15653			0.499091
$41$	−7.20632	+	7.20632i	−1.12544	+	1.12544i	−0.134529	+	0.990910i	$0.542952\pi$
$41$	−7.20632	+	7.20632i	−1.12544	+	1.12544i	−0.990910	+	0.134529i	$0.957048\pi$
$42$	−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
$45$	−8.54506	−	4.08106i	−1.27382	−	0.608368i
$46$	4.71664	−	4.71664i	0.695430	−	0.695430i
$47$	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
$50$	−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	$0.0633253\pi$
$53$			2.87757i			0.395265i	−0.980276	+	0.197633i	$0.936675\pi$
$54$	−2.53553	−	4.53553i	−0.345042	−	0.617208i
$55$	−15.1264			−2.03965
$56$	−1.00000			−0.133631
$57$	1.75295	+	10.2170i	0.232184	+	1.35327i
$58$	2.97432	+	2.97432i	0.390547	+	0.390547i
$59$	2.48463	+	2.48463i	0.323472	+	0.323472i	0.850097	−	0.526626i	$-0.176543\pi$
$59$	2.48463	+	2.48463i	0.323472	+	0.323472i	−0.526626	+	0.850097i	$0.676543\pi$
$60$	−0.924526	−	5.38853i	−0.119356	−	0.695657i
$61$	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
$63$	2.70711	+	1.29289i	0.341063	+	0.162889i
$64$			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	−0.560331	−	0.828269i	$-0.689326\pi$
$71$	2.25768	−	2.25768i	0.267938	−	0.267938i	0.828269	+	0.560331i	$0.189326\pi$
$72$	1.29289	−	2.70711i	0.152369	−	0.319036i
$73$	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
$78$	1.64622	−	6.02412i	0.186397	−	0.682097i
$79$	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	−0.959039	−	0.283272i	$-0.908580\pi$
$83$	−6.15653	+	6.15653i	−0.675767	+	0.675767i	0.283272	+	0.959039i	$0.408580\pi$
$84$	0.292893	+	1.70711i	0.0319573	+	0.186261i
$85$	−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	$-0.995866\pi$
$89$	−9.55570	−	9.55570i	−1.01290	−	1.01290i	−0.0129867	−	0.999916i	$-0.504134\pi$
$90$	−8.92802	+	3.15653i	−0.941096	+	0.332728i
$91$	1.23200	+	3.38853i	0.129149	+	0.355215i
$92$		−	6.67033i		−	0.695430i
$93$	−1.41421	−	8.24264i	−0.146647	−	0.854722i
$94$	6.00000			0.618853
$95$	18.8917			1.93825
$96$	1.70711	−	0.292893i	0.174231	−	0.0298933i
$97$	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
$99$	−6.19569	+	12.9728i	−0.622690	+	1.30381i
$100$	−4.96368			−0.496368
$101$	−0.291788			−0.0290340			−0.0145170	−	0.999895i	$-0.504621\pi$
$101$	−0.291788			−0.0290340			−0.0145170	+	0.999895i	$0.504621\pi$
$102$	−8.80275	+	1.51031i	−0.871602	+	0.149543i
$103$			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	$0.0749821\pi$
$107$			4.82843i			0.466782i	−0.972383	+	0.233391i	$0.925018\pi$
$108$	−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
$111$	0.0619948	−	0.0106366i	0.00588428	−	0.00100958i
$112$	−0.707107	+	0.707107i	−0.0668153	+	0.0668153i
$113$			12.4853i			1.17452i	0.809400	+	0.587258i	$0.199793\pi$
$113$			12.4853i			1.17452i	−0.809400	+	0.587258i	$0.800207\pi$
$114$	8.46401	+	5.98496i	0.792727	+	0.560543i
$115$	−14.8882	+	14.8882i	−1.38833	+	1.38833i
$116$	4.20632			0.390547
$117$	−10.7660	−	1.04585i	−0.995315	−	0.0966886i
$118$	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
$123$	17.3976	−	2.98496i	1.56869	−	0.269145i
$124$	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	$-0.967273\pi$
$131$		−	2.34938i		−	0.205266i	0.994719	−	0.102633i	$-0.0327267\pi$
$132$	−8.18065	+	1.40358i	−0.712034	+	0.122166i
$133$	−5.98496			−0.518962
$134$	−10.1700			−0.878555
$135$	8.00349	+	14.3166i	0.688831	+	1.23217i
$136$	−3.64622	−	3.64622i	−0.312661	−	0.312661i
$137$	−12.1102	−	12.1102i	−1.03465	−	1.03465i	−0.999378	−	0.0352685i	$-0.988771\pi$
$137$	−12.1102	−	12.1102i	−1.03465	−	1.03465i	−0.0352685	−	0.999378i	$-0.511229\pi$
$138$	−11.3870	+	1.95370i	−0.969323	+	0.166310i
$139$	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
$141$	−1.75736	−	10.2426i	−0.147996	−	0.862586i
$142$		−	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	−0.0390856	−	0.999236i	$-0.512445\pi$
$149$	11.7201	−	11.7201i	0.960150	−	0.960150i	0.999236	+	0.0390856i	$0.0124445\pi$
$150$	1.45383	+	8.47354i	0.118705	+	0.691862i
$151$	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
$156$	−3.09564	−	5.42374i	−0.247850	−	0.434247i
$157$	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
$162$	−0.949747	+	8.94975i	−0.0746192	+	0.703159i
$163$	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	0.470743	−	0.882271i	$-0.343986\pi$
$167$	−5.31811	−	5.31811i	−0.411528	−	0.411528i	−0.882271	+	0.470743i	$0.843986\pi$
$168$	1.41421	+	1.00000i	0.109109	+	0.0771517i
$169$	−8.34938	−	9.96433i	−0.642260	−	0.766487i
$170$			16.2767i			1.24837i
$171$	7.73791	−	16.2019i	0.591733	−	1.23899i
$172$	8.08455			0.616441
$173$	14.0425			1.06764			0.533818	−	0.845600i	$-0.320757\pi$
$173$	14.0425			1.06764			0.533818	+	0.845600i	$0.320757\pi$
$174$	−1.23200	−	7.18065i	−0.0933980	−	0.544363i
$175$	−3.50985	−	3.50985i	−0.265320	−	0.265320i
$176$	−3.38853	−	3.38853i	−0.255420	−	0.255420i
$177$	−1.02917	−	5.99844i	−0.0773571	−	0.450870i
$178$	−13.5138			−1.01290
$179$	−2.05136			−0.153326			−0.0766629	−	0.997057i	$-0.524427\pi$
$179$	−2.05136			−0.153326			−0.0766629	+	0.997057i	$0.524427\pi$
$180$	−4.08106	+	8.54506i	−0.304184	+	0.636912i
$181$		−	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
$189$	−2.53553	−	4.53553i	−0.184433	−	0.329912i
$190$	13.3584	−	13.3584i	0.969124	−	0.969124i
$191$			10.0141i			0.724597i	0.932062	+	0.362298i	$0.118008\pi$
$191$			10.0141i			0.724597i	−0.932062	+	0.362298i	$0.881992\pi$
$192$	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
$195$	−5.19634	+	19.0153i	−0.372117	+	1.36171i
$196$	−1.00000			−0.0714286
$197$	−4.64116	+	4.64116i	−0.330669	+	0.330669i	−0.852841	−	0.522171i	$-0.825122\pi$
$197$	−4.64116	+	4.64116i	−0.330669	+	0.330669i	0.522171	+	0.852841i	$0.325122\pi$
$198$	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
$201$	2.97873	+	17.3613i	0.210103	+	1.22457i
$202$	−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
$210$	−0.924526	−	5.38853i	−0.0637984	−	0.371844i
$211$	−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
$213$	−5.45053	+	0.935163i	−0.373464	+	0.0640763i
$214$	3.41421	+	3.41421i	0.233391	+	0.233391i
$215$	−18.0447	−	18.0447i	−1.23064	−	1.23064i
$216$	−4.53553	+	2.53553i	−0.308604	+	0.172521i
$217$	4.82843			0.327775
$218$	−17.5178			−1.18646
$219$	−19.6675	+	3.37441i	−1.32901	+	0.228021i
$220$			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	−0.768189	−	0.640223i	$-0.778842\pi$
$227$	−1.92802	+	1.92802i	−0.127967	+	0.127967i	0.640223	+	0.768189i	$0.278842\pi$
$228$	10.2170	−	1.75295i	0.676635	−	0.116092i
$229$	−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	$-0.273325\pi$
$233$	19.9486			1.30688			0.653439	+	0.756979i	$0.273325\pi$
$234$	−8.35222	+	6.87317i	−0.546002	+	0.449313i
$235$	−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	−0.422311	−	0.906451i	$-0.638781\pi$
$239$	7.48463	−	7.48463i	0.484141	−	0.484141i	0.906451	+	0.422311i	$0.138781\pi$
$240$	−5.38853	+	0.924526i	−0.347828	+	0.0596779i
$241$	−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
$249$	14.8632	−	2.55012i	0.941916	−	0.161607i
$250$	−0.114632			−0.00724994
$251$	8.93425			0.563925			0.281962	−	0.959425i	$-0.409015\pi$
$251$	8.93425			0.563925			0.281962	+	0.959425i	$0.409015\pi$
$252$	1.29289	−	2.70711i	0.0814446	−	0.170532i
$253$	22.6027	+	22.6027i	1.42102	+	1.42102i
$254$	−9.52095	−	9.52095i	−0.597397	−	0.597397i
$255$	27.7861	−	4.76735i	1.74004	−	0.298543i
$256$	1.00000			0.0625000
$257$	−6.75580			−0.421415			−0.210707	−	0.977549i	$-0.567577\pi$
$257$	−6.75580			−0.421415			−0.210707	+	0.977549i	$0.567577\pi$
$258$	−2.36791	−	13.8012i	−0.147420	−	0.859224i
$259$			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	$-0.943016\pi$
$263$		−	5.77551i		−	0.356133i	0.984018	−	0.178066i	$-0.0569842\pi$
$264$	−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
$267$	3.95810	+	23.0695i	0.242232	+	1.41183i
$268$	−7.19128	+	7.19128i	−0.439277	+	0.439277i
$269$		−	5.94864i		−	0.362695i	−0.983419	−	0.181348i	$-0.941954\pi$
$269$		−	5.94864i		−	0.362695i	0.983419	−	0.181348i	$-0.0580459\pi$
$270$	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
$273$	1.64622	−	6.02412i	0.0996336	−	0.364596i
$274$	−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
$279$	−6.24264	+	13.0711i	−0.373737	+	0.782544i
$280$	2.23200	−	2.23200i	0.133388	−	0.133388i
$281$	−10.6340	−	10.6340i	−0.634372	−	0.634372i	0.314789	−	0.949162i	$-0.398066\pi$
$281$	−10.6340	−	10.6340i	−0.634372	−	0.634372i	−0.949162	+	0.314789i	$0.898066\pi$
$282$	−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
$288$	−2.70711	−	1.29289i	−0.159518	−	0.0761845i
$289$	9.58981			0.564106
$290$	−13.2774			−0.779675
$291$	−1.07107	−	6.24264i	−0.0627871	−	0.365950i
$292$	−8.14654	−	8.14654i	−0.476740	−	0.476740i
$293$	12.3613	+	12.3613i	0.722154	+	0.722154i	0.969044	−	0.246889i	$-0.0794084\pi$
$293$	12.3613	+	12.3613i	0.722154	+	0.722154i	−0.246889	+	0.969044i	$0.579408\pi$
$294$	0.292893	+	1.70711i	0.0170819	+	0.0995605i
$295$	−11.0914			−0.645768
$296$	0.0363157			0.00211081
$297$	21.7348	−	12.1506i	1.26118	−	0.705047i
$298$		−	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
$306$	13.9593	+	6.66684i	0.797999	+	0.381118i
$307$	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	$-0.742698\pi$
$311$	−24.3613			−1.38140			−0.690701	+	0.723140i	$0.742698\pi$
$312$	−6.02412	−	1.64622i	−0.341048	−	0.0931987i
$313$	−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	−0.967899	−	0.251338i	$-0.919129\pi$
$317$	−12.7580	+	12.7580i	−0.716561	+	0.716561i	0.251338	+	0.967899i	$0.419129\pi$
$318$	−0.842822	−	4.91233i	−0.0472631	−	0.275470i
$319$	−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
$327$	5.13085	+	29.9048i	0.283737	+	1.65374i
$328$	10.1913			0.562719
$329$	6.00000			0.330791
$330$	25.8225	−	4.43043i	1.42148	−	0.243887i
$331$	−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
$333$	−0.0983105	−	0.0469523i	−0.00538738	−	0.00257297i
$334$	−7.52095			−0.411528
$335$	32.1019			1.75392
$336$	1.70711	−	0.292893i	0.0931303	−	0.0159786i
$337$		−	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
$345$	35.9433	−	6.16690i	1.93512	−	0.332015i
$346$	9.92958	−	9.92958i	0.533818	−	0.533818i
$347$			2.65621i			0.142593i	0.997455	+	0.0712963i	$0.0227136\pi$
$347$			2.65621i			0.142593i	−0.997455	+	0.0712963i	$0.977286\pi$
$348$	−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
$351$	14.1795	+	12.2450i	0.756848	+	0.653591i
$352$	−4.79211			−0.255420
$353$	18.4837	−	18.4837i	0.983789	−	0.983789i	−0.0160816	−	0.999871i	$-0.505119\pi$
$353$	18.4837	−	18.4837i	0.983789	−	0.983789i	0.999871	+	0.0160816i	$0.00511917\pi$
$354$	−4.96927	−	3.51380i	−0.264114	−	0.186757i
$355$			10.0783i			0.534901i
$356$	−9.55570	+	9.55570i	−0.506451	+	0.506451i
$357$	−8.80275	+	1.51031i	−0.465891	+	0.0799342i
$358$	−1.45053	+	1.45053i	−0.0766629	+	0.0766629i
$359$	19.1556	+	19.1556i	1.01099	+	1.01099i	0.999939	+	0.0110558i	$0.00351924\pi$
$359$	19.1556	+	19.1556i	1.01099	+	1.01099i	0.0110558	+	0.999939i	$0.496481\pi$
$360$	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
$366$	−4.21853	+	0.723784i	−0.220506	+	0.0378328i
$367$	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
$369$	−27.5889	−	13.1762i	−1.43622	−	0.685928i
$370$	−0.0810568	−	0.0810568i	−0.00421394	−	0.00421394i
$371$	2.03475	+	2.03475i	0.105639	+	0.105639i
$372$	−8.24264	+	1.41421i	−0.427361	+	0.0733236i
$373$	−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
$375$	0.0335748	+	0.195688i	0.00173380	+	0.0101053i
$376$		−	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	−0.151172	−	0.988507i	$-0.548305\pi$
$383$	16.3870	−	16.3870i	0.837335	−	0.837335i	0.988507	+	0.151172i	$0.0483048\pi$
$384$	−0.292893	−	1.70711i	−0.0149466	−	0.0871154i
$385$	−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	$-0.248066\pi$
$389$	28.0616			1.42278			0.711390	+	0.702797i	$0.248066\pi$
$390$	9.77149	+	17.1202i	0.494798	+	0.866916i
$391$	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
$396$	12.9728	+	6.19569i	0.651906	+	0.311345i
$397$	−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	0.395018	−	0.918673i	$-0.370738\pi$
$401$	−10.4862	−	10.4862i	−0.523656	−	0.523656i	−0.918673	+	0.395018i	$0.870738\pi$
$402$	14.3826	+	10.1700i	0.717337	+	0.507234i
$403$	−16.3613	+	5.94864i	−0.815014	+	0.296323i
$404$			0.291788i			0.0145170i
$405$	2.99791	−	28.2502i	0.148967	−	1.40376i
$406$	4.20632			0.208756
$407$	−0.174029			−0.00862629
$408$	1.51031	+	8.80275i	0.0747716	+	0.435801i
$409$	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
$411$	5.01622	+	29.2367i	0.247432	+	1.44214i
$412$	18.2758			0.900385
$413$	3.51380			0.172903
$414$	18.0573	+	8.62403i	0.887468	+	0.423848i
$415$		−	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	$0.0287543\pi$
$419$			3.69317i			0.180423i	−0.995923	+	0.0902116i	$0.971246\pi$
$420$	−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
$423$	−7.75736	+	16.2426i	−0.377176	+	0.789744i
$424$	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
$429$	28.8682	+	7.88886i	1.39377	+	0.380878i
$430$	−25.5191			−1.23064
$431$	7.55635	−	7.55635i	0.363977	−	0.363977i	−0.501298	−	0.865275i	$-0.667144\pi$
$431$	7.55635	−	7.55635i	0.363977	−	0.363977i	0.865275	+	0.501298i	$0.167144\pi$
$432$	−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
$435$	3.88886	+	22.6659i	0.186456	+	1.08675i
$436$	−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	$-0.943976\pi$
$443$		−	7.37075i		−	0.350195i	0.984551	−	0.175097i	$-0.0560241\pi$
$444$	−0.0106366	−	0.0619948i	−0.000504792	−	0.00294214i
$445$	42.6567			2.02212
$446$	22.9762			1.08796
$447$	−28.2949	+	4.85464i	−1.33830	+	0.229616i
$448$	0.707107	+	0.707107i	0.0334077	+	0.0334077i
$449$	−9.39255	−	9.39255i	−0.443262	−	0.443262i	0.449845	−	0.893107i	$-0.351479\pi$
$449$	−9.39255	−	9.39255i	−0.443262	−	0.443262i	−0.893107	+	0.449845i	$0.851479\pi$
$450$	6.41751	−	13.4372i	0.302525	−	0.633437i
$451$	−48.8378			−2.29968
$452$	12.4853			0.587258
$453$	−19.0454	+	3.26767i	−0.894830	+	0.153529i
$454$			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	−0.995057	−	0.0993033i	$-0.968339\pi$
$461$	−19.2327	+	19.2327i	−0.895754	+	0.895754i	0.0993033	+	0.995057i	$0.468339\pi$
$462$	−8.18065	+	1.40358i	−0.380598	+	0.0653003i
$463$	−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	$-0.493128\pi$
$467$	0.932952			0.0431719			0.0215859	+	0.999767i	$0.493128\pi$
$468$	−1.04585	+	10.7660i	−0.0483443	+	0.497657i
$469$	−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
$474$	−4.03632	+	0.692522i	−0.185394	+	0.0318086i
$475$	−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	$-0.937248\pi$
$479$	−25.7489	−	25.7489i	−1.17650	−	1.17650i	−0.195867	−	0.980630i	$-0.562752\pi$
$480$	−3.15653	+	4.46401i	−0.144075	+	0.203753i
$481$	−0.0447411	−	0.123057i	−0.00204002	−	0.00561092i
$482$			4.85851i			0.221299i
$483$	−11.3870	+	1.95370i	−0.518125	+	0.0888962i
$484$	11.9643			0.543833
$485$	−11.5430			−0.524139
$486$	10.2929	−	11.7071i	0.466895	−	0.531045i
$487$	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
$489$	−17.7257	+	3.04125i	−0.801584	+	0.137530i
$490$	3.15653			0.142598
$491$	1.56608			0.0706761			0.0353380	−	0.999375i	$-0.488749\pi$
$491$	1.56608			0.0706761			0.0353380	+	0.999375i	$0.488749\pi$
$492$	−2.98496	−	17.3976i	−0.134572	−	0.784345i
$493$			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
$501$	2.20284	+	12.8391i	0.0984154	+	0.573607i
$502$	6.31747	−	6.31747i	0.281962	−	0.281962i
$503$		−	16.4853i		−	0.735042i	−0.930015	−	0.367521i	$-0.880207\pi$
$503$		−	16.4853i		−	0.735042i	0.930015	−	0.367521i	$-0.119793\pi$
$504$	−1.00000	−	2.82843i	−0.0445435	−	0.125988i
$505$	0.651271	−	0.651271i	0.0289812	−	0.0289812i
$506$	31.9650			1.42102
$507$	1.84347	+	22.4411i	0.0818714	+	0.996643i
$508$	−13.4647			−0.597397
$509$	−11.2526	+	11.2526i	−0.498764	+	0.498764i	−0.911053	−	0.412289i	$-0.864729\pi$
$509$	−11.2526	+	11.2526i	−0.498764	+	0.498764i	0.412289	+	0.911053i	$0.364729\pi$
$510$	16.2767	−	23.0188i	0.720746	−	1.01929i
$511$		−	11.5209i		−	0.509657i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−27.1450	+	15.1751i	−1.19848	+	0.669995i
$514$	−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	$0.0885069\pi$
$521$			12.5304i			0.548967i	−0.961592	+	0.274484i	$0.911493\pi$
$522$	−5.43833	+	11.3870i	−0.238029	+	0.498394i
$523$	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
$525$	1.45383	+	8.47354i	0.0634503	+	0.369816i
$526$	−4.08390	−	4.08390i	−0.178066	−	0.178066i
$527$	17.6055	+	17.6055i	0.766907	+	0.766907i
$528$	1.40358	+	8.18065i	0.0610828	+	0.356017i
$529$	21.4933			0.934493
$530$	−9.08315			−0.394547
$531$	−4.54297	+	9.51224i	−0.197148	+	0.412796i
$532$			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
$540$	14.3166	−	8.00349i	0.616086	−	0.344415i
$541$	−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
$546$	−3.09564	−	5.42374i	−0.132481	−	0.232115i
$547$	−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
$552$	1.95370	+	11.3870i	0.0831548	+	0.484662i
$553$	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	0.979910	−	0.199439i	$-0.0639118\pi$
$557$	18.4198	+	18.4198i	0.780472	+	0.780472i	−0.199439	+	0.979910i	$0.563912\pi$
$558$	4.82843	+	13.6569i	0.204404	+	0.578141i
$559$	−26.4139	−	12.3281i	−1.11719	−	0.521423i
$560$		−	3.15653i		−	0.133388i
$561$	−7.23759	−	42.1837i	−0.305571	−	1.78100i
$562$	−15.0388			−0.634372
$563$	22.9944			0.969099			0.484550	−	0.874764i	$-0.338984\pi$
$563$	22.9944			0.969099			0.484550	+	0.874764i	$0.338984\pi$
$564$	−10.2426	+	1.75736i	−0.431293	+	0.0739982i
$565$	−27.8672	−	27.8672i	−1.17238	−	1.17238i
$566$	−22.7208	−	22.7208i	−0.955025	−	0.955025i
$567$	−0.949747	+	8.94975i	−0.0398856	+	0.375854i
$568$	−3.19285			−0.133969
$569$	−44.0664			−1.84736			−0.923679	−	0.383166i	$-0.874834\pi$
$569$	−44.0664			−1.84736			−0.923679	+	0.383166i	$0.874834\pi$
$570$	−32.2502	+	5.53325i	−1.35081	+	0.231762i
$571$		−	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
$579$	23.1762	−	3.97641i	0.963172	−	0.165254i
$580$	−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
$585$	26.3640	−	21.6954i	1.09002	−	0.896993i
$586$	17.4815			0.722154
$587$	−10.7264	+	10.7264i	−0.442724	+	0.442724i	−0.892927	−	0.450202i	$-0.851352\pi$
$587$	−10.7264	+	10.7264i	−0.442724	+	0.442724i	0.450202	+	0.892927i	$0.351352\pi$
$588$	1.41421	+	1.00000i	0.0583212	+	0.0412393i
$589$		−	28.8979i		−	1.19072i
$590$	−7.84282	+	7.84282i	−0.322884	+	0.322884i
$591$	11.2048	−	1.92243i	0.460902	−	0.0790783i
$592$	0.0256791	−	0.0256791i	0.00105540	−	0.00105540i
$593$	28.7454	+	28.7454i	1.18043	+	1.18043i	0.979632	+	0.200801i	$0.0643544\pi$
$593$	28.7454	+	28.7454i	1.18043	+	1.18043i	0.200801	+	0.979632i	$0.435646\pi$
$594$	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	$-0.882651\pi$
$599$		−	17.6396i		−	0.720735i	0.932811	−	0.360367i	$-0.117349\pi$
$600$	8.47354	−	1.45383i	0.345931	−	0.0593523i
$601$	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
$603$	13.1487	−	27.5313i	0.535458	−	1.12116i
$604$	−7.88886	−	7.88886i	−0.320993	−	0.320993i
$605$	−26.7044	−	26.7044i	−1.08569	−	1.08569i
$606$	0.498113	−	0.0854626i	0.0202344	−	0.00347168i
$607$	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
$609$	−1.23200	−	7.18065i	−0.0499233	−	0.290974i
$610$			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	$0.556036\pi$
$617$	−28.8059	+	28.8059i	−1.15968	+	1.15968i	−0.984544	+	0.175136i	$0.943964\pi$
$618$	−5.35287	−	31.1988i	−0.215324	−	1.25500i
$619$	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
$624$	−5.42374	+	3.09564i	−0.217124	+	0.123925i
$625$	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
$630$	−4.08106	+	8.54506i	−0.162593	+	0.340444i
$631$	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
$639$	8.64338	+	4.12801i	0.341927	+	0.163302i
$640$	−3.15653			−0.124773
$641$	−19.7733			−0.780998			−0.390499	−	0.920603i	$-0.627698\pi$
$641$	−19.7733			−0.780998			−0.390499	+	0.920603i	$0.627698\pi$
$642$	−1.41421	−	8.24264i	−0.0558146	−	0.325311i
$643$	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
$645$	7.47438	+	43.5639i	0.294303	+	1.71533i
$646$	−30.8616			−1.21423
$647$	−3.91856			−0.154054			−0.0770272	−	0.997029i	$-0.524543\pi$
$647$	−3.91856			−0.154054			−0.0770272	+	0.997029i	$0.524543\pi$
$648$	8.94975	+	0.949747i	0.351579	+	0.0373096i
$649$			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	$-0.984716\pi$
$653$		−	2.45301i		−	0.0959937i	0.998847	−	0.0479968i	$-0.0152837\pi$
$654$	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
$657$	31.1884	+	14.8954i	1.21678	+	0.581123i
$658$	4.24264	−	4.24264i	0.165395	−	0.165395i
$659$			21.5272i			0.838580i	0.907852	+	0.419290i	$0.137721\pi$
$659$			21.5272i			0.838580i	−0.907852	+	0.419290i	$0.862279\pi$
$660$	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
$663$	27.9677	−	15.9628i	1.08618	−	0.619943i
$664$	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
$669$	−6.72959	−	39.2229i	−0.260181	−	1.51645i
$670$	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	$0.0341007\pi$
$677$			5.56424i			0.213851i	−0.994267	+	0.106926i	$0.965899\pi$
$678$	−3.65685	−	21.3137i	−0.140441	−	0.818548i
$679$	3.65685			0.140337
$680$	16.2767			0.624185
$681$	4.65464	−	0.798610i	0.178366	−	0.0306028i
$682$	16.3613	+	16.3613i	0.626506	+	0.626506i
$683$	22.6991	+	22.6991i	0.868558	+	0.868558i	0.992313	−	0.123755i	$-0.0394938\pi$
$683$	22.6991	+	22.6991i	0.868558	+	0.868558i	−0.123755	+	0.992313i	$0.539494\pi$
$684$	−16.2019	−	7.73791i	−0.619496	−	0.295866i
$685$	54.0601			2.06553
$686$	−1.00000			−0.0381802
$687$	2.87979	−	0.494093i	0.109871	−	0.0188508i
$688$		−	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
$696$	−7.18065	+	1.23200i	−0.272182	+	0.0466990i
$697$	−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	$-0.487309\pi$
$701$	2.11061			0.0797167			0.0398584	+	0.999205i	$0.487309\pi$
$702$	18.6850	−	1.36791i	0.705219	−	0.0516284i
$703$	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
$708$	−5.99844	+	1.02917i	−0.225435	+	0.0386785i
$709$	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
$717$	−18.0695	+	3.10024i	−0.674818	+	0.115780i
$718$	27.0901			1.01099
$719$	47.6706			1.77781			0.888906	−	0.458089i	$-0.151466\pi$
$719$	47.6706			1.77781			0.888906	+	0.458089i	$0.151466\pi$
$720$	8.54506	+	4.08106i	0.318456	+	0.152092i
$721$	12.9230	+	12.9230i	0.481276	+	0.481276i
$722$	11.8933	+	11.8933i	0.442624	+	0.442624i
$723$	8.29400	−	1.42303i	0.308457	−	0.0529229i
$724$	−14.5344			−0.540168
$725$	20.8789			0.775422
$726$	−3.50427	−	20.4244i	−0.130056	−	0.758020i
$727$			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
$735$	−0.924526	−	5.38853i	−0.0341017	−	0.198759i
$736$	−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
$741$	−36.0541	−	9.85254i	−1.32448	−	0.361942i
$742$	2.87757			0.105639
$743$	−15.2292	+	15.2292i	−0.558704	+	0.558704i	−0.928938	−	0.370235i	$-0.879277\pi$
$743$	−15.2292	+	15.2292i	−0.558704	+	0.558704i	0.370235	+	0.928938i	$0.379277\pi$
$744$	−4.82843	+	6.82843i	−0.177019	+	0.250342i
$745$			52.3187i			1.91681i
$746$	−2.25768	+	2.25768i	−0.0826597	+	0.0826597i
$747$	−23.5698	−	11.2568i	−0.862375	−	0.411864i
$748$	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
$756$	−4.53553	+	2.53553i	−0.164956	+	0.0922165i
$757$	−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
$759$	−9.36233	−	54.5676i	−0.339831	−	1.98068i
$760$	−13.3584	−	13.3584i	−0.484562	−	0.484562i
$761$	−8.02284	−	8.02284i	−0.290828	−	0.290828i	0.546580	−	0.837407i	$-0.315930\pi$
$761$	−8.02284	−	8.02284i	−0.290828	−	0.290828i	−0.837407	+	0.546580i	$0.815930\pi$
$762$	3.94371	+	22.9856i	0.142865	+	0.832681i
$763$	−17.5178			−0.634188
$764$	10.0141			0.362298
$765$	−44.0629	−	21.0441i	−1.59310	−	0.760851i
$766$		−	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	$-0.435813\pi$
$773$	32.8081	−	32.8081i	1.18002	−	1.18002i	0.979737	−	0.200287i	$-0.0641874\pi$
$774$	−10.4525	+	21.8857i	−0.375706	+	0.786666i
$775$	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
$780$	19.0153	+	5.19634i	0.680857	+	0.186059i
$781$	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
$786$	0.688116	+	4.01064i	0.0245443	+	0.143055i
$787$	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
$795$	2.66039	+	15.5059i	0.0943544	+	0.549938i
$796$	−9.76046			−0.345950
$797$	8.12086			0.287656			0.143828	−	0.989603i	$-0.454059\pi$
$797$	8.12086			0.287656			0.143828	+	0.989603i	$0.454059\pi$
$798$	10.2170	−	1.75295i	0.361677	−	0.0620539i
$799$	21.8773	+	21.8773i	0.773963	+	0.773963i
$800$	3.50985	+	3.50985i	0.124092	+	0.124092i
$801$	17.4719	−	36.5833i	0.617339	−	1.29261i
$802$	−14.8297			−0.523656
$803$	55.2097			1.94831
$804$	17.3613	−	2.97873i	0.612286	−	0.105052i
$805$			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	$0.0776309\pi$
$809$			13.7365i			0.482948i	−0.970407	+	0.241474i	$0.922369\pi$
$810$	−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
$813$	2.03632	−	0.349377i	0.0714167	−	0.0122532i
$814$	−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
$819$	−8.35222	+	6.87317i	−0.291850	+	0.240168i
$820$	−32.1691			−1.12339
$821$	−1.49566	+	1.49566i	−0.0521988	+	0.0521988i	−0.732724	−	0.680526i	$-0.761752\pi$
$821$	−1.49566	+	1.49566i	−0.0521988	+	0.0521988i	0.680526	+	0.732724i	$0.261752\pi$
$822$	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
$825$	−40.6061	+	6.96691i	−1.41372	+	0.242557i
$826$	2.48463	−	2.48463i	0.0864515	−	0.0864515i
$827$	3.72157	+	3.72157i	0.129412	+	0.129412i	0.768846	−	0.639434i	$-0.220831\pi$
$827$	3.72157	+	3.72157i	0.129412	+	0.129412i	−0.639434	+	0.768846i	$0.720831\pi$
$828$	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
$834$	−14.5366	+	2.49409i	−0.503363	+	0.0863634i
$835$	23.7401			0.821560
$836$	−28.6806			−0.991939
$837$	21.8995	−	12.2426i	0.756957	−	0.423168i
$838$	2.61147	+	2.61147i	0.0902116	+	0.0902116i
$839$	−10.8049	−	10.8049i	−0.373028	−	0.373028i	0.495551	−	0.868579i	$-0.334966\pi$
$839$	−10.8049	−	10.8049i	−0.373028	−	0.373028i	−0.868579	+	0.495551i	$0.834966\pi$
$840$	−5.38853	+	0.924526i	−0.185922	+	0.0318992i
$841$	11.3068			0.389891
$842$	28.8365			0.993770
$843$	4.40475	+	25.6728i	0.151708	+	0.884218i
$844$			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
$852$	0.935163	+	5.45053i	0.0320382	+	0.186732i
$853$	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	$-0.612722\pi$
$857$	−20.3032			−0.693544			−0.346772	+	0.937950i	$0.612722\pi$
$858$	25.9912	−	14.8347i	0.887325	−	0.506447i
$859$	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	−0.891646	−	0.452733i	$-0.850449\pi$
$863$	−12.8939	+	12.8939i	−0.438914	+	0.438914i	0.452733	+	0.891646i	$0.350449\pi$
$864$	2.53553	+	4.53553i	0.0862606	+	0.154302i
$865$	−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
$873$	−4.72792	+	9.89949i	−0.160016	+	0.335047i
$874$	−39.9217			−1.35037
$875$	−0.114632			−0.00387526
$876$	3.37441	+	19.6675i	0.114011	+	0.664503i
$877$	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
$879$	−5.12021	−	29.8428i	−0.172701	−	1.00657i
$880$	15.1264			0.509912
$881$	40.1553			1.35287			0.676434	−	0.736503i	$-0.263524\pi$
$881$	40.1553			1.35287			0.676434	+	0.736503i	$0.263524\pi$
$882$	1.29289	−	2.70711i	0.0435340	−	0.0911530i
$883$		−	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	$-0.864866\pi$
$887$		−	24.5348i		−	0.823798i	0.911229	−	0.411899i	$-0.135134\pi$
$888$	−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
$891$	−42.8882	−	4.55130i	−1.43681	−	0.152474i
$892$	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
$897$	36.1782	−	20.6490i	1.20795	−	0.689449i
$898$	−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
$903$	−2.36791	−	13.8012i	−0.0787991	−	0.459275i
$904$	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	$-0.859205\pi$
$911$		−	25.8388i		−	0.856077i	0.903761	−	0.428038i	$-0.140795\pi$
$912$	−1.75295	−	10.2170i	−0.0580461	−	0.338317i
$913$	−41.7232			−1.38084
$914$	12.4348			0.411308
$915$	13.3159	−	2.28465i	0.440210	−	0.0755281i
$916$	1.19285	+	1.19285i	0.0394127	+	0.0394127i
$917$	−1.66126	−	1.66126i	−0.0548596	−	0.0548596i
$918$	−13.0746	−	23.3876i	−0.431525	−	0.771906i
$919$	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
$921$	−29.9154	+	5.13268i	−0.985747	+	0.169127i
$922$			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	−0.637363	−	0.770564i	$-0.719975\pi$
$929$	4.05990	−	4.05990i	0.133201	−	0.133201i	0.770564	+	0.637363i	$0.219975\pi$
$930$	26.0181	−	4.46401i	0.853169	−	0.146381i
$931$	−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
$936$	6.87317	+	8.35222i	0.224657	+	0.273001i
$937$	−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	−0.570215	−	0.821496i	$-0.693140\pi$
$941$	7.70821	−	7.70821i	0.251281	−	0.251281i	0.821496	+	0.570215i	$0.193140\pi$
$942$	−31.6969	+	5.43833i	−1.03274	+	0.177190i
$943$	−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	0.283904	−	0.958853i	$-0.408370\pi$
$947$	−20.7705	−	20.7705i	−0.674949	−	0.674949i	−0.958853	+	0.283904i	$0.908370\pi$
$948$	−2.36442	+	3.34379i	−0.0767928	+	0.108601i
$949$	14.1939	+	39.0391i	0.460752	+	1.26726i
$950$			29.7074i			0.963837i
$951$	30.8006	−	5.28454i	0.998776	−	0.171363i
$952$	−5.15653			−0.167124
$953$	41.5409			1.34564			0.672821	−	0.739805i	$-0.265082\pi$
$953$	41.5409			1.34564			0.672821	+	0.739805i	$0.265082\pi$
$954$	−3.72040	+	7.78990i	−0.120452	+	0.252207i
$955$	−22.3516	−	22.3516i	−0.723280	−	0.723280i
$956$	−7.48463	−	7.48463i	−0.242070	−	0.242070i
$957$	34.4105	−	5.90390i	1.11233	−	0.190846i
$958$	−36.4145			−1.17650
$959$	−17.1264			−0.553042
$960$	0.924526	+	5.38853i	0.0298390	+	0.173914i
$961$		−	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
$969$	9.03916	+	52.6841i	0.290380	+	1.69246i
$970$	−8.16211	+	8.16211i	−0.262070	+	0.262070i
$971$			15.6680i			0.502811i	0.967882	+	0.251405i	$0.0808927\pi$
$971$			15.6680i			0.502811i	−0.967882	+	0.251405i	$0.919107\pi$
$972$	−1.00000	−	15.5563i	−0.0320750	−	0.498970i
$973$	6.02127	−	6.02127i	0.193033	−	0.193033i
$974$	26.1121			0.836684
$975$	−15.3658	−	26.9218i	−0.492099	−	0.862186i
$976$	−2.47115			−0.0790997
$977$	−3.39698	+	3.39698i	−0.108679	+	0.108679i	−0.759355	−	0.650676i	$-0.774485\pi$
$977$	−3.39698	+	3.39698i	−0.108679	+	0.108679i	0.650676	+	0.759355i	$0.274485\pi$
$978$	−10.3835	+	14.6845i	−0.332027	+	0.469557i
$979$		−	64.7596i		−	2.06973i
$980$	2.23200	−	2.23200i	0.0712988	−	0.0712988i
$981$	22.6487	−	47.4226i	0.723116	−	1.51409i
$982$	1.10738	−	1.10738i	0.0353380	−	0.0353380i
$983$	0.279343	+	0.279343i	0.00890965	+	0.00890965i	0.711548	−	0.702638i	$-0.247995\pi$
$983$	0.279343	+	0.279343i	0.00890965	+	0.00890965i	−0.702638	+	0.711548i	$0.747995\pi$
$984$	−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
$990$	−40.9489	−	19.5569i	−1.30144	−	0.621558i
$991$	−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
$993$	5.31306	+	30.9668i	0.168605	+	0.982701i
$994$	−2.25768	−	2.25768i	−0.0716094	−	0.0716094i
$995$	21.7854	+	21.7854i	0.690643	+	0.690643i
$996$	−2.55012	−	14.8632i	−0.0808036	−	0.470958i
$997$	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
$999$	0.0920797	+	0.164711i	0.00291327	+	0.00521123i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.41421 - 1.00000i) q^{3} -1.00000i q^{4} +(-2.23200 + 2.23200i) q^{5} +(-1.70711 + 0.292893i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.41421 - 1.00000i) q^{3} -1.00000i q^{4} +(-2.23200 + 2.23200i) 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} +3.15653i q^{10} +(3.38853 + 3.38853i) q^{11} +(-1.00000 + 1.41421i) q^{12} +(-1.52490 + 3.26721i) q^{13} -1.00000i q^{14} +(5.38853 - 0.924526i) q^{15} -1.00000 q^{16} +5.15653 q^{17} +(2.70711 + 1.29289i) q^{18} +(-4.23200 - 4.23200i) q^{19} +(2.23200 + 2.23200i) q^{20} +(-1.70711 + 0.292893i) q^{21} +4.79211 q^{22} +6.67033 q^{23} +(0.292893 + 1.70711i) 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} +(-1.40358 - 8.18065i) 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} +(5.42374 - 3.09564i) 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} +(-8.54506 - 4.08106i) 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} +(-2.53553 - 4.53553i) q^{54} -15.1264 q^{55} -1.00000 q^{56} +(1.75295 + 10.2170i) q^{57} +(2.97432 + 2.97432i) q^{58} +(2.48463 + 2.48463i) q^{59} +(-0.924526 - 5.38853i) q^{60} +2.47115 q^{61} +4.82843 q^{62} +(2.70711 + 1.29289i) 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} +(1.29289 - 2.70711i) 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} +(1.64622 - 6.02412i) 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} +(0.292893 + 1.70711i) 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} +(-1.41421 - 8.24264i) q^{93} +6.00000 q^{94} +18.8917 q^{95} +(1.70711 - 0.292893i) q^{96} +(2.58579 + 2.58579i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(-6.19569 + 12.9728i) 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	\( 8 q - 4 q^{5} - 8 q^{6} + 8 q^{9} - 8 q^{11} - 8 q^{12} - 4 q^{13} + 8 q^{15} - 8 q^{16} + 20 q^{17} + 16 q^{18} - 20 q^{19} + 4 q^{20} - 8 q^{21} + 12 q^{22} - 12 q^{23} + 8 q^{24} - 4 q^{26} + 4 q^{30} + 16 q^{31} - 20 q^{33} + 4 q^{34} - 24 q^{37} - 4 q^{38} + 4 q^{39} + 4 q^{40} - 20 q^{41} - 8 q^{42} - 8 q^{44} - 12 q^{45} + 4 q^{46} + 24 q^{50} - 8 q^{51} + 8 q^{52} + 8 q^{54} - 12 q^{55} - 8 q^{56} - 16 q^{57} + 20 q^{61} + 16 q^{62} + 16 q^{63} + 28 q^{65} + 16 q^{66} + 24 q^{67} - 8 q^{69} + 4 q^{70} + 28 q^{71} + 16 q^{72} + 16 q^{73} - 36 q^{75} - 20 q^{76} + 12 q^{77} - 12 q^{78} + 24 q^{79} + 4 q^{80} - 56 q^{81} - 28 q^{83} + 8 q^{84} + 16 q^{85} + 12 q^{86} - 4 q^{87} - 16 q^{90} - 4 q^{91} + 48 q^{94} + 92 q^{95} + 8 q^{96} + 32 q^{97} - 32 q^{99}+O(q^{100}) \) 8 * q - 4 * q^5 - 8 * q^6 + 8 * q^9 - 8 * q^11 - 8 * q^12 - 4 * q^13 + 8 * q^15 - 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 - 20 * q^33 + 4 * q^34 - 24 * q^37 - 4 * q^38 + 4 * q^39 + 4 * q^40 - 20 * q^41 - 8 * q^42 - 8 * q^44 - 12 * q^45 + 4 * q^46 + 24 * q^50 - 8 * q^51 + 8 * q^52 + 8 * q^54 - 12 * q^55 - 8 * q^56 - 16 * q^57 + 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 - 12 * 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 + 48 * q^94 + 92 * q^95 + 8 * q^96 + 32 * q^97 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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