LMFDB - Embedded newform 546.2.p.d.239.5

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:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 8 x^{18} - 20 x^{17} + 56 x^{16} - 140 x^{15} + 288 x^{14} - 532 x^{13} + \cdots + 59049 $ x^20 - 4x^19 + 8x^18 - 20x^17 + 56x^16 - 140x^15 + 288x^14 - 532x^13 + 1065x^12 - 2080x^11 + 3712x^10 - 6240x^9 + 9585x^8 - 14364x^7 + 23328x^6 - 34020x^5 + 40824x^4 - 43740x^3 + 52488x^2 - 78732*x + 59049
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			239.5
Root			$-1.39758 + 1.02312i$ of defining polynomial
Character	$\chi$	$=$	546.239
Dual form			546.2.p.d.281.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(1.71169 - 0.264783i) q^{3} +1.00000i q^{4} +(-0.790081 - 0.790081i) q^{5} +(-1.39758 - 1.02312i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.85978 - 0.906454i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(1.71169 - 0.264783i) q^{3} +1.00000i q^{4} +(-0.790081 - 0.790081i) q^{5} +(-1.39758 - 1.02312i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.85978 - 0.906454i) q^{9} +1.11734i q^{10} +(3.45508 - 3.45508i) q^{11} +(0.264783 + 1.71169i) q^{12} +(-1.18766 + 3.40433i) q^{13} +1.00000i q^{14} +(-1.56157 - 1.14317i) q^{15} -1.00000 q^{16} -0.401161 q^{17} +(-2.66313 - 1.38121i) q^{18} +(4.88536 - 4.88536i) q^{19} +(0.790081 - 0.790081i) q^{20} +(-1.39758 - 1.02312i) q^{21} -4.88622 q^{22} -6.12089 q^{23} +(1.02312 - 1.39758i) q^{24} -3.75155i q^{25} +(3.24703 - 1.56742i) q^{26} +(4.65505 - 2.30879i) q^{27} +(0.707107 - 0.707107i) q^{28} +1.16528i q^{29} +(0.295853 + 1.91255i) q^{30} +(2.88418 - 2.88418i) q^{31} +(0.707107 + 0.707107i) q^{32} +(4.99918 - 6.82887i) q^{33} +(0.283664 + 0.283664i) q^{34} +1.11734i q^{35} +(0.906454 + 2.85978i) q^{36} +(-4.48595 - 4.48595i) q^{37} -6.90894 q^{38} +(-1.13151 + 6.14164i) q^{39} -1.11734 q^{40} +(6.76896 + 6.76896i) q^{41} +(0.264783 + 1.71169i) q^{42} +2.74375i q^{43} +(3.45508 + 3.45508i) q^{44} +(-2.97563 - 1.54328i) q^{45} +(4.32812 + 4.32812i) q^{46} +(5.67285 - 5.67285i) q^{47} +(-1.71169 + 0.264783i) q^{48} +1.00000i q^{49} +(-2.65274 + 2.65274i) q^{50} +(-0.686665 + 0.106221i) q^{51} +(-3.40433 - 1.18766i) q^{52} +3.46244i q^{53} +(-4.92418 - 1.65905i) q^{54} -5.45958 q^{55} -1.00000 q^{56} +(7.06867 - 9.65578i) q^{57} +(0.823979 - 0.823979i) q^{58} +(-8.03324 + 8.03324i) q^{59} +(1.14317 - 1.56157i) q^{60} -0.717748 q^{61} -4.07885 q^{62} +(-2.66313 - 1.38121i) q^{63} -1.00000i q^{64} +(3.62804 - 1.75134i) q^{65} +(-8.36370 + 1.29379i) q^{66} +(-0.693547 + 0.693547i) q^{67} -0.401161i q^{68} +(-10.4771 + 1.62071i) q^{69} +(0.790081 - 0.790081i) q^{70} +(5.15463 + 5.15463i) q^{71} +(1.38121 - 2.66313i) q^{72} +(-0.0455596 - 0.0455596i) q^{73} +6.34409i q^{74} +(-0.993346 - 6.42149i) q^{75} +(4.88536 + 4.88536i) q^{76} -4.88622 q^{77} +(5.14289 - 3.54270i) q^{78} -4.24647 q^{79} +(0.790081 + 0.790081i) q^{80} +(7.35668 - 5.18452i) q^{81} -9.57276i q^{82} +(-1.74175 - 1.74175i) q^{83} +(1.02312 - 1.39758i) q^{84} +(0.316950 + 0.316950i) q^{85} +(1.94012 - 1.94012i) q^{86} +(0.308547 + 1.99461i) q^{87} -4.88622i q^{88} +(8.55005 - 8.55005i) q^{89} +(1.01282 + 3.19535i) q^{90} +(3.24703 - 1.56742i) q^{91} -6.12089i q^{92} +(4.17315 - 5.70051i) q^{93} -8.02263 q^{94} -7.71965 q^{95} +(1.39758 + 1.02312i) q^{96} +(-7.03452 + 7.03452i) q^{97} +(0.707107 - 0.707107i) q^{98} +(6.74889 - 13.0126i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{5} + 4 q^{6} - 8 q^{9}+O(q^{10}) $ 20 * q + 4 * q^5 + 4 * q^6 - 8 * q^9	$ 20 q + 4 q^{5} + 4 q^{6} - 8 q^{9} + 16 q^{11} + 8 q^{12} + 4 q^{13} - 4 q^{15} - 20 q^{16} - 12 q^{17} - 16 q^{18} + 12 q^{19} - 4 q^{20} + 4 q^{21} - 12 q^{22} + 4 q^{23} - 4 q^{24} + 24 q^{27} - 12 q^{30} - 8 q^{31} + 16 q^{33} - 4 q^{34} + 32 q^{37} + 4 q^{38} + 8 q^{39} - 4 q^{40} - 8 q^{41} + 8 q^{42} + 16 q^{44} - 32 q^{45} - 8 q^{46} - 32 q^{50} + 8 q^{51} - 8 q^{52} + 20 q^{54} + 28 q^{55} - 20 q^{56} + 36 q^{57} - 4 q^{58} - 20 q^{59} - 4 q^{60} - 4 q^{61} - 48 q^{62} - 16 q^{63} - 52 q^{65} - 36 q^{67} - 68 q^{69} - 4 q^{70} + 28 q^{71} - 8 q^{72} - 24 q^{73} + 76 q^{75} + 12 q^{76} - 12 q^{77} + 56 q^{78} - 64 q^{79} - 4 q^{80} + 32 q^{81} + 24 q^{83} - 4 q^{84} + 24 q^{85} - 4 q^{86} + 4 q^{87} + 4 q^{89} + 8 q^{90} + 16 q^{93} - 40 q^{94} + 76 q^{95} - 4 q^{96} + 32 q^{97} - 36 q^{99}+O(q^{100}) $ 20 * q + 4 * q^5 + 4 * q^6 - 8 * q^9 + 16 * q^11 + 8 * q^12 + 4 * q^13 - 4 * q^15 - 20 * q^16 - 12 * q^17 - 16 * q^18 + 12 * q^19 - 4 * q^20 + 4 * q^21 - 12 * q^22 + 4 * q^23 - 4 * q^24 + 24 * q^27 - 12 * q^30 - 8 * q^31 + 16 * q^33 - 4 * q^34 + 32 * q^37 + 4 * q^38 + 8 * q^39 - 4 * q^40 - 8 * q^41 + 8 * q^42 + 16 * q^44 - 32 * q^45 - 8 * q^46 - 32 * q^50 + 8 * q^51 - 8 * q^52 + 20 * q^54 + 28 * q^55 - 20 * q^56 + 36 * q^57 - 4 * q^58 - 20 * q^59 - 4 * q^60 - 4 * q^61 - 48 * q^62 - 16 * q^63 - 52 * q^65 - 36 * q^67 - 68 * q^69 - 4 * q^70 + 28 * q^71 - 8 * q^72 - 24 * q^73 + 76 * q^75 + 12 * q^76 - 12 * q^77 + 56 * q^78 - 64 * q^79 - 4 * q^80 + 32 * q^81 + 24 * q^83 - 4 * q^84 + 24 * q^85 - 4 * q^86 + 4 * q^87 + 4 * q^89 + 8 * q^90 + 16 * q^93 - 40 * q^94 + 76 * q^95 - 4 * q^96 + 32 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	1.71169	−	0.264783i	0.988246	−	0.152873i
$3$	1.71169	−	0.264783i	0.988246	−	0.152873i
$4$			1.00000i			0.500000i
$5$	−0.790081	−	0.790081i	−0.353335	−	0.353335i	0.508014	−	0.861349i	$-0.330380\pi$
$5$	−0.790081	−	0.790081i	−0.353335	−	0.353335i	−0.861349	+	0.508014i	$0.830380\pi$
$6$	−1.39758	−	1.02312i	−0.570559	−	0.417687i
$7$	−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
$9$	2.85978	−	0.906454i	0.953260	−	0.302151i
$10$			1.11734i			0.353335i
$11$	3.45508	−	3.45508i	1.04174	−	1.04174i	0.0426547	−	0.999090i	$-0.486418\pi$
$11$	3.45508	−	3.45508i	1.04174	−	1.04174i	0.999090	−	0.0426547i	$-0.0135815\pi$
$12$	0.264783	+	1.71169i	0.0764363	+	0.494123i
$13$	−1.18766	+	3.40433i	−0.329399	+	0.944191i
$13$	−1.18766	+	3.40433i	−0.329399	+	0.944191i
$14$			1.00000i			0.267261i
$15$	−1.56157	−	1.14317i	−0.403197	−	0.295166i
$16$	−1.00000			−0.250000
$17$	−0.401161			−0.0972959			−0.0486480	−	0.998816i	$-0.515491\pi$
$17$	−0.401161			−0.0972959			−0.0486480	+	0.998816i	$0.515491\pi$
$18$	−2.66313	−	1.38121i	−0.627706	−	0.325554i
$19$	4.88536	−	4.88536i	1.12078	−	1.12078i	0.129153	−	0.991625i	$-0.458774\pi$
$19$	4.88536	−	4.88536i	1.12078	−	1.12078i	0.991625	−	0.129153i	$-0.0412258\pi$
$20$	0.790081	−	0.790081i	0.176667	−	0.176667i
$21$	−1.39758	−	1.02312i	−0.304977	−	0.223263i
$22$	−4.88622			−1.04174
$23$	−6.12089			−1.27629			−0.638147	−	0.769915i	$-0.720299\pi$
$23$	−6.12089			−1.27629			−0.638147	+	0.769915i	$0.720299\pi$
$24$	1.02312	−	1.39758i	0.208843	−	0.285280i
$25$		−	3.75155i		−	0.750309i
$26$	3.24703	−	1.56742i	0.636795	−	0.307396i
$27$	4.65505	−	2.30879i	0.895865	−	0.444327i
$28$	0.707107	−	0.707107i	0.133631	−	0.133631i
$29$			1.16528i			0.216388i	0.994130	+	0.108194i	$0.0345067\pi$
$29$			1.16528i			0.216388i	−0.994130	+	0.108194i	$0.965493\pi$
$30$	0.295853	+	1.91255i	0.0540152	+	0.349182i
$31$	2.88418	−	2.88418i	0.518014	−	0.518014i	−0.398956	−	0.916970i	$-0.630627\pi$
$31$	2.88418	−	2.88418i	0.518014	−	0.518014i	0.916970	+	0.398956i	$0.130627\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	4.99918	−	6.82887i	0.870246	−	1.18875i
$34$	0.283664	+	0.283664i	0.0486480	+	0.0486480i
$35$			1.11734i			0.188865i
$36$	0.906454	+	2.85978i	0.151076	+	0.476630i
$37$	−4.48595	−	4.48595i	−0.737486	−	0.737486i	0.234605	−	0.972091i	$-0.424620\pi$
$37$	−4.48595	−	4.48595i	−0.737486	−	0.737486i	−0.972091	+	0.234605i	$0.924620\pi$
$38$	−6.90894			−1.12078
$39$	−1.13151	+	6.14164i	−0.181186	+	0.983449i
$40$	−1.11734			−0.176667
$41$	6.76896	+	6.76896i	1.05713	+	1.05713i	0.998266	+	0.0588688i	$0.0187494\pi$
$41$	6.76896	+	6.76896i	1.05713	+	1.05713i	0.0588688	+	0.998266i	$0.481251\pi$
$42$	0.264783	+	1.71169i	0.0408569	+	0.264120i
$43$			2.74375i			0.418418i	0.977871	+	0.209209i	$0.0670889\pi$
$43$			2.74375i			0.418418i	−0.977871	+	0.209209i	$0.932911\pi$
$44$	3.45508	+	3.45508i	0.520872	+	0.520872i
$45$	−2.97563	−	1.54328i	−0.443580	−	0.230059i
$46$	4.32812	+	4.32812i	0.638147	+	0.638147i
$47$	5.67285	−	5.67285i	0.827471	−	0.827471i	−0.159696	−	0.987166i	$-0.551051\pi$
$47$	5.67285	−	5.67285i	0.827471	−	0.827471i	0.987166	+	0.159696i	$0.0510513\pi$
$48$	−1.71169	+	0.264783i	−0.247061	+	0.0382181i
$49$			1.00000i			0.142857i
$50$	−2.65274	+	2.65274i	−0.375155	+	0.375155i
$51$	−0.686665	+	0.106221i	−0.0961523	+	0.0148739i
$52$	−3.40433	−	1.18766i	−0.472095	−	0.164699i
$53$			3.46244i			0.475603i	0.971314	+	0.237801i	$0.0764267\pi$
$53$			3.46244i			0.475603i	−0.971314	+	0.237801i	$0.923573\pi$
$54$	−4.92418	−	1.65905i	−0.670096	−	0.225769i
$55$	−5.45958			−0.736169
$56$	−1.00000			−0.133631
$57$	7.06867	−	9.65578i	0.936268	−	1.27894i
$58$	0.823979	−	0.823979i	0.108194	−	0.108194i
$59$	−8.03324	+	8.03324i	−1.04584	+	1.04584i	−0.0469418	+	0.998898i	$0.514948\pi$
$59$	−8.03324	+	8.03324i	−1.04584	+	1.04584i	−0.998898	+	0.0469418i	$0.985052\pi$
$60$	1.14317	−	1.56157i	0.147583	−	0.201598i
$61$	−0.717748			−0.0918983			−0.0459491	−	0.998944i	$-0.514631\pi$
$61$	−0.717748			−0.0918983			−0.0459491	+	0.998944i	$0.514631\pi$
$62$	−4.07885			−0.518014
$63$	−2.66313	−	1.38121i	−0.335523	−	0.174016i
$64$		−	1.00000i		−	0.125000i
$65$	3.62804	−	1.75134i	0.450003	−	0.217228i
$66$	−8.36370	+	1.29379i	−1.02950	+	0.159254i
$67$	−0.693547	+	0.693547i	−0.0847303	+	0.0847303i	−0.748202	−	0.663471i	$-0.769082\pi$
$67$	−0.693547	+	0.693547i	−0.0847303	+	0.0847303i	0.663471	+	0.748202i	$0.269082\pi$
$68$		−	0.401161i		−	0.0486480i
$69$	−10.4771	+	1.62071i	−1.26129	+	0.195110i
$70$	0.790081	−	0.790081i	0.0944327	−	0.0944327i
$71$	5.15463	+	5.15463i	0.611742	+	0.611742i	0.943400	−	0.331658i	$-0.107608\pi$
$71$	5.15463	+	5.15463i	0.611742	+	0.611742i	−0.331658	+	0.943400i	$0.607608\pi$
$72$	1.38121	−	2.66313i	0.162777	−	0.313853i
$73$	−0.0455596	−	0.0455596i	−0.00533235	−	0.00533235i	0.704436	−	0.709768i	$-0.251200\pi$
$73$	−0.0455596	−	0.0455596i	−0.00533235	−	0.00533235i	−0.709768	+	0.704436i	$0.751200\pi$
$74$			6.34409i			0.737486i
$75$	−0.993346	−	6.42149i	−0.114702	−	0.741490i
$76$	4.88536	+	4.88536i	0.560389	+	0.560389i
$77$	−4.88622			−0.556836
$78$	5.14289	−	3.54270i	0.582317	−	0.401132i
$79$	−4.24647			−0.477765			−0.238882	−	0.971048i	$-0.576781\pi$
$79$	−4.24647			−0.477765			−0.238882	+	0.971048i	$0.576781\pi$
$80$	0.790081	+	0.790081i	0.0883337	+	0.0883337i
$81$	7.35668	−	5.18452i	0.817409	−	0.576058i
$82$		−	9.57276i		−	1.05713i
$83$	−1.74175	−	1.74175i	−0.191182	−	0.191182i	0.605025	−	0.796207i	$-0.293163\pi$
$83$	−1.74175	−	1.74175i	−0.191182	−	0.191182i	−0.796207	+	0.605025i	$0.793163\pi$
$84$	1.02312	−	1.39758i	0.111631	−	0.152488i
$85$	0.316950	+	0.316950i	0.0343780	+	0.0343780i
$86$	1.94012	−	1.94012i	0.209209	−	0.209209i
$87$	0.308547	+	1.99461i	0.0330797	+	0.213844i
$88$		−	4.88622i		−	0.520872i
$89$	8.55005	−	8.55005i	0.906304	−	0.906304i	−0.0896678	−	0.995972i	$-0.528581\pi$
$89$	8.55005	−	8.55005i	0.906304	−	0.906304i	0.995972	+	0.0896678i	$0.0285805\pi$
$90$	1.01282	+	3.19535i	0.106761	+	0.336820i
$91$	3.24703	−	1.56742i	0.340381	−	0.164310i
$92$		−	6.12089i		−	0.638147i
$93$	4.17315	−	5.70051i	0.432735	−	0.591115i
$94$	−8.02263			−0.827471
$95$	−7.71965			−0.792019
$96$	1.39758	+	1.02312i	0.142640	+	0.104422i
$97$	−7.03452	+	7.03452i	−0.714247	+	0.714247i	−0.967421	−	0.253174i	$-0.918525\pi$
$97$	−7.03452	+	7.03452i	−0.714247	+	0.714247i	0.253174	+	0.967421i	$0.418525\pi$
$98$	0.707107	−	0.707107i	0.0714286	−	0.0714286i
$99$	6.74889	−	13.0126i	0.678289	−	1.30782i
$100$	3.75155			0.375155
$101$	−3.38548			−0.336868			−0.168434	−	0.985713i	$-0.553871\pi$
$101$	−3.38548			−0.336868			−0.168434	+	0.985713i	$0.553871\pi$
$102$	0.560655	+	0.410436i	0.0555131	+	0.0406392i
$103$			13.1959i			1.30023i	0.759835	+	0.650116i	$0.225280\pi$
$103$			13.1959i			1.30023i	−0.759835	+	0.650116i	$0.774720\pi$
$104$	1.56742	+	3.24703i	0.153698	+	0.318397i
$105$	0.295853	+	1.91255i	0.0288723	+	0.186645i
$106$	2.44831	−	2.44831i	0.237801	−	0.237801i
$107$			18.9481i			1.83178i	0.401432	+	0.915889i	$0.368513\pi$
$107$			18.9481i			1.83178i	−0.401432	+	0.915889i	$0.631487\pi$
$108$	2.30879	+	4.65505i	0.222164	+	0.447932i
$109$	−5.81740	+	5.81740i	−0.557206	+	0.557206i	−0.928511	−	0.371305i	$-0.878910\pi$
$109$	−5.81740	+	5.81740i	−0.557206	+	0.557206i	0.371305	+	0.928511i	$0.378910\pi$
$110$	3.86050	+	3.86050i	0.368085	+	0.368085i
$111$	−8.86637	−	6.49076i	−0.841559	−	0.616076i
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$			14.8579i			1.39771i	0.715262	+	0.698856i	$0.246307\pi$
$113$			14.8579i			1.39771i	−0.715262	+	0.698856i	$0.753693\pi$
$114$	−11.8260	+	1.82937i	−1.10760	+	0.171336i
$115$	4.83599	+	4.83599i	0.450959	+	0.450959i
$116$	−1.16528			−0.108194
$117$	−0.310587	+	10.8122i	−0.0287138	+	0.999588i
$118$	11.3607			1.04584
$119$	0.283664	+	0.283664i	0.0260034	+	0.0260034i
$120$	−1.91255	+	0.295853i	−0.174591	+	0.0270076i
$121$		−	12.8751i		−	1.17046i
$122$	0.507525	+	0.507525i	0.0459491	+	0.0459491i
$123$	13.3787	+	9.79407i	1.20632	+	0.883102i
$124$	2.88418	+	2.88418i	0.259007	+	0.259007i
$125$	−6.91443	+	6.91443i	−0.618445	+	0.618445i
$126$	0.906454	+	2.85978i	0.0807534	+	0.254769i
$127$			2.26219i			0.200737i	0.994950	+	0.100368i	$0.0320021\pi$
$127$			2.26219i			0.200737i	−0.994950	+	0.100368i	$0.967998\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	0.726498	+	4.69645i	0.0639646	+	0.413500i
$130$	−3.80380	−	1.32703i	−0.333615	−	0.116388i
$131$		−	12.7200i		−	1.11135i	−0.831400	−	0.555675i	$-0.812460\pi$
$131$		−	12.7200i		−	1.11135i	0.831400	−	0.555675i	$-0.187540\pi$
$132$	6.82887	+	4.99918i	0.594377	+	0.435123i
$133$	−6.90894			−0.599081
$134$	0.980824			0.0847303
$135$	−5.50200	−	1.85373i	−0.473536	−	0.159544i
$136$	−0.283664	+	0.283664i	−0.0243240	+	0.0243240i
$137$	−15.4491	+	15.4491i	−1.31991	+	1.31991i	−0.406065	+	0.913844i	$0.633099\pi$
$137$	−15.4491	+	15.4491i	−1.31991	+	1.31991i	−0.913844	+	0.406065i	$0.866901\pi$
$138$	8.55442	+	6.26240i	0.728201	+	0.533091i
$139$	2.96141			0.251184			0.125592	−	0.992082i	$-0.459917\pi$
$139$	2.96141			0.251184			0.125592	+	0.992082i	$0.459917\pi$
$140$	−1.11734			−0.0944327
$141$	8.20810	−	11.2123i	0.691247	−	0.944242i
$142$		−	7.28975i		−	0.611742i
$143$	7.65875	+	15.8657i	0.640457	+	1.32676i
$144$	−2.85978	+	0.906454i	−0.238315	+	0.0755379i
$145$	0.920667	−	0.920667i	0.0764572	−	0.0764572i
$146$			0.0644310i			0.00533235i
$147$	0.264783	+	1.71169i	0.0218389	+	0.141178i
$148$	4.48595	−	4.48595i	0.368743	−	0.368743i
$149$	3.74411	+	3.74411i	0.306730	+	0.306730i	0.843640	−	0.536910i	$-0.180409\pi$
$149$	3.74411	+	3.74411i	0.306730	+	0.306730i	−0.536910	+	0.843640i	$0.680409\pi$
$150$	−3.83828	+	5.24308i	−0.313394	+	0.428096i
$151$	12.1505	+	12.1505i	0.988794	+	0.988794i	0.999938	−	0.0111437i	$-0.00354723\pi$
$151$	12.1505	+	12.1505i	0.988794	+	0.988794i	−0.0111437	+	0.999938i	$0.503547\pi$
$152$		−	6.90894i		−	0.560389i
$153$	−1.14723	+	0.363634i	−0.0927483	+	0.0293981i
$154$	3.45508	+	3.45508i	0.278418	+	0.278418i
$155$	−4.55747			−0.366065
$156$	−6.14164	−	1.13151i	−0.491724	−	0.0905929i
$157$	20.3675			1.62550			0.812750	−	0.582613i	$-0.197970\pi$
$157$	20.3675			1.62550			0.812750	+	0.582613i	$0.197970\pi$
$158$	3.00271	+	3.00271i	0.238882	+	0.238882i
$159$	0.916795	+	5.92663i	0.0727066	+	0.470012i
$160$		−	1.11734i		−	0.0883337i
$161$	4.32812	+	4.32812i	0.341104	+	0.341104i
$162$	−8.86797	−	1.53595i	−0.696733	−	0.120676i
$163$	8.52261	+	8.52261i	0.667542	+	0.667542i	0.957147	−	0.289604i	$-0.0935237\pi$
$163$	8.52261	+	8.52261i	0.667542	+	0.667542i	−0.289604	+	0.957147i	$0.593524\pi$
$164$	−6.76896	+	6.76896i	−0.528567	+	0.528567i
$165$	−9.34511	+	1.44560i	−0.727516	+	0.112540i
$166$			2.46321i			0.191182i
$167$	12.4225	−	12.4225i	0.961284	−	0.961284i	−0.0379938	−	0.999278i	$-0.512097\pi$
$167$	12.4225	−	12.4225i	0.961284	−	0.961284i	0.999278	+	0.0379938i	$0.0120967\pi$
$168$	−1.71169	+	0.264783i	−0.132060	+	0.0204285i
$169$	−10.1789	−	8.08639i	−0.782993	−	0.622030i
$170$		−	0.448235i		−	0.0343780i
$171$	9.54269	−	18.3994i	0.729748	−	1.40704i
$172$	−2.74375			−0.209209
$173$	21.8487			1.66112			0.830562	−	0.556926i	$-0.188019\pi$
$173$	21.8487			1.66112			0.830562	+	0.556926i	$0.188019\pi$
$174$	1.19222	−	1.62857i	0.0903822	−	0.123462i
$175$	−2.65274	+	2.65274i	−0.200529	+	0.200529i
$176$	−3.45508	+	3.45508i	−0.260436	+	0.260436i
$177$	−11.6234	+	15.8775i	−0.873666	+	1.19343i
$178$	−12.0916			−0.906304
$179$	−13.0946			−0.978737			−0.489369	−	0.872077i	$-0.662773\pi$
$179$	−13.0946			−0.978737			−0.489369	+	0.872077i	$0.662773\pi$
$180$	1.54328	−	2.97563i	0.115030	−	0.221790i
$181$			18.6617i			1.38711i	0.720403	+	0.693556i	$0.243957\pi$
$181$			18.6617i			1.38711i	−0.720403	+	0.693556i	$0.756043\pi$
$182$	−3.40433	−	1.18766i	−0.252346	−	0.0880355i
$183$	−1.22856	+	0.190048i	−0.0908181	+	0.0140487i
$184$	−4.32812	+	4.32812i	−0.319073	+	0.319073i
$185$			7.08853i			0.521159i
$186$	−6.98173	+	1.08001i	−0.511925	+	0.0791901i
$187$	−1.38604	+	1.38604i	−0.101358	+	0.101358i
$188$	5.67285	+	5.67285i	0.413735	+	0.413735i
$189$	−4.92418	−	1.65905i	−0.358181	−	0.120678i
$190$	5.45862	+	5.45862i	0.396010	+	0.396010i
$191$			7.22379i			0.522695i	0.965245	+	0.261347i	$0.0841668\pi$
$191$			7.22379i			0.522695i	−0.965245	+	0.261347i	$0.915833\pi$
$192$	−0.264783	−	1.71169i	−0.0191091	−	0.123531i
$193$	−19.1571	−	19.1571i	−1.37896	−	1.37896i	−0.846387	−	0.532568i	$-0.821227\pi$
$193$	−19.1571	−	19.1571i	−1.37896	−	1.37896i	−0.532568	−	0.846387i	$-0.678773\pi$
$194$	9.94831			0.714247
$195$	5.74637	−	3.95841i	0.411506	−	0.283467i
$196$	−1.00000			−0.0714286
$197$	−17.1364	−	17.1364i	−1.22092	−	1.22092i	−0.967307	−	0.253610i	$-0.918382\pi$
$197$	−17.1364	−	17.1364i	−1.22092	−	1.22092i	−0.253610	−	0.967307i	$-0.581618\pi$
$198$	−13.9735	+	4.42913i	−0.993053	+	0.314765i
$199$			9.75133i			0.691253i	0.938372	+	0.345627i	$0.112334\pi$
$199$			9.75133i			0.691253i	−0.938372	+	0.345627i	$0.887666\pi$
$200$	−2.65274	−	2.65274i	−0.187577	−	0.187577i
$201$	−1.00350	+	1.37078i	−0.0707814	+	0.0966873i
$202$	2.39390	+	2.39390i	0.168434	+	0.168434i
$203$	0.823979	−	0.823979i	0.0578320	−	0.0578320i
$204$	−0.106221	−	0.686665i	−0.00743694	−	0.0480762i
$205$		−	10.6961i		−	0.747045i
$206$	9.33092	−	9.33092i	0.650116	−	0.650116i
$207$	−17.5044	+	5.54830i	−1.21664	+	0.385634i
$208$	1.18766	−	3.40433i	0.0823496	−	0.236048i
$209$		−	33.7586i		−	2.33513i
$210$	1.14317	−	1.56157i	0.0788865	−	0.107759i
$211$	7.32056			0.503968			0.251984	−	0.967731i	$-0.418917\pi$
$211$	7.32056			0.503968			0.251984	+	0.967731i	$0.418917\pi$
$212$	−3.46244			−0.237801
$213$	10.1880	+	7.45828i	0.698070	+	0.511033i
$214$	13.3983	−	13.3983i	0.915889	−	0.915889i
$215$	2.16778	−	2.16778i	0.147842	−	0.147842i
$216$	1.65905	−	4.92418i	0.112884	−	0.335048i
$217$	−4.07885			−0.276890
$218$	8.22704			0.557206
$219$	−0.0900475	−	0.0659206i	−0.00608484	−	0.00445450i
$220$		−	5.45958i		−	0.368085i
$221$	0.476445	−	1.36569i	0.0320491	−	0.0918659i
$222$	1.67981	+	10.8591i	0.112741	+	0.728818i
$223$	−5.34679	+	5.34679i	−0.358047	+	0.358047i	−0.863093	−	0.505045i	$-0.831476\pi$
$223$	−5.34679	+	5.34679i	−0.358047	+	0.358047i	0.505045	+	0.863093i	$0.331476\pi$
$224$		−	1.00000i		−	0.0668153i
$225$	−3.40060	−	10.7286i	−0.226707	−	0.715240i
$226$	10.5061	−	10.5061i	0.698856	−	0.698856i
$227$	−3.12944	−	3.12944i	−0.207708	−	0.207708i	0.595584	−	0.803293i	$-0.296921\pi$
$227$	−3.12944	−	3.12944i	−0.207708	−	0.207708i	−0.803293	+	0.595584i	$0.796921\pi$
$228$	9.65578	+	7.06867i	0.639470	+	0.468134i
$229$	−18.3485	−	18.3485i	−1.21250	−	1.21250i	−0.970201	−	0.242300i	$-0.922098\pi$
$229$	−18.3485	−	18.3485i	−1.21250	−	1.21250i	−0.242300	−	0.970201i	$-0.577902\pi$
$230$		−	6.83913i		−	0.450959i
$231$	−8.36370	+	1.29379i	−0.550291	+	0.0851249i
$232$	0.823979	+	0.823979i	0.0540969	+	0.0540969i
$233$	11.2420			0.736486			0.368243	−	0.929730i	$-0.379959\pi$
$233$	11.2420			0.736486			0.368243	+	0.929730i	$0.379959\pi$
$234$	7.86499	−	7.42576i	0.514151	−	0.485437i
$235$	−8.96402			−0.584748
$236$	−8.03324	−	8.03324i	−0.522920	−	0.522920i
$237$	−7.26864	+	1.12439i	−0.472149	+	0.0730372i
$238$		−	0.401161i		−	0.0260034i
$239$	5.38574	+	5.38574i	0.348375	+	0.348375i	0.859504	−	0.511129i	$-0.170773\pi$
$239$	5.38574	+	5.38574i	0.348375	+	0.348375i	−0.511129	+	0.859504i	$0.670773\pi$
$240$	1.56157	+	1.14317i	0.100799	+	0.0737916i
$241$	−6.88932	−	6.88932i	−0.443780	−	0.443780i	0.449500	−	0.893280i	$-0.351602\pi$
$241$	−6.88932	−	6.88932i	−0.443780	−	0.443780i	−0.893280	+	0.449500i	$0.851602\pi$
$242$	−9.10407	+	9.10407i	−0.585232	+	0.585232i
$243$	11.2196	−	10.8222i	0.719738	−	0.694246i
$244$		−	0.717748i		−	0.0459491i
$245$	0.790081	−	0.790081i	0.0504764	−	0.0504764i
$246$	−2.53471	−	16.3856i	−0.161607	−	1.04471i
$247$	10.8292	+	22.4335i	0.689045	+	1.42741i
$248$		−	4.07885i		−	0.259007i
$249$	−3.44253	−	2.52015i	−0.218161	−	0.159708i
$250$	9.77847			0.618445
$251$	7.66247			0.483651			0.241825	−	0.970320i	$-0.422254\pi$
$251$	7.66247			0.483651			0.241825	+	0.970320i	$0.422254\pi$
$252$	1.38121	−	2.66313i	0.0870080	−	0.167761i
$253$	−21.1481	+	21.1481i	−1.32957	+	1.32957i
$254$	1.59961	−	1.59961i	0.100368	−	0.100368i
$255$	0.626443	+	0.458598i	0.0392294	+	0.0287185i
$256$	1.00000			0.0625000
$257$	−16.8782			−1.05283			−0.526417	−	0.850227i	$-0.676465\pi$
$257$	−16.8782			−1.05283			−0.526417	+	0.850227i	$0.676465\pi$
$258$	2.80718	−	3.83461i	0.174768	−	0.238732i
$259$			6.34409i			0.394203i
$260$	1.75134	+	3.62804i	0.108614	+	0.225002i
$261$	1.05628	+	3.33245i	0.0653818	+	0.206274i
$262$	−8.99439	+	8.99439i	−0.555675	+	0.555675i
$263$		−	8.93905i		−	0.551206i	−0.961272	−	0.275603i	$-0.911123\pi$
$263$		−	8.93905i		−	0.551206i	0.961272	−	0.275603i	$-0.0888774\pi$
$264$	−1.29379	−	8.36370i	−0.0796271	−	0.514750i
$265$	2.73561	−	2.73561i	0.168047	−	0.168047i
$266$	4.88536	+	4.88536i	0.299540	+	0.299540i
$267$	12.3712	−	16.8990i	0.757102	−	1.03420i
$268$	−0.693547	−	0.693547i	−0.0423651	−	0.0423651i
$269$		−	12.7919i		−	0.779934i	−0.920829	−	0.389967i	$-0.872486\pi$
$269$		−	12.7919i		−	0.779934i	0.920829	−	0.389967i	$-0.127514\pi$
$270$	2.57971	+	5.20128i	0.156996	+	0.316540i
$271$	8.84670	+	8.84670i	0.537399	+	0.537399i	0.922764	−	0.385365i	$-0.125925\pi$
$271$	8.84670	+	8.84670i	0.537399	+	0.537399i	−0.385365	+	0.922764i	$0.625925\pi$
$272$	0.401161			0.0243240
$273$	5.14289	−	3.54270i	0.311262	−	0.214414i
$274$	21.8484			1.31991
$275$	−12.9619	−	12.9619i	−0.781630	−	0.781630i
$276$	−1.62071	−	10.4771i	−0.0975551	−	0.630646i
$277$		−	20.8417i		−	1.25226i	−0.779720	−	0.626128i	$-0.784639\pi$
$277$		−	20.8417i		−	1.25226i	0.779720	−	0.626128i	$-0.215361\pi$
$278$	−2.09403	−	2.09403i	−0.125592	−	0.125592i
$279$	5.63374	−	10.8625i	0.337283	−	0.650321i
$280$	0.790081	+	0.790081i	0.0472163	+	0.0472163i
$281$	16.1377	−	16.1377i	0.962693	−	0.962693i	−0.0366360	−	0.999329i	$-0.511664\pi$
$281$	16.1377	−	16.1377i	0.962693	−	0.962693i	0.999329	+	0.0366360i	$0.0116642\pi$
$282$	−13.7323	+	2.12426i	−0.817745	+	0.126498i
$283$			10.2026i			0.606483i	0.952914	+	0.303242i	$0.0980690\pi$
$283$			10.2026i			0.606483i	−0.952914	+	0.303242i	$0.901931\pi$
$284$	−5.15463	+	5.15463i	−0.305871	+	0.305871i
$285$	−13.2137	+	2.04403i	−0.782710	+	0.121078i
$286$	5.80318	−	16.6343i	0.343149	−	0.983606i
$287$		−	9.57276i		−	0.565062i
$288$	2.66313	+	1.38121i	0.156926	+	0.0813886i
$289$	−16.8391			−0.990534
$290$	−1.30202			−0.0764572
$291$	−10.1783	+	13.9035i	−0.596663	+	0.815040i
$292$	0.0455596	−	0.0455596i	0.00266618	−	0.00266618i
$293$	21.5130	−	21.5130i	1.25680	−	1.25680i	0.304189	−	0.952612i	$-0.401614\pi$
$293$	21.5130	−	21.5130i	1.25680	−	1.25680i	0.952612	−	0.304189i	$-0.0983856\pi$
$294$	1.02312	−	1.39758i	0.0596695	−	0.0815085i
$295$	12.6938			0.739063
$296$	−6.34409			−0.368743
$297$	8.10650	−	24.0606i	0.470387	−	1.39614i
$298$		−	5.29497i		−	0.306730i
$299$	7.26955	−	20.8375i	0.420409	−	1.20506i
$300$	6.42149	−	0.993346i	0.370745	−	0.0573508i
$301$	1.94012	−	1.94012i	0.111827	−	0.111827i
$302$		−	17.1834i		−	0.988794i
$303$	−5.79490	+	0.896418i	−0.332908	+	0.0514979i
$304$	−4.88536	+	4.88536i	−0.280194	+	0.280194i
$305$	0.567079	+	0.567079i	0.0324709	+	0.0324709i
$306$	1.06834	+	0.554088i	0.0610732	+	0.0316751i
$307$	6.55827	+	6.55827i	0.374300	+	0.374300i	0.869041	−	0.494741i	$-0.164737\pi$
$307$	6.55827	+	6.55827i	0.374300	+	0.374300i	−0.494741	+	0.869041i	$0.664737\pi$
$308$		−	4.88622i		−	0.278418i
$309$	3.49405	+	22.5873i	0.198770	+	1.28495i
$310$	3.22262	+	3.22262i	0.183032	+	0.183032i
$311$	−13.0914			−0.742343			−0.371171	−	0.928564i	$-0.621044\pi$
$311$	−13.0914			−0.742343			−0.371171	+	0.928564i	$0.621044\pi$
$312$	3.54270	+	5.14289i	0.200566	+	0.291159i
$313$	4.62512			0.261427			0.130714	−	0.991420i	$-0.458273\pi$
$313$	4.62512			0.261427			0.130714	+	0.991420i	$0.458273\pi$
$314$	−14.4020	−	14.4020i	−0.812750	−	0.812750i
$315$	1.01282	+	3.19535i	0.0570659	+	0.180038i
$316$		−	4.24647i		−	0.238882i
$317$	−10.8188	−	10.8188i	−0.607643	−	0.607643i	0.334686	−	0.942330i	$-0.391370\pi$
$317$	−10.8188	−	10.8188i	−0.607643	−	0.607643i	−0.942330	+	0.334686i	$0.891370\pi$
$318$	3.54249	−	4.83903i	0.198653	−	0.271359i
$319$	4.02614	+	4.02614i	0.225421	+	0.225421i
$320$	−0.790081	+	0.790081i	−0.0441668	+	0.0441668i
$321$	5.01712	+	32.4332i	0.280029	+	1.81025i
$322$		−	6.12089i		−	0.341104i
$323$	−1.95982	+	1.95982i	−0.109047	+	0.109047i
$324$	5.18452	+	7.35668i	0.288029	+	0.408705i
$325$	12.7715	+	4.45557i	0.708435	+	0.247151i
$326$		−	12.0528i		−	0.667542i
$327$	−8.41725	+	11.4979i	−0.465475	+	0.635838i
$328$	9.57276			0.528567
$329$	−8.02263			−0.442302
$330$	7.63019	+	5.58580i	0.420028	+	0.307488i
$331$	−4.19602	+	4.19602i	−0.230634	+	0.230634i	−0.812957	−	0.582323i	$-0.802144\pi$
$331$	−4.19602	+	4.19602i	−0.230634	+	0.230634i	0.582323	+	0.812957i	$0.302144\pi$
$332$	1.74175	−	1.74175i	0.0955910	−	0.0955910i
$333$	−16.8951	−	8.76253i	−0.925848	−	0.480183i
$334$	−17.5681			−0.961284
$335$	1.09592			0.0598763
$336$	1.39758	+	1.02312i	0.0762442	+	0.0558157i
$337$			13.8715i			0.755631i	0.925881	+	0.377815i	$0.123325\pi$
$337$			13.8715i			0.755631i	−0.925881	+	0.377815i	$0.876675\pi$
$338$	1.47963	+	12.9155i	0.0804815	+	0.702512i
$339$	3.93412	+	25.4321i	0.213672	+	1.38128i
$340$	−0.316950	+	0.316950i	−0.0171890	+	0.0171890i
$341$		−	19.9301i		−	1.07928i
$342$	−19.7580	+	6.26263i	−1.06839	+	0.338644i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	1.94012	+	1.94012i	0.104604	+	0.104604i
$345$	9.55822	+	6.99724i	0.514597	+	0.376719i
$346$	−15.4494	−	15.4494i	−0.830562	−	0.830562i
$347$			31.5445i			1.69340i	0.532072	+	0.846699i	$0.321414\pi$
$347$			31.5445i			1.69340i	−0.532072	+	0.846699i	$0.678586\pi$
$348$	−1.99461	+	0.308547i	−0.106922	+	0.0165399i
$349$	−17.5248	−	17.5248i	−0.938083	−	0.938083i	0.0601086	−	0.998192i	$-0.480855\pi$
$349$	−17.5248	−	17.5248i	−0.938083	−	0.938083i	−0.998192	+	0.0601086i	$0.980855\pi$
$350$	3.75155			0.200529
$351$	2.33126	+	18.5894i	0.124433	+	0.992228i
$352$	4.88622			0.260436
$353$	−13.8691	−	13.8691i	−0.738177	−	0.738177i	0.234048	−	0.972225i	$-0.424803\pi$
$353$	−13.8691	−	13.8691i	−0.738177	−	0.738177i	−0.972225	+	0.234048i	$0.924803\pi$
$354$	19.4461	−	3.00813i	1.03355	−	0.159880i
$355$		−	8.14514i		−	0.432299i
$356$	8.55005	+	8.55005i	0.453152	+	0.453152i
$357$	0.560655	+	0.410436i	0.0296730	+	0.0217226i
$358$	9.25929	+	9.25929i	0.489369	+	0.489369i
$359$	−3.97606	+	3.97606i	−0.209848	+	0.209848i	−0.804203	−	0.594355i	$-0.797408\pi$
$359$	−3.97606	+	3.97606i	−0.209848	+	0.209848i	0.594355	+	0.804203i	$0.297408\pi$
$360$	−3.19535	+	1.01282i	−0.168410	+	0.0533803i
$361$		−	28.7334i		−	1.51228i
$362$	13.1958	−	13.1958i	0.693556	−	0.693556i
$363$	−3.40911	−	22.0382i	−0.178932	−	1.15671i
$364$	1.56742	+	3.24703i	0.0821551	+	0.170191i
$365$			0.0719915i			0.00376821i
$366$	1.00311	+	0.734342i	0.0524334	+	0.0383847i
$367$	−0.717511			−0.0374538			−0.0187269	−	0.999825i	$-0.505961\pi$
$367$	−0.717511			−0.0374538			−0.0187269	+	0.999825i	$0.505961\pi$
$368$	6.12089			0.319073
$369$	25.4935	+	13.2220i	1.32714	+	0.688309i
$370$	5.01235	−	5.01235i	0.260579	−	0.260579i
$371$	2.44831	−	2.44831i	0.127110	−	0.127110i
$372$	5.70051	+	4.17315i	0.295558	+	0.216368i
$373$	−9.28116			−0.480560			−0.240280	−	0.970704i	$-0.577239\pi$
$373$	−9.28116			−0.480560			−0.240280	+	0.970704i	$0.577239\pi$
$374$	1.96016			0.101358
$375$	−10.0045	+	13.6662i	−0.516632	+	0.705719i
$376$		−	8.02263i		−	0.413735i
$377$	−3.96701	−	1.38396i	−0.204311	−	0.0712777i
$378$	2.30879	+	4.65505i	0.118751	+	0.239430i
$379$	12.4251	−	12.4251i	0.638236	−	0.638236i	−0.311884	−	0.950120i	$-0.600960\pi$
$379$	12.4251	−	12.4251i	0.638236	−	0.638236i	0.950120	+	0.311884i	$0.100960\pi$
$380$		−	7.71965i		−	0.396010i
$381$	0.598989	+	3.87217i	0.0306871	+	0.198377i
$382$	5.10799	−	5.10799i	0.261347	−	0.261347i
$383$	13.7627	+	13.7627i	0.703243	+	0.703243i	0.965105	−	0.261863i	$-0.0843367\pi$
$383$	13.7627	+	13.7627i	0.703243	+	0.703243i	−0.261863	+	0.965105i	$0.584337\pi$
$384$	−1.02312	+	1.39758i	−0.0522108	+	0.0713199i
$385$	3.86050	+	3.86050i	0.196749	+	0.196749i
$386$			27.0922i			1.37896i
$387$	2.48708	+	7.84652i	0.126426	+	0.398861i
$388$	−7.03452	−	7.03452i	−0.357123	−	0.357123i
$389$	4.94989			0.250970			0.125485	−	0.992096i	$-0.459951\pi$
$389$	4.94989			0.250970			0.125485	+	0.992096i	$0.459951\pi$
$390$	−6.86231	−	1.26428i	−0.347487	−	0.0640193i
$391$	2.45546			0.124178
$392$	0.707107	+	0.707107i	0.0357143	+	0.0357143i
$393$	−3.36804	−	21.7727i	−0.169895	−	1.09829i
$394$			24.2345i			1.22092i
$395$	3.35505	+	3.35505i	0.168811	+	0.168811i
$396$	13.0126	+	6.74889i	0.653909	+	0.339144i
$397$	9.83277	+	9.83277i	0.493493	+	0.493493i	0.909405	−	0.415912i	$-0.136538\pi$
$397$	9.83277	+	9.83277i	0.493493	+	0.493493i	−0.415912	+	0.909405i	$0.636538\pi$
$398$	6.89523	−	6.89523i	0.345627	−	0.345627i
$399$	−11.8260	+	1.82937i	−0.592039	+	0.0915830i
$400$			3.75155i			0.187577i
$401$	1.18747	−	1.18747i	0.0592992	−	0.0592992i	−0.676835	−	0.736134i	$-0.736649\pi$
$401$	1.18747	−	1.18747i	0.0592992	−	0.0592992i	0.736134	+	0.676835i	$0.236649\pi$
$402$	1.67887	−	0.259706i	0.0837343	−	0.0129529i
$403$	6.39326	+	13.2441i	0.318471	+	0.659737i
$404$		−	3.38548i		−	0.168434i
$405$	−9.90856	−	1.71618i	−0.492360	−	0.0852778i
$406$	−1.16528			−0.0578320
$407$	−30.9986			−1.53654
$408$	−0.410436	+	0.560655i	−0.0203196	+	0.0277565i
$409$	−1.16592	+	1.16592i	−0.0576512	+	0.0576512i	−0.735345	−	0.677693i	$-0.762980\pi$
$409$	−1.16592	+	1.16592i	−0.0576512	+	0.0576512i	0.677693	+	0.735345i	$0.262980\pi$
$410$	−7.56325	+	7.56325i	−0.373522	+	0.373522i
$411$	−22.3535	+	30.5348i	−1.10262	+	1.50617i
$412$	−13.1959			−0.650116
$413$	11.3607			0.559025
$414$	16.3007	+	8.45423i	0.801137	+	0.415503i
$415$			2.75225i			0.135102i
$416$	−3.24703	+	1.56742i	−0.159199	+	0.0768491i
$417$	5.06902	−	0.784131i	0.248231	−	0.0383991i
$418$	−23.8709	+	23.8709i	−1.16756	+	1.16756i
$419$			13.3819i			0.653748i	0.945068	+	0.326874i	$0.105995\pi$
$419$			13.3819i			0.653748i	−0.945068	+	0.326874i	$0.894005\pi$
$420$	−1.91255	+	0.295853i	−0.0933227	+	0.0144362i
$421$	−25.6047	+	25.6047i	−1.24790	+	1.24790i	−0.291253	+	0.956646i	$0.594072\pi$
$421$	−25.6047	+	25.6047i	−1.24790	+	1.24790i	−0.956646	+	0.291253i	$0.905928\pi$
$422$	−5.17642	−	5.17642i	−0.251984	−	0.251984i
$423$	11.0809	−	21.3653i	0.538773	−	1.03882i
$424$	2.44831	+	2.44831i	0.118901	+	0.118901i
$425$			1.50498i			0.0730020i
$426$	−1.93020	−	12.4778i	−0.0935186	−	0.604551i
$427$	0.507525	+	0.507525i	0.0245608	+	0.0245608i
$428$	−18.9481			−0.915889
$429$	17.3104	+	25.1293i	0.835753	+	1.21325i
$430$	−3.06571			−0.147842
$431$	−1.57749	−	1.57749i	−0.0759852	−	0.0759852i	0.668093	−	0.744078i	$-0.267111\pi$
$431$	−1.57749	−	1.57749i	−0.0759852	−	0.0759852i	−0.744078	+	0.668093i	$0.767111\pi$
$432$	−4.65505	+	2.30879i	−0.223966	+	0.111082i
$433$			4.98342i			0.239488i	0.992805	+	0.119744i	$0.0382074\pi$
$433$			4.98342i			0.239488i	−0.992805	+	0.119744i	$0.961793\pi$
$434$	2.88418	+	2.88418i	0.138445	+	0.138445i
$435$	1.33212	−	1.81968i	0.0638703	−	0.0872468i
$436$	−5.81740	−	5.81740i	−0.278603	−	0.278603i
$437$	−29.9027	+	29.9027i	−1.43044	+	1.43044i
$438$	0.0170602	+	0.110286i	0.000815170	+	0.00526967i
$439$		−	16.2436i		−	0.775265i	−0.921814	−	0.387633i	$-0.873293\pi$
$439$		−	16.2436i		−	0.775265i	0.921814	−	0.387633i	$-0.126707\pi$
$440$	−3.86050	+	3.86050i	−0.184042	+	0.184042i
$441$	0.906454	+	2.85978i	0.0431645	+	0.136180i
$442$	−1.30258	+	0.628788i	−0.0619575	+	0.0299084i
$443$		−	36.6212i		−	1.73993i	−0.493115	−	0.869964i	$-0.664142\pi$
$443$		−	36.6212i		−	1.73993i	0.493115	−	0.869964i	$-0.335858\pi$
$444$	6.49076	−	8.86637i	0.308038	−	0.420779i
$445$	−13.5105			−0.640457
$446$	7.56150			0.358047
$447$	7.40014	+	5.41739i	0.350015	+	0.256234i
$448$	−0.707107	+	0.707107i	−0.0334077	+	0.0334077i
$449$	−15.8676	+	15.8676i	−0.748839	+	0.748839i	−0.974261	−	0.225422i	$-0.927624\pi$
$449$	−15.8676	+	15.8676i	−0.748839	+	0.748839i	0.225422	+	0.974261i	$0.427624\pi$
$450$	−5.18167	+	9.99085i	−0.244266	+	0.470973i
$451$	46.7746			2.20253
$452$	−14.8579			−0.698856
$453$	24.0152	+	17.5807i	1.12833	+	0.826012i
$454$			4.42570i			0.207708i
$455$	−3.80380	−	1.32703i	−0.178325	−	0.0622120i
$456$	−1.82937	−	11.8260i	−0.0856681	−	0.553802i
$457$	4.36244	−	4.36244i	0.204066	−	0.204066i	−0.597673	−	0.801740i	$-0.703908\pi$
$457$	4.36244	−	4.36244i	0.204066	−	0.204066i	0.801740	+	0.597673i	$0.203908\pi$
$458$			25.9487i			1.21250i
$459$	−1.86743	+	0.926198i	−0.0871640	+	0.0432312i
$460$	−4.83599	+	4.83599i	−0.225479	+	0.225479i
$461$	10.1936	+	10.1936i	0.474762	+	0.474762i	0.903452	−	0.428690i	$-0.141025\pi$
$461$	10.1936	+	10.1936i	0.474762	+	0.474762i	−0.428690	+	0.903452i	$0.641025\pi$
$462$	6.82887	+	4.99918i	0.317708	+	0.232583i
$463$	−26.1202	−	26.1202i	−1.21391	−	1.21391i	−0.969730	−	0.244181i	$-0.921481\pi$
$463$	−26.1202	−	26.1202i	−1.21391	−	1.21391i	−0.244181	−	0.969730i	$-0.578519\pi$
$464$		−	1.16528i		−	0.0540969i
$465$	−7.80098	+	1.20674i	−0.361762	+	0.0559613i
$466$	−7.94927	−	7.94927i	−0.368243	−	0.368243i
$467$	−12.0016			−0.555368			−0.277684	−	0.960673i	$-0.589567\pi$
$467$	−12.0016			−0.555368			−0.277684	+	0.960673i	$0.589567\pi$
$468$	−10.8122	−	0.310587i	−0.499794	−	0.0143569i
$469$	0.980824			0.0452902
$470$	6.33852	+	6.33852i	0.292374	+	0.292374i
$471$	34.8628	−	5.39296i	1.60639	−	0.248494i
$472$			11.3607i			0.522920i
$473$	9.47986	+	9.47986i	0.435885	+	0.435885i
$474$	5.93477	+	4.34464i	0.272593	+	0.199556i
$475$	−18.3276	−	18.3276i	−0.840930	−	0.840930i
$476$	−0.283664	+	0.283664i	−0.0130017	+	0.0130017i
$477$	3.13854	+	9.90181i	0.143704	+	0.453373i
$478$		−	7.61659i		−	0.348375i
$479$	27.0032	−	27.0032i	1.23381	−	1.23381i	0.271317	−	0.962490i	$-0.412541\pi$
$479$	27.0032	−	27.0032i	1.23381	−	1.23381i	0.962490	−	0.271317i	$-0.0874593\pi$
$480$	−0.295853	−	1.91255i	−0.0135038	−	0.0872954i
$481$	20.5995	−	9.94386i	0.939254	−	0.453401i
$482$			9.74296i			0.443780i
$483$	8.55442	+	6.26240i	0.389240	+	0.284949i
$484$	12.8751			0.585232
$485$	11.1157			0.504736
$486$	−15.5859	−	0.280987i	−0.706992	−	0.0127458i
$487$	−25.0734	+	25.0734i	−1.13618	+	1.13618i	−0.147055	+	0.989128i	$0.546980\pi$
$487$	−25.0734	+	25.0734i	−1.13618	+	1.13618i	−0.989128	+	0.147055i	$0.953020\pi$
$488$	−0.507525	+	0.507525i	−0.0229746	+	0.0229746i
$489$	16.8447	+	12.3314i	0.761745	+	0.557647i
$490$	−1.11734			−0.0504764
$491$	−5.26963			−0.237815			−0.118907	−	0.992905i	$-0.537939\pi$
$491$	−5.26963			−0.237815			−0.118907	+	0.992905i	$0.537939\pi$
$492$	−9.79407	+	13.3787i	−0.441551	+	0.603158i
$493$		−	0.467466i		−	0.0210536i
$494$	8.20549	−	23.5203i	0.369182	−	1.05823i
$495$	−15.6132	+	4.94886i	−0.701761	+	0.222435i
$496$	−2.88418	+	2.88418i	−0.129503	+	0.129503i
$497$		−	7.28975i		−	0.326990i
$498$	0.652216	+	4.21625i	0.0292265	+	0.188935i
$499$	2.56674	−	2.56674i	0.114903	−	0.114903i	−0.647317	−	0.762221i	$-0.724109\pi$
$499$	2.56674	−	2.56674i	0.114903	−	0.114903i	0.762221	+	0.647317i	$0.224109\pi$
$500$	−6.91443	−	6.91443i	−0.309223	−	0.309223i
$501$	17.9743	−	24.5528i	0.803031	−	1.09694i
$502$	−5.41818	−	5.41818i	−0.241825	−	0.241825i
$503$			9.03215i			0.402724i	0.979517	+	0.201362i	$0.0645367\pi$
$503$			9.03215i			0.402724i	−0.979517	+	0.201362i	$0.935463\pi$
$504$	−2.85978	+	0.906454i	−0.127385	+	0.0403767i
$505$	2.67480	+	2.67480i	0.119027	+	0.119027i
$506$	29.9080			1.32957
$507$	−19.5643	−	11.1462i	−0.868881	−	0.495021i
$508$	−2.26219			−0.100368
$509$	13.7882	+	13.7882i	0.611152	+	0.611152i	0.943246	−	0.332094i	$-0.107755\pi$
$509$	13.7882	+	13.7882i	0.611152	+	0.611152i	−0.332094	+	0.943246i	$0.607755\pi$
$510$	−0.118685	−	0.767240i	−0.00525546	−	0.0339740i
$511$			0.0644310i			0.00285026i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	11.4623	−	34.0208i	0.506073	−	1.50206i
$514$	11.9347	+	11.9347i	0.526417	+	0.526417i
$515$	10.4258	−	10.4258i	0.459417	−	0.459417i
$516$	−4.69645	+	0.726498i	−0.206750	+	0.0319823i
$517$		−	39.2003i		−	1.72403i
$518$	4.48595	−	4.48595i	0.197101	−	0.197101i
$519$	37.3982	−	5.78516i	1.64160	−	0.253940i
$520$	1.32703	−	3.80380i	0.0581940	−	0.166808i
$521$			23.1627i			1.01477i	0.861718	+	0.507387i	$0.169389\pi$
$521$			23.1627i			1.01477i	−0.861718	+	0.507387i	$0.830611\pi$
$522$	1.60950	−	3.10330i	0.0704459	−	0.135828i
$523$	32.4378			1.41840			0.709202	−	0.705005i	$-0.249055\pi$
$523$	32.4378			1.41840			0.709202	+	0.705005i	$0.249055\pi$
$524$	12.7200			0.555675
$525$	−3.83828	+	5.24308i	−0.167516	+	0.228827i
$526$	−6.32086	+	6.32086i	−0.275603	+	0.275603i
$527$	−1.15702	+	1.15702i	−0.0504007	+	0.0504007i
$528$	−4.99918	+	6.82887i	−0.217561	+	0.297189i
$529$	14.4653			0.628925
$530$	−3.86873			−0.168047
$531$	−15.6915	+	30.2551i	−0.680955	+	1.31296i
$532$		−	6.90894i		−	0.299540i
$533$	−31.0830	+	15.0045i	−1.34636	+	0.649918i
$534$	−20.6971	+	3.20165i	−0.895651	+	0.138549i
$535$	14.9705	−	14.9705i	0.647231	−	0.647231i
$536$			0.980824i			0.0423651i
$537$	−22.4139	+	3.46723i	−0.967233	+	0.149622i
$538$	−9.04522	+	9.04522i	−0.389967	+	0.389967i
$539$	3.45508	+	3.45508i	0.148821	+	0.148821i
$540$	1.85373	−	5.50200i	0.0797719	−	0.236768i
$541$	−4.03020	−	4.03020i	−0.173272	−	0.173272i	0.615143	−	0.788415i	$-0.289098\pi$
$541$	−4.03020	−	4.03020i	−0.173272	−	0.173272i	−0.788415	+	0.615143i	$0.789098\pi$
$542$		−	12.5111i		−	0.537399i
$543$	4.94130	+	31.9431i	0.212051	+	1.37081i
$544$	−0.283664	−	0.283664i	−0.0121620	−	0.0121620i
$545$	9.19243			0.393760
$546$	−6.14164	−	1.13151i	−0.262838	−	0.0484240i
$547$	−26.2318			−1.12159			−0.560795	−	0.827955i	$-0.689505\pi$
$547$	−26.2318			−1.12159			−0.560795	+	0.827955i	$0.689505\pi$
$548$	−15.4491	−	15.4491i	−0.659955	−	0.659955i
$549$	−2.05260	+	0.650606i	−0.0876029	+	0.0277672i
$550$			18.3309i			0.781630i
$551$	5.69282	+	5.69282i	0.242522	+	0.242522i
$552$	−6.26240	+	8.55442i	−0.266545	+	0.364100i
$553$	3.00271	+	3.00271i	0.127688	+	0.127688i
$554$	−14.7373	+	14.7373i	−0.626128	+	0.626128i
$555$	1.87692	+	12.1334i	0.0796709	+	0.515033i
$556$			2.96141i			0.125592i
$557$	16.9451	−	16.9451i	0.717988	−	0.717988i	−0.250205	−	0.968193i	$-0.580498\pi$
$557$	16.9451	−	16.9451i	0.717988	−	0.717988i	0.968193	+	0.250205i	$0.0804981\pi$
$558$	−11.6646	+	3.69729i	−0.493802	+	0.156519i
$559$	−9.34063	−	3.25865i	−0.395066	−	0.137826i
$560$		−	1.11734i		−	0.0472163i
$561$	−2.00548	+	2.73948i	−0.0846714	+	0.115661i
$562$	−22.8221			−0.962693
$563$	43.2433			1.82249			0.911243	−	0.411869i	$-0.135124\pi$
$563$	43.2433			1.82249			0.911243	+	0.411869i	$0.135124\pi$
$564$	11.2123	+	8.20810i	0.472121	+	0.345623i
$565$	11.7389	−	11.7389i	0.493860	−	0.493860i
$566$	7.21435	−	7.21435i	0.303242	−	0.303242i
$567$	−8.86797	−	1.53595i	−0.372420	−	0.0645039i
$568$	7.28975			0.305871
$569$	12.0354			0.504549			0.252274	−	0.967656i	$-0.418821\pi$
$569$	12.0354			0.504549			0.252274	+	0.967656i	$0.418821\pi$
$570$	10.7888	+	7.89812i	0.451894	+	0.330816i
$571$		−	35.0986i		−	1.46883i	−0.678699	−	0.734416i	$-0.737456\pi$
$571$		−	35.0986i		−	1.46883i	0.678699	−	0.734416i	$-0.262544\pi$
$572$	−15.8657	+	7.65875i	−0.663378	+	0.320228i
$573$	1.91274	+	12.3649i	0.0799057	+	0.516551i
$574$	−6.76896	+	6.76896i	−0.282531	+	0.282531i
$575$			22.9628i			0.957615i
$576$	−0.906454	−	2.85978i	−0.0377689	−	0.119157i
$577$	8.36869	−	8.36869i	0.348393	−	0.348393i	−0.511118	−	0.859511i	$-0.670768\pi$
$577$	8.36869	−	8.36869i	0.348393	−	0.348393i	0.859511	+	0.511118i	$0.170768\pi$
$578$	11.9070	+	11.9070i	0.495267	+	0.495267i
$579$	−37.8635	−	27.7185i	−1.57355	−	1.15194i
$580$	0.920667	+	0.920667i	0.0382286	+	0.0382286i
$581$			2.46321i			0.102191i
$582$	17.0284	−	2.63414i	0.705851	−	0.109189i
$583$	11.9630	+	11.9630i	0.495456	+	0.495456i
$584$	−0.0644310			−0.00266618
$585$	8.78789	−	8.29711i	0.363335	−	0.343043i
$586$	−30.4239			−1.25680
$587$	−23.2366	−	23.2366i	−0.959076	−	0.959076i	0.0401193	−	0.999195i	$-0.487226\pi$
$587$	−23.2366	−	23.2366i	−0.959076	−	0.959076i	−0.999195	+	0.0401193i	$0.987226\pi$
$588$	−1.71169	+	0.264783i	−0.0705890	+	0.0109195i
$589$		−	28.1805i		−	1.16116i
$590$	−8.97589	−	8.97589i	−0.369531	−	0.369531i
$591$	−33.8696	−	24.7948i	−1.39321	−	1.01992i
$592$	4.48595	+	4.48595i	0.184371	+	0.184371i
$593$	−14.2518	+	14.2518i	−0.585250	+	0.585250i	−0.936341	−	0.351091i	$-0.885811\pi$
$593$	−14.2518	+	14.2518i	−0.585250	+	0.585250i	0.351091	+	0.936341i	$0.385811\pi$
$594$	−22.7456	+	11.2813i	−0.933262	+	0.462875i
$595$		−	0.448235i		−	0.0183758i
$596$	−3.74411	+	3.74411i	−0.153365	+	0.153365i
$597$	2.58199	+	16.6913i	0.105674	+	0.683128i
$598$	−19.8747	+	9.59400i	−0.812737	+	0.392328i
$599$		−	13.6271i		−	0.556787i	−0.960467	−	0.278394i	$-0.910198\pi$
$599$		−	13.6271i		−	0.556787i	0.960467	−	0.278394i	$-0.0898020\pi$
$600$	−5.24308	−	3.83828i	−0.214048	−	0.156697i
$601$	−8.52974			−0.347936			−0.173968	−	0.984751i	$-0.555659\pi$
$601$	−8.52974			−0.347936			−0.173968	+	0.984751i	$0.555659\pi$
$602$	−2.74375			−0.111827
$603$	−1.35472	+	2.61206i	−0.0551686	+	0.106371i
$604$	−12.1505	+	12.1505i	−0.494397	+	0.494397i
$605$	−10.1724	+	10.1724i	−0.413566	+	0.413566i
$606$	4.73148	+	3.46375i	0.192203	+	0.140705i
$607$	−7.46360			−0.302938			−0.151469	−	0.988462i	$-0.548400\pi$
$607$	−7.46360			−0.302938			−0.151469	+	0.988462i	$0.548400\pi$
$608$	6.90894			0.280194
$609$	1.19222	−	1.62857i	0.0483113	−	0.0659932i
$610$		−	0.801971i		−	0.0324709i
$611$	12.5748	+	26.0497i	0.508723	+	1.05386i
$612$	−0.363634	−	1.14723i	−0.0146991	−	0.0463742i
$613$	30.4690	−	30.4690i	1.23063	−	1.23063i	0.266910	−	0.963721i	$-0.413997\pi$
$613$	30.4690	−	30.4690i	1.23063	−	1.23063i	0.963721	−	0.266910i	$-0.0860026\pi$
$614$		−	9.27479i		−	0.374300i
$615$	−2.83213	−	18.3083i	−0.114203	−	0.738264i
$616$	−3.45508	+	3.45508i	−0.139209	+	0.139209i
$617$	21.2814	+	21.2814i	0.856755	+	0.856755i	0.990954	−	0.134199i	$-0.0428462\pi$
$617$	21.2814	+	21.2814i	0.856755	+	0.856755i	−0.134199	+	0.990954i	$0.542846\pi$
$618$	13.5010	−	18.4423i	0.543089	−	0.741859i
$619$	1.08316	+	1.08316i	0.0435359	+	0.0435359i	0.728540	−	0.685004i	$-0.240199\pi$
$619$	1.08316	+	1.08316i	0.0435359	+	0.0435359i	−0.685004	+	0.728540i	$0.740199\pi$
$620$		−	4.55747i		−	0.183032i
$621$	−28.4930	+	14.1319i	−1.14339	+	0.567092i
$622$	9.25699	+	9.25699i	0.371171	+	0.371171i
$623$	−12.0916			−0.484440
$624$	1.13151	−	6.14164i	0.0452965	−	0.245862i
$625$	−7.83182			−0.313273
$626$	−3.27045	−	3.27045i	−0.130714	−	0.130714i
$627$	−8.93869	−	57.7842i	−0.356977	−	2.30768i
$628$			20.3675i			0.812750i
$629$	1.79959	+	1.79959i	0.0717544	+	0.0717544i
$630$	1.54328	−	2.97563i	0.0614859	−	0.118552i
$631$	−7.38311	−	7.38311i	−0.293917	−	0.293917i	0.544709	−	0.838625i	$-0.316640\pi$
$631$	−7.38311	−	7.38311i	−0.293917	−	0.293917i	−0.838625	+	0.544709i	$0.816640\pi$
$632$	−3.00271	+	3.00271i	−0.119441	+	0.119441i
$633$	12.5305	−	1.93836i	0.498044	−	0.0770429i
$634$			15.3001i			0.607643i
$635$	1.78731	−	1.78731i	0.0709272	−	0.0709272i
$636$	−5.92663	+	0.916795i	−0.235006	+	0.0363533i
$637$	−3.40433	−	1.18766i	−0.134884	−	0.0470569i
$638$		−	5.69382i		−	0.225421i
$639$	19.4135	+	10.0687i	0.767988	+	0.398310i
$640$	1.11734			0.0441668
$641$	18.4812			0.729964			0.364982	−	0.931015i	$-0.381075\pi$
$641$	18.4812			0.729964			0.364982	+	0.931015i	$0.381075\pi$
$642$	19.3861	−	26.4814i	0.765109	−	1.04514i
$643$	29.6076	−	29.6076i	1.16761	−	1.16761i	0.184844	−	0.982768i	$-0.440822\pi$
$643$	29.6076	−	29.6076i	1.16761	−	1.16761i	0.982768	−	0.184844i	$-0.0591779\pi$
$644$	−4.32812	+	4.32812i	−0.170552	+	0.170552i
$645$	3.13659	−	4.28457i	0.123503	−	0.168705i
$646$	2.77160			0.109047
$647$	−22.8592			−0.898690			−0.449345	−	0.893358i	$-0.648343\pi$
$647$	−22.8592			−0.898690			−0.449345	+	0.893358i	$0.648343\pi$
$648$	1.53595	−	8.86797i	0.0603378	−	0.348367i
$649$			55.5109i			2.17900i
$650$	−5.88024	−	12.1814i	−0.230642	−	0.477793i
$651$	−6.98173	+	1.08001i	−0.273636	+	0.0423289i
$652$	−8.52261	+	8.52261i	−0.333771	+	0.333771i
$653$		−	20.8455i		−	0.815748i	−0.913038	−	0.407874i	$-0.866270\pi$
$653$		−	20.8455i		−	0.815748i	0.913038	−	0.407874i	$-0.133730\pi$
$654$	14.0822	−	2.17838i	0.550656	−	0.0851815i
$655$	−10.0498	+	10.0498i	−0.392679	+	0.392679i
$656$	−6.76896	−	6.76896i	−0.264284	−	0.264284i
$657$	−0.171588	−	0.0889928i	−0.00669429	−	0.00347194i
$658$	5.67285	+	5.67285i	0.221151	+	0.221151i
$659$			20.6669i			0.805067i	0.915405	+	0.402534i	$0.131870\pi$
$659$			20.6669i			0.805067i	−0.915405	+	0.402534i	$0.868130\pi$
$660$	−1.44560	−	9.34511i	−0.0562700	−	0.363758i
$661$	8.65092	+	8.65092i	0.336482	+	0.336482i	0.855041	−	0.518560i	$-0.173532\pi$
$661$	8.65092	+	8.65092i	0.336482	+	0.336482i	−0.518560	+	0.855041i	$0.673532\pi$
$662$	5.93406			0.230634
$663$	0.453916	−	2.46379i	0.0176286	−	0.0956856i
$664$	−2.46321			−0.0955910
$665$	5.45862	+	5.45862i	0.211676	+	0.211676i
$666$	5.75063	+	18.1427i	0.222832	+	0.703016i
$667$		−	7.13256i		−	0.276174i
$668$	12.4225	+	12.4225i	0.480642	+	0.480642i
$669$	−7.73631	+	10.5678i	−0.299103	+	0.408574i
$670$	−0.774930	−	0.774930i	−0.0299381	−	0.0299381i
$671$	−2.47988	+	2.47988i	−0.0957345	+	0.0957345i
$672$	−0.264783	−	1.71169i	−0.0102142	−	0.0660300i
$673$			31.6297i			1.21924i	0.792696	+	0.609618i	$0.208677\pi$
$673$			31.6297i			1.21924i	−0.792696	+	0.609618i	$0.791323\pi$
$674$	9.80866	−	9.80866i	0.377815	−	0.377815i
$675$	−8.66154	−	17.4636i	−0.333383	−	0.672175i
$676$	8.08639	−	10.1789i	0.311015	−	0.391497i
$677$			13.4729i			0.517805i	0.965903	+	0.258903i	$0.0833609\pi$
$677$			13.4729i			0.517805i	−0.965903	+	0.258903i	$0.916639\pi$
$678$	15.2014	−	20.7651i	0.583806	−	0.797478i
$679$	9.94831			0.381781
$680$	0.448235			0.0171890
$681$	−6.18526	−	4.52802i	−0.237020	−	0.173514i
$682$	−14.0927	+	14.0927i	−0.539638	+	0.539638i
$683$	−4.78530	+	4.78530i	−0.183104	+	0.183104i	−0.792707	−	0.609603i	$-0.791329\pi$
$683$	−4.78530	+	4.78530i	−0.183104	+	0.183104i	0.609603	+	0.792707i	$0.291329\pi$
$684$	18.3994	+	9.54269i	0.703518	+	0.364874i
$685$	24.4121			0.932739
$686$	−1.00000			−0.0381802
$687$	−36.2653	−	26.5486i	−1.38361	−	1.01289i
$688$		−	2.74375i		−	0.104604i
$689$	−11.7873	−	4.11221i	−0.449060	−	0.156663i
$690$	−1.81089	−	11.7065i	−0.0689392	−	0.445658i
$691$	23.2258	−	23.2258i	0.883552	−	0.883552i	−0.110342	−	0.993894i	$-0.535195\pi$
$691$	23.2258	−	23.2258i	0.883552	−	0.883552i	0.993894	+	0.110342i	$0.0351946\pi$
$692$			21.8487i			0.830562i
$693$	−13.9735	+	4.42913i	−0.530809	+	0.168249i
$694$	22.3053	−	22.3053i	0.846699	−	0.846699i
$695$	−2.33975	−	2.33975i	−0.0887519	−	0.0887519i
$696$	1.62857	+	1.19222i	0.0617310	+	0.0451911i
$697$	−2.71545	−	2.71545i	−0.102855	−	0.102855i
$698$			24.7839i			0.938083i
$699$	19.2428	−	2.97668i	0.727829	−	0.112589i
$700$	−2.65274	−	2.65274i	−0.100264	−	0.100264i
$701$	−4.56217			−0.172311			−0.0861554	−	0.996282i	$-0.527458\pi$
$701$	−4.56217			−0.172311			−0.0861554	+	0.996282i	$0.527458\pi$
$702$	11.4962	−	14.7931i	0.433897	−	0.558331i
$703$	−43.8309			−1.65312
$704$	−3.45508	−	3.45508i	−0.130218	−	0.130218i
$705$	−15.3436	+	2.37352i	−0.577875	+	0.0893920i
$706$			19.6139i			0.738177i
$707$	2.39390	+	2.39390i	0.0900318	+	0.0900318i
$708$	−15.8775	−	11.6234i	−0.596713	−	0.436833i
$709$	−6.99329	−	6.99329i	−0.262638	−	0.262638i	0.563487	−	0.826125i	$-0.309460\pi$
$709$	−6.99329	−	6.99329i	−0.262638	−	0.262638i	−0.826125	+	0.563487i	$0.809460\pi$
$710$	−5.75949	+	5.75949i	−0.216150	+	0.216150i
$711$	−12.1440	+	3.84923i	−0.455434	+	0.144357i
$712$		−	12.0916i		−	0.453152i
$713$	−17.6537	+	17.6537i	−0.661138	+	0.661138i
$714$	−0.106221	−	0.686665i	−0.00397521	−	0.0256978i
$715$	6.48414	−	18.5862i	0.242493	−	0.695084i
$716$		−	13.0946i		−	0.489369i
$717$	10.6448	+	7.79268i	0.397537	+	0.291023i
$718$	5.62299			0.209848
$719$	16.1959			0.604005			0.302002	−	0.953307i	$-0.402345\pi$
$719$	16.1959			0.604005			0.302002	+	0.953307i	$0.402345\pi$
$720$	2.97563	+	1.54328i	0.110895	+	0.0575148i
$721$	9.33092	−	9.33092i	0.347502	−	0.347502i
$722$	−20.3176	+	20.3176i	−0.756142	+	0.756142i
$723$	−13.6166	−	9.96821i	−0.506405	−	0.370722i
$724$	−18.6617			−0.693556
$725$	4.37161			0.162358
$726$	−13.1728	+	17.9940i	−0.488887	+	0.667819i
$727$			11.3030i			0.419205i	0.977787	+	0.209602i	$0.0672169\pi$
$727$			11.3030i			0.419205i	−0.977787	+	0.209602i	$0.932783\pi$
$728$	1.18766	−	3.40433i	0.0440177	−	0.126173i
$729$	16.3390	−	21.4951i	0.605147	−	0.796114i
$730$	0.0509057	−	0.0509057i	0.00188410	−	0.00188410i
$731$		−	1.10069i		−	0.0407104i
$732$	−0.190048	−	1.22856i	−0.00702436	−	0.0454090i
$733$	−9.73470	+	9.73470i	−0.359559	+	0.359559i	−0.863650	−	0.504091i	$-0.831828\pi$
$733$	−9.73470	+	9.73470i	−0.359559	+	0.359559i	0.504091	+	0.863650i	$0.331828\pi$
$734$	0.507357	+	0.507357i	0.0187269	+	0.0187269i
$735$	1.14317	−	1.56157i	0.0421666	−	0.0575995i
$736$	−4.32812	−	4.32812i	−0.159537	−	0.159537i
$737$			4.79252i			0.176535i
$738$	−8.67727	−	27.3760i	−0.319415	−	1.00772i
$739$	36.2462	+	36.2462i	1.33334	+	1.33334i	0.902366	+	0.430971i	$0.141829\pi$
$739$	36.2462	+	36.2462i	1.33334	+	1.33334i	0.430971	+	0.902366i	$0.358171\pi$
$740$	−7.08853			−0.260579
$741$	24.4763	+	35.5319i	0.899158	+	1.30530i
$742$	−3.46244			−0.127110
$743$	2.02620	+	2.02620i	0.0743340	+	0.0743340i	0.743296	−	0.668962i	$-0.233261\pi$
$743$	2.02620	+	2.02620i	0.0743340	+	0.0743340i	−0.668962	+	0.743296i	$0.733261\pi$
$744$	−1.08001	−	6.98173i	−0.0395951	−	0.255963i
$745$		−	5.91630i		−	0.216756i
$746$	6.56277	+	6.56277i	0.240280	+	0.240280i
$747$	−6.55984	−	3.40221i	−0.240012	−	0.124480i
$748$	−1.38604	−	1.38604i	−0.0506788	−	0.0506788i
$749$	13.3983	−	13.3983i	0.489563	−	0.489563i
$750$	16.7377	−	2.58917i	0.611176	−	0.0945433i
$751$			21.0845i			0.769385i	0.923045	+	0.384692i	$0.125692\pi$
$751$			21.0845i			0.769385i	−0.923045	+	0.384692i	$0.874308\pi$
$752$	−5.67285	+	5.67285i	−0.206868	+	0.206868i
$753$	13.1158	−	2.02889i	0.477966	−	0.0739369i
$754$	1.82649	+	3.78371i	0.0665167	+	0.137794i
$755$		−	19.1998i		−	0.698751i
$756$	1.65905	−	4.92418i	0.0603392	−	0.179091i
$757$	6.62915			0.240941			0.120470	−	0.992717i	$-0.461560\pi$
$757$	6.62915			0.240941			0.120470	+	0.992717i	$0.461560\pi$
$758$	−17.5718			−0.638236
$759$	−30.5994	+	41.7988i	−1.11069	+	1.51720i
$760$	−5.45862	+	5.45862i	−0.198005	+	0.198005i
$761$	−13.3011	+	13.3011i	−0.482165	+	0.482165i	−0.905822	−	0.423658i	$-0.860746\pi$
$761$	−13.3011	+	13.3011i	−0.482165	+	0.482165i	0.423658	+	0.905822i	$0.360746\pi$
$762$	2.31449	−	3.16158i	0.0838450	−	0.114532i
$763$	8.22704			0.297839
$764$	−7.22379			−0.261347
$765$	1.19371	+	0.619106i	0.0431586	+	0.0223838i
$766$		−	19.4634i		−	0.703243i
$767$	−17.8070	−	36.8886i	−0.642974	−	1.33197i
$768$	1.71169	−	0.264783i	0.0617654	−	0.00955454i
$769$	−30.0658	+	30.0658i	−1.08420	+	1.08420i	−0.0880872	+	0.996113i	$0.528075\pi$
$769$	−30.0658	+	30.0658i	−1.08420	+	1.08420i	−0.996113	+	0.0880872i	$0.971925\pi$
$770$		−	5.45958i		−	0.196749i
$771$	−28.8903	+	4.46906i	−1.04046	+	0.160949i
$772$	19.1571	−	19.1571i	0.689478	−	0.689478i
$773$	9.37726	+	9.37726i	0.337276	+	0.337276i	0.855341	−	0.518065i	$-0.173347\pi$
$773$	9.37726	+	9.37726i	0.337276	+	0.337276i	−0.518065	+	0.855341i	$0.673347\pi$
$774$	3.78969	−	7.30696i	0.136218	−	0.262643i
$775$	−10.8201	−	10.8201i	−0.388671	−	0.388671i
$776$			9.94831i			0.357123i
$777$	1.67981	+	10.8591i	0.0602628	+	0.389569i
$778$	−3.50010	−	3.50010i	−0.125485	−	0.125485i
$779$	66.1376			2.36963
$780$	3.95841	+	5.74637i	0.141734	+	0.205753i
$781$	35.6193			1.27456
$782$	−1.73628	−	1.73628i	−0.0620891	−	0.0620891i
$783$	2.69040	+	5.42445i	0.0961469	+	0.193854i
$784$		−	1.00000i		−	0.0357143i
$785$	−16.0919	−	16.0919i	−0.574345	−	0.574345i
$786$	−13.0141	+	17.7772i	−0.464196	+	0.634091i
$787$	19.9564	+	19.9564i	0.711370	+	0.711370i	0.966822	−	0.255452i	$-0.0822242\pi$
$787$	19.9564	+	19.9564i	0.711370	+	0.711370i	−0.255452	+	0.966822i	$0.582224\pi$
$788$	17.1364	−	17.1364i	0.610458	−	0.610458i
$789$	−2.36691	−	15.3009i	−0.0842642	−	0.544727i
$790$		−	4.74476i		−	0.168811i
$791$	10.5061	−	10.5061i	0.373554	−	0.373554i
$792$	−4.42913	−	13.9735i	−0.157382	−	0.496527i
$793$	0.852444	−	2.44345i	0.0302712	−	0.0867695i
$794$		−	13.9056i		−	0.493493i
$795$	3.95817	−	5.40686i	0.140382	−	0.191761i
$796$	−9.75133			−0.345627
$797$	−45.7135			−1.61926			−0.809628	−	0.586943i	$-0.800331\pi$
$797$	−45.7135			−1.61926			−0.809628	+	0.586943i	$0.800331\pi$
$798$	9.65578	+	7.06867i	0.341811	+	0.250228i
$799$	−2.27573	+	2.27573i	−0.0805095	+	0.0805095i
$800$	2.65274	−	2.65274i	0.0937886	−	0.0937886i
$801$	16.7010	−	32.2015i	0.590102	−	1.13778i
$802$	−1.67933			−0.0592992
$803$	−0.314824			−0.0111099
$804$	−1.37078	−	1.00350i	−0.0483436	−	0.0353907i
$805$		−	6.83913i		−	0.241048i
$806$	4.84430	−	13.8857i	0.170633	−	0.489104i
$807$	−3.38707	−	21.8958i	−0.119231	−	0.770767i
$808$	−2.39390	+	2.39390i	−0.0842170	+	0.0842170i
$809$		−	4.26659i		−	0.150005i	−0.997183	−	0.0750026i	$-0.976103\pi$
$809$		−	4.26659i		−	0.150005i	0.997183	−	0.0750026i	$-0.0238965\pi$
$810$	5.79288	+	8.21993i	0.203541	+	0.288819i
$811$	−32.9674	+	32.9674i	−1.15764	+	1.15764i	−0.172660	+	0.984981i	$0.555236\pi$
$811$	−32.9674	+	32.9674i	−1.15764	+	1.15764i	−0.984981	+	0.172660i	$0.944764\pi$
$812$	0.823979	+	0.823979i	0.0289160	+	0.0289160i
$813$	17.4853	+	12.8004i	0.613236	+	0.448929i
$814$	21.9193	+	21.9193i	0.768272	+	0.768272i
$815$		−	13.4671i		−	0.471732i
$816$	0.686665	−	0.106221i	0.0240381	−	0.00371847i
$817$	13.4042	+	13.4042i	0.468953	+	0.468953i
$818$	1.64886			0.0576512
$819$	7.86499	−	7.42576i	0.274825	−	0.259477i
$820$	10.6961			0.373522
$821$	−17.3300	−	17.3300i	−0.604822	−	0.604822i	0.336766	−	0.941588i	$-0.390667\pi$
$821$	−17.3300	−	17.3300i	−0.604822	−	0.604822i	−0.941588	+	0.336766i	$0.890667\pi$
$822$	37.3977	−	5.78508i	1.30439	−	0.201778i
$823$			39.4252i			1.37428i	0.726526	+	0.687139i	$0.241134\pi$
$823$			39.4252i			1.37428i	−0.726526	+	0.687139i	$0.758866\pi$
$824$	9.33092	+	9.33092i	0.325058	+	0.325058i
$825$	−25.6188	−	18.7547i	−0.891933	−	0.652953i
$826$	−8.03324	−	8.03324i	−0.279512	−	0.279512i
$827$	−18.4845	+	18.4845i	−0.642768	+	0.642768i	−0.951235	−	0.308467i	$-0.900184\pi$
$827$	−18.4845	+	18.4845i	−0.642768	+	0.642768i	0.308467	+	0.951235i	$0.400184\pi$
$828$	−5.54830	−	17.5044i	−0.192817	−	0.608320i
$829$		−	12.9895i		−	0.451143i	−0.974227	−	0.225571i	$-0.927575\pi$
$829$		−	12.9895i		−	0.451143i	0.974227	−	0.225571i	$-0.0724248\pi$
$830$	1.94613	−	1.94613i	0.0675512	−	0.0675512i
$831$	−5.51853	−	35.6746i	−0.191436	−	1.23754i
$832$	3.40433	+	1.18766i	0.118024	+	0.0411748i
$833$		−	0.401161i		−	0.0138994i
$834$	−4.13880	−	3.02988i	−0.143315	−	0.104916i
$835$	−19.6296			−0.679310
$836$	33.7586			1.16756
$837$	6.76703	−	20.0850i	0.233903	−	0.694238i
$838$	9.46243	−	9.46243i	0.326874	−	0.326874i
$839$	−3.51977	+	3.51977i	−0.121516	+	0.121516i	−0.765250	−	0.643734i	$-0.777384\pi$
$839$	−3.51977	+	3.51977i	−0.121516	+	0.121516i	0.643734	+	0.765250i	$0.277384\pi$
$840$	1.56157	+	1.14317i	0.0538794	+	0.0394433i
$841$	27.6421			0.953176
$842$	36.2106			1.24790
$843$	23.3497	−	31.8957i	0.804208	−	1.09855i
$844$			7.32056i			0.251984i
$845$	1.65326	+	14.4311i	0.0568738	+	0.496444i
$846$	−22.9429	+	7.27214i	−0.788795	+	0.250021i
$847$	−9.10407	+	9.10407i	−0.312820	+	0.312820i
$848$		−	3.46244i		−	0.118901i
$849$	2.70148	+	17.4638i	0.0927147	+	0.599355i
$850$	1.06418	−	1.06418i	0.0365010	−	0.0365010i
$851$	27.4580	+	27.4580i	0.941248	+	0.941248i
$852$	−7.45828	+	10.1880i	−0.255516	+	0.349035i
$853$	22.3026	+	22.3026i	0.763626	+	0.763626i	0.976976	−	0.213350i	$-0.0684373\pi$
$853$	22.3026	+	22.3026i	0.763626	+	0.763626i	−0.213350	+	0.976976i	$0.568437\pi$
$854$		−	0.717748i		−	0.0245608i
$855$	−22.0765	+	6.99751i	−0.755000	+	0.239310i
$856$	13.3983	+	13.3983i	0.457944	+	0.457944i
$857$	0.612444			0.0209207			0.0104603	−	0.999945i	$-0.496670\pi$
$857$	0.612444			0.0209207			0.0104603	+	0.999945i	$0.496670\pi$
$858$	5.52878	−	30.0094i	0.188749	−	1.02450i
$859$	26.4751			0.903319			0.451659	−	0.892190i	$-0.350832\pi$
$859$	26.4751			0.903319			0.451659	+	0.892190i	$0.350832\pi$
$860$	2.16778	+	2.16778i	0.0739208	+	0.0739208i
$861$	−2.53471	−	16.3856i	−0.0863825	−	0.558420i
$862$			2.23091i			0.0759852i
$863$	−36.8495	−	36.8495i	−1.25437	−	1.25437i	−0.953741	−	0.300630i	$-0.902803\pi$
$863$	−36.8495	−	36.8495i	−1.25437	−	1.25437i	−0.300630	−	0.953741i	$-0.597197\pi$
$864$	4.92418	+	1.65905i	0.167524	+	0.0564422i
$865$	−17.2622	−	17.2622i	−0.586933	−	0.586933i
$866$	3.52381	−	3.52381i	0.119744	−	0.119744i
$867$	−28.8233	+	4.45870i	−0.978891	+	0.151425i
$868$		−	4.07885i		−	0.138445i
$869$	−14.6719	+	14.6719i	−0.497709	+	0.497709i
$870$	−2.22866	+	0.344753i	−0.0755586	+	0.0116882i
$871$	−1.53736	−	3.18476i	−0.0520915	−	0.107912i
$872$			8.22704i			0.278603i
$873$	−13.7407	+	26.4936i	−0.465052	+	0.896674i
$874$	42.2888			1.43044
$875$	9.77847			0.330573
$876$	0.0659206	−	0.0900475i	0.00222725	−	0.00304242i
$877$	39.5160	−	39.5160i	1.33436	−	1.33436i	0.432934	−	0.901426i	$-0.357478\pi$
$877$	39.5160	−	39.5160i	1.33436	−	1.33436i	0.901426	−	0.432934i	$-0.142522\pi$
$878$	−11.4860	+	11.4860i	−0.387633	+	0.387633i
$879$	31.1273	−	42.5198i	1.04990	−	1.43416i
$880$	5.45958			0.184042
$881$	12.5247			0.421968			0.210984	−	0.977489i	$-0.432333\pi$
$881$	12.5247			0.421968			0.210984	+	0.977489i	$0.432333\pi$
$882$	1.38121	−	2.66313i	0.0465078	−	0.0896722i
$883$		−	54.3967i		−	1.83059i	−0.402780	−	0.915297i	$-0.631956\pi$
$883$		−	54.3967i		−	1.83059i	0.402780	−	0.915297i	$-0.368044\pi$
$884$	1.36569	+	0.476445i	0.0459330	+	0.0160246i
$885$	21.7279	−	3.36111i	0.730376	−	0.112982i
$886$	−25.8951	+	25.8951i	−0.869964	+	0.869964i
$887$			17.4377i			0.585499i	0.956189	+	0.292750i	$0.0945702\pi$
$887$			17.4377i			0.585499i	−0.956189	+	0.292750i	$0.905430\pi$
$888$	−10.8591	+	1.67981i	−0.364409	+	0.0563707i
$889$	1.59961	−	1.59961i	0.0536491	−	0.0536491i
$890$	9.55334	+	9.55334i	0.320229	+	0.320229i
$891$	7.50499	−	43.3308i	0.251426	−	1.45164i
$892$	−5.34679	−	5.34679i	−0.179024	−	0.179024i
$893$		−	55.4278i		−	1.85482i
$894$	−1.40202	−	9.06337i	−0.0468905	−	0.303124i
$895$	10.3458	+	10.3458i	0.345822	+	0.345822i
$896$	1.00000			0.0334077
$897$	6.92582	−	37.5923i	0.231246	−	1.25517i
$898$	22.4402			0.748839
$899$	3.36088	+	3.36088i	0.112092	+	0.112092i
$900$	10.7286	−	3.40060i	0.357620	−	0.113353i
$901$		−	1.38900i		−	0.0462742i
$902$	−33.0746	−	33.0746i	−1.10126	−	1.10126i
$903$	2.80718	−	3.83461i	0.0934172	−	0.127608i
$904$	10.5061	+	10.5061i	0.349428	+	0.349428i
$905$	14.7442	−	14.7442i	0.490115	−	0.490115i
$906$	−4.54988	−	29.4127i	−0.151160	−	0.977172i
$907$			8.21025i			0.272617i	0.990666	+	0.136308i	$0.0435238\pi$
$907$			8.21025i			0.272617i	−0.990666	+	0.136308i	$0.956476\pi$
$908$	3.12944	−	3.12944i	0.103854	−	0.103854i
$909$	−9.68173	+	3.06878i	−0.321123	+	0.101785i
$910$	1.75134	+	3.62804i	0.0580565	+	0.120268i
$911$		−	12.8821i		−	0.426803i	−0.976965	−	0.213401i	$-0.931546\pi$
$911$		−	12.8821i		−	0.426803i	0.976965	−	0.213401i	$-0.0684542\pi$
$912$	−7.06867	+	9.65578i	−0.234067	+	0.319735i
$913$	−12.0358			−0.398326
$914$	−6.16942			−0.204066
$915$	1.12082	+	0.820512i	0.0370531	+	0.0271253i
$916$	18.3485	−	18.3485i	0.606251	−	0.606251i
$917$	−8.99439	+	8.99439i	−0.297021	+	0.297021i
$918$	1.97539	+	0.665549i	0.0651976	+	0.0219664i
$919$	−9.54855			−0.314978			−0.157489	−	0.987521i	$-0.550340\pi$
$919$	−9.54855			−0.314978			−0.157489	+	0.987521i	$0.550340\pi$
$920$	6.83913			0.225479
$921$	12.9622	+	9.48921i	0.427121	+	0.312680i
$922$		−	14.4159i		−	0.474762i
$923$	−23.6700	+	11.4261i	−0.779108	+	0.376094i
$924$	−1.29379	−	8.36370i	−0.0425625	−	0.275145i
$925$	−16.8293	+	16.8293i	−0.553342	+	0.553342i
$926$			36.9396i			1.21391i
$927$	11.9615	+	37.7374i	0.392867	+	1.23946i
$928$	−0.823979	+	0.823979i	−0.0270484	+	0.0270484i
$929$	−16.1245	−	16.1245i	−0.529029	−	0.529029i	0.391254	−	0.920283i	$-0.372041\pi$
$929$	−16.1245	−	16.1245i	−0.529029	−	0.529029i	−0.920283	+	0.391254i	$0.872041\pi$
$930$	6.36942	+	4.66283i	0.208862	+	0.152900i
$931$	4.88536	+	4.88536i	0.160111	+	0.160111i
$932$			11.2420i			0.368243i
$933$	−22.4084	+	3.46637i	−0.733617	+	0.113484i
$934$	8.48641	+	8.48641i	0.277684	+	0.277684i
$935$	2.19017			0.0716263
$936$	7.42576	+	7.86499i	0.242718	+	0.257075i
$937$	−6.42931			−0.210037			−0.105018	−	0.994470i	$-0.533490\pi$
$937$	−6.42931			−0.210037			−0.105018	+	0.994470i	$0.533490\pi$
$938$	−0.693547	−	0.693547i	−0.0226451	−	0.0226451i
$939$	7.91678	−	1.22465i	0.258354	−	0.0399651i
$940$		−	8.96402i		−	0.292374i
$941$	−2.88070	−	2.88070i	−0.0939081	−	0.0939081i	0.658592	−	0.752500i	$-0.271152\pi$
$941$	−2.88070	−	2.88070i	−0.0939081	−	0.0939081i	−0.752500	+	0.658592i	$0.771152\pi$
$942$	−28.4651	−	20.8383i	−0.927444	−	0.678949i
$943$	−41.4321	−	41.4321i	−1.34921	−	1.34921i
$944$	8.03324	−	8.03324i	0.261460	−	0.261460i
$945$	2.57971	+	5.20128i	0.0839180	+	0.169198i
$946$		−	13.4066i		−	0.435885i
$947$	−28.0551	+	28.0551i	−0.911669	+	0.911669i	−0.996404	−	0.0847346i	$-0.972996\pi$
$947$	−28.0551	+	28.0551i	−0.911669	+	0.911669i	0.0847346	+	0.996404i	$0.472996\pi$
$948$	−1.12439	−	7.26864i	−0.0365186	−	0.236075i
$949$	0.209209	−	0.100990i	0.00679123	−	0.00327829i
$950$			25.9192i			0.840930i
$951$	−21.3830	−	15.6538i	−0.693393	−	0.507609i
$952$	0.401161			0.0130017
$953$	−9.21108			−0.298376			−0.149188	−	0.988809i	$-0.547666\pi$
$953$	−9.21108			−0.298376			−0.149188	+	0.988809i	$0.547666\pi$
$954$	4.78235	−	9.22092i	0.154834	−	0.298538i
$955$	5.70737	−	5.70737i	0.184686	−	0.184686i
$956$	−5.38574	+	5.38574i	−0.174187	+	0.174187i
$957$	7.95757	+	5.82546i	0.257232	+	0.188310i
$958$	−38.1883			−1.23381
$959$	21.8484			0.705521
$960$	−1.14317	+	1.56157i	−0.0368958	+	0.0503996i
$961$			14.3630i			0.463323i
$962$	−21.5974	−	7.53465i	−0.696328	−	0.242927i
$963$	17.1755	+	54.1873i	0.553474	+	1.74616i
$964$	6.88932	−	6.88932i	0.221890	−	0.221890i
$965$			30.2712i			0.974466i
$966$	−1.62071	−	10.4771i	−0.0521454	−	0.337094i
$967$	−18.1772	+	18.1772i	−0.584539	+	0.584539i	−0.936147	−	0.351608i	$-0.885635\pi$
$967$	−18.1772	+	18.1772i	−0.584539	+	0.584539i	0.351608	+	0.936147i	$0.385635\pi$
$968$	−9.10407	−	9.10407i	−0.292616	−	0.292616i
$969$	−2.83568	+	3.87353i	−0.0910950	+	0.124436i
$970$	−7.85996	−	7.85996i	−0.252368	−	0.252368i
$971$			12.9466i			0.415476i	0.978184	+	0.207738i	$0.0666102\pi$
$971$			12.9466i			0.415476i	−0.978184	+	0.207738i	$0.933390\pi$
$972$	10.8222	+	11.2196i	0.347123	+	0.359869i
$973$	−2.09403	−	2.09403i	−0.0671316	−	0.0671316i
$974$	35.4591			1.13618
$975$	23.0406	+	4.24489i	0.737891	+	0.135945i
$976$	0.717748			0.0229746
$977$	6.63981	+	6.63981i	0.212426	+	0.212426i	0.805297	−	0.592871i	$-0.202006\pi$
$977$	6.63981	+	6.63981i	0.212426	+	0.212426i	−0.592871	+	0.805297i	$0.702006\pi$
$978$	−3.19138	−	20.6307i	−0.102049	−	0.659696i
$979$		−	59.0822i		−	1.88827i
$980$	0.790081	+	0.790081i	0.0252382	+	0.0252382i
$981$	−11.3633	+	21.9097i	−0.362801	+	0.699522i
$982$	3.72619	+	3.72619i	0.118907	+	0.118907i
$983$	−19.2743	+	19.2743i	−0.614756	+	0.614756i	−0.944181	−	0.329426i	$-0.893145\pi$
$983$	−19.2743	+	19.2743i	−0.614756	+	0.614756i	0.329426	+	0.944181i	$0.393145\pi$
$984$	16.3856	−	2.53471i	0.522354	−	0.0808034i
$985$			27.0782i			0.862784i
$986$	−0.330549	+	0.330549i	−0.0105268	+	0.0105268i
$987$	−13.7323	+	2.12426i	−0.437103	+	0.0676158i
$988$	−22.4335	+	10.8292i	−0.713705	+	0.344523i
$989$		−	16.7942i		−	0.534024i
$990$	14.5396	+	7.54082i	0.462098	+	0.239663i
$991$	−26.9609			−0.856442			−0.428221	−	0.903674i	$-0.640859\pi$
$991$	−26.9609			−0.856442			−0.428221	+	0.903674i	$0.640859\pi$
$992$	4.07885			0.129503
$993$	−6.07126	+	8.29332i	−0.192665	+	0.263181i
$994$	−5.15463	+	5.15463i	−0.163495	+	0.163495i
$995$	7.70434	−	7.70434i	0.244244	−	0.244244i
$996$	2.52015	−	3.44253i	0.0798541	−	0.109081i
$997$	48.0588			1.52204			0.761018	−	0.648730i	$-0.224700\pi$
$997$	48.0588			1.52204			0.761018	+	0.648730i	$0.224700\pi$
$998$	−3.62992			−0.114903
$999$	−31.2395	−	10.5252i	−0.988373	−	0.333002i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.p.d.239.5	yes	20
3.2	odd	2		546.2.p.c.239.10	✓	20
13.8	odd	4		546.2.p.c.281.10	yes	20
39.8	even	4	inner	546.2.p.d.281.5	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.p.c.239.10	✓	20	3.2	odd	2
546.2.p.c.281.10	yes	20	13.8	odd	4
546.2.p.d.239.5	yes	20	1.1	even	1	trivial
546.2.p.d.281.5	yes	20	39.8	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.71169 - 0.264783i) q^{3} +1.00000i q^{4} +(-0.790081 - 0.790081i) q^{5} +(-1.39758 - 1.02312i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.85978 - 0.906454i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.71169 - 0.264783i) q^{3} +1.00000i q^{4} +(-0.790081 - 0.790081i) q^{5} +(-1.39758 - 1.02312i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.85978 - 0.906454i) q^{9} +1.11734i q^{10} +(3.45508 - 3.45508i) q^{11} +(0.264783 + 1.71169i) q^{12} +(-1.18766 + 3.40433i) q^{13} +1.00000i q^{14} +(-1.56157 - 1.14317i) q^{15} -1.00000 q^{16} -0.401161 q^{17} +(-2.66313 - 1.38121i) q^{18} +(4.88536 - 4.88536i) q^{19} +(0.790081 - 0.790081i) q^{20} +(-1.39758 - 1.02312i) q^{21} -4.88622 q^{22} -6.12089 q^{23} +(1.02312 - 1.39758i) q^{24} -3.75155i q^{25} +(3.24703 - 1.56742i) q^{26} +(4.65505 - 2.30879i) q^{27} +(0.707107 - 0.707107i) q^{28} +1.16528i q^{29} +(0.295853 + 1.91255i) q^{30} +(2.88418 - 2.88418i) q^{31} +(0.707107 + 0.707107i) q^{32} +(4.99918 - 6.82887i) q^{33} +(0.283664 + 0.283664i) q^{34} +1.11734i q^{35} +(0.906454 + 2.85978i) q^{36} +(-4.48595 - 4.48595i) q^{37} -6.90894 q^{38} +(-1.13151 + 6.14164i) q^{39} -1.11734 q^{40} +(6.76896 + 6.76896i) q^{41} +(0.264783 + 1.71169i) q^{42} +2.74375i q^{43} +(3.45508 + 3.45508i) q^{44} +(-2.97563 - 1.54328i) q^{45} +(4.32812 + 4.32812i) q^{46} +(5.67285 - 5.67285i) q^{47} +(-1.71169 + 0.264783i) q^{48} +1.00000i q^{49} +(-2.65274 + 2.65274i) q^{50} +(-0.686665 + 0.106221i) q^{51} +(-3.40433 - 1.18766i) q^{52} +3.46244i q^{53} +(-4.92418 - 1.65905i) q^{54} -5.45958 q^{55} -1.00000 q^{56} +(7.06867 - 9.65578i) q^{57} +(0.823979 - 0.823979i) q^{58} +(-8.03324 + 8.03324i) q^{59} +(1.14317 - 1.56157i) q^{60} -0.717748 q^{61} -4.07885 q^{62} +(-2.66313 - 1.38121i) q^{63} -1.00000i q^{64} +(3.62804 - 1.75134i) q^{65} +(-8.36370 + 1.29379i) q^{66} +(-0.693547 + 0.693547i) q^{67} -0.401161i q^{68} +(-10.4771 + 1.62071i) q^{69} +(0.790081 - 0.790081i) q^{70} +(5.15463 + 5.15463i) q^{71} +(1.38121 - 2.66313i) q^{72} +(-0.0455596 - 0.0455596i) q^{73} +6.34409i q^{74} +(-0.993346 - 6.42149i) q^{75} +(4.88536 + 4.88536i) q^{76} -4.88622 q^{77} +(5.14289 - 3.54270i) q^{78} -4.24647 q^{79} +(0.790081 + 0.790081i) q^{80} +(7.35668 - 5.18452i) q^{81} -9.57276i q^{82} +(-1.74175 - 1.74175i) q^{83} +(1.02312 - 1.39758i) q^{84} +(0.316950 + 0.316950i) q^{85} +(1.94012 - 1.94012i) q^{86} +(0.308547 + 1.99461i) q^{87} -4.88622i q^{88} +(8.55005 - 8.55005i) q^{89} +(1.01282 + 3.19535i) q^{90} +(3.24703 - 1.56742i) q^{91} -6.12089i q^{92} +(4.17315 - 5.70051i) q^{93} -8.02263 q^{94} -7.71965 q^{95} +(1.39758 + 1.02312i) q^{96} +(-7.03452 + 7.03452i) q^{97} +(0.707107 - 0.707107i) q^{98} +(6.74889 - 13.0126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{5} + 4 q^{6} - 8 q^{9}+O(q^{10}) \) 20 * q + 4 * q^5 + 4 * q^6 - 8 * q^9	\( 20 q + 4 q^{5} + 4 q^{6} - 8 q^{9} + 16 q^{11} + 8 q^{12} + 4 q^{13} - 4 q^{15} - 20 q^{16} - 12 q^{17} - 16 q^{18} + 12 q^{19} - 4 q^{20} + 4 q^{21} - 12 q^{22} + 4 q^{23} - 4 q^{24} + 24 q^{27} - 12 q^{30} - 8 q^{31} + 16 q^{33} - 4 q^{34} + 32 q^{37} + 4 q^{38} + 8 q^{39} - 4 q^{40} - 8 q^{41} + 8 q^{42} + 16 q^{44} - 32 q^{45} - 8 q^{46} - 32 q^{50} + 8 q^{51} - 8 q^{52} + 20 q^{54} + 28 q^{55} - 20 q^{56} + 36 q^{57} - 4 q^{58} - 20 q^{59} - 4 q^{60} - 4 q^{61} - 48 q^{62} - 16 q^{63} - 52 q^{65} - 36 q^{67} - 68 q^{69} - 4 q^{70} + 28 q^{71} - 8 q^{72} - 24 q^{73} + 76 q^{75} + 12 q^{76} - 12 q^{77} + 56 q^{78} - 64 q^{79} - 4 q^{80} + 32 q^{81} + 24 q^{83} - 4 q^{84} + 24 q^{85} - 4 q^{86} + 4 q^{87} + 4 q^{89} + 8 q^{90} + 16 q^{93} - 40 q^{94} + 76 q^{95} - 4 q^{96} + 32 q^{97} - 36 q^{99}+O(q^{100}) \) 20 * q + 4 * q^5 + 4 * q^6 - 8 * q^9 + 16 * q^11 + 8 * q^12 + 4 * q^13 - 4 * q^15 - 20 * q^16 - 12 * q^17 - 16 * q^18 + 12 * q^19 - 4 * q^20 + 4 * q^21 - 12 * q^22 + 4 * q^23 - 4 * q^24 + 24 * q^27 - 12 * q^30 - 8 * q^31 + 16 * q^33 - 4 * q^34 + 32 * q^37 + 4 * q^38 + 8 * q^39 - 4 * q^40 - 8 * q^41 + 8 * q^42 + 16 * q^44 - 32 * q^45 - 8 * q^46 - 32 * q^50 + 8 * q^51 - 8 * q^52 + 20 * q^54 + 28 * q^55 - 20 * q^56 + 36 * q^57 - 4 * q^58 - 20 * q^59 - 4 * q^60 - 4 * q^61 - 48 * q^62 - 16 * q^63 - 52 * q^65 - 36 * q^67 - 68 * q^69 - 4 * q^70 + 28 * q^71 - 8 * q^72 - 24 * q^73 + 76 * q^75 + 12 * q^76 - 12 * q^77 + 56 * q^78 - 64 * q^79 - 4 * q^80 + 32 * q^81 + 24 * q^83 - 4 * q^84 + 24 * q^85 - 4 * q^86 + 4 * q^87 + 4 * q^89 + 8 * q^90 + 16 * q^93 - 40 * q^94 + 76 * q^95 - 4 * q^96 + 32 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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