LMFDB - Embedded newform 546.2.bm.b.205.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(205,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("546.205");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bm (of order $6$, 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 $\Q(\zeta_{6})$
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} + 56 x^{18} + 1306 x^{16} + 16508 x^{14} + 123139 x^{12} + 552164 x^{10} + 1447090 x^{8} + \cdots + 576 $ x^20 + 56x^18 + 1306x^16 + 16508x^14 + 123139x^12 + 552164x^10 + 1447090x^8 + 2035844x^6 + 1263505x^4 + 215520*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			205.3
Root			$-0.0521119i$ of defining polynomial
Character	$\chi$	$=$	546.205
Dual form			546.2.bm.b.277.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +(0.0451302 + 0.0260560i) q^{5} +(0.866025 + 0.500000i) q^{6} +(-1.11788 + 2.39799i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +(0.0451302 + 0.0260560i) q^{5} +(0.866025 + 0.500000i) q^{6} +(-1.11788 + 2.39799i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.0260560 - 0.0451302i) q^{10} +(-3.79791 - 2.19272i) q^{11} +(0.500000 - 0.866025i) q^{12} +(1.30825 - 3.35983i) q^{13} +(2.39799 + 1.11788i) q^{14} +(-0.0451302 + 0.0260560i) q^{15} +1.00000 q^{16} -4.44977 q^{17} +(-0.866025 + 0.500000i) q^{18} +(-1.86685 + 1.07783i) q^{19} +(-0.0451302 - 0.0260560i) q^{20} +(-1.51777 - 2.16711i) q^{21} +(-2.19272 + 3.79791i) q^{22} -4.70483 q^{23} +(-0.866025 - 0.500000i) q^{24} +(-2.49864 - 4.32778i) q^{25} +(-3.35983 - 1.30825i) q^{26} +1.00000 q^{27} +(1.11788 - 2.39799i) q^{28} +(-1.37847 - 2.38758i) q^{29} +(0.0260560 + 0.0451302i) q^{30} +(0.373728 - 0.215772i) q^{31} -1.00000i q^{32} +(3.79791 - 2.19272i) q^{33} +4.44977i q^{34} +(-0.112932 + 0.0790941i) q^{35} +(0.500000 + 0.866025i) q^{36} +5.68921i q^{37} +(1.07783 + 1.86685i) q^{38} +(2.25557 + 2.81290i) q^{39} +(-0.0260560 + 0.0451302i) q^{40} +(0.0861982 - 0.0497666i) q^{41} +(-2.16711 + 1.51777i) q^{42} +(-5.18663 + 8.98351i) q^{43} +(3.79791 + 2.19272i) q^{44} -0.0521119i q^{45} +4.70483i q^{46} +(0.0347347 + 0.0200541i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(-4.50067 - 5.36134i) q^{49} +(-4.32778 + 2.49864i) q^{50} +(2.22488 - 3.85361i) q^{51} +(-1.30825 + 3.35983i) q^{52} +(-0.481787 - 0.834479i) q^{53} -1.00000i q^{54} +(-0.114267 - 0.197916i) q^{55} +(-2.39799 - 1.11788i) q^{56} -2.15566i q^{57} +(-2.38758 + 1.37847i) q^{58} -4.88264i q^{59} +(0.0451302 - 0.0260560i) q^{60} +(2.04213 + 3.53707i) q^{61} +(-0.215772 - 0.373728i) q^{62} +(2.63566 - 0.230877i) q^{63} -1.00000 q^{64} +(0.146585 - 0.117542i) q^{65} +(-2.19272 - 3.79791i) q^{66} +(5.76483 + 3.32833i) q^{67} +4.44977 q^{68} +(2.35241 - 4.07450i) q^{69} +(0.0790941 + 0.112932i) q^{70} +(-4.23255 - 2.44366i) q^{71} +(0.866025 - 0.500000i) q^{72} +(1.34197 - 0.774785i) q^{73} +5.68921 q^{74} +4.99728 q^{75} +(1.86685 - 1.07783i) q^{76} +(9.50374 - 6.65612i) q^{77} +(2.81290 - 2.25557i) q^{78} +(-8.28968 + 14.3582i) q^{79} +(0.0451302 + 0.0260560i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.0497666 - 0.0861982i) q^{82} -10.7018i q^{83} +(1.51777 + 2.16711i) q^{84} +(-0.200819 - 0.115943i) q^{85} +(8.98351 + 5.18663i) q^{86} +2.75694 q^{87} +(2.19272 - 3.79791i) q^{88} -6.67156i q^{89} -0.0521119 q^{90} +(6.59436 + 6.89307i) q^{91} +4.70483 q^{92} +0.431544i q^{93} +(0.0200541 - 0.0347347i) q^{94} -0.112335 q^{95} +(0.866025 + 0.500000i) q^{96} +(3.77317 + 2.17844i) q^{97} +(-5.36134 + 4.50067i) q^{98} +4.38545i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 10 q^{3} - 20 q^{4} - 10 q^{9}+O(q^{10}) $ 20 * q - 10 * q^3 - 20 * q^4 - 10 * q^9	$ 20 q - 10 q^{3} - 20 q^{4} - 10 q^{9} + 4 q^{10} + 6 q^{11} + 10 q^{12} + 8 q^{13} + 4 q^{14} + 20 q^{16} - 8 q^{17} - 12 q^{19} + 6 q^{21} - 10 q^{22} - 16 q^{23} + 6 q^{25} + 8 q^{26} + 20 q^{27} + 8 q^{29} + 4 q^{30} + 12 q^{31} - 6 q^{33} + 10 q^{35} + 10 q^{36} + 6 q^{38} - 10 q^{39} - 4 q^{40} - 18 q^{41} - 2 q^{42} + 18 q^{43} - 6 q^{44} - 6 q^{47} - 10 q^{48} - 20 q^{49} + 12 q^{50} + 4 q^{51} - 8 q^{52} + 18 q^{53} - 12 q^{55} - 4 q^{56} + 24 q^{58} - 6 q^{61} - 6 q^{63} - 20 q^{64} - 6 q^{65} - 10 q^{66} + 24 q^{67} + 8 q^{68} + 8 q^{69} + 42 q^{70} - 6 q^{71} + 24 q^{73} + 36 q^{74} - 12 q^{75} + 12 q^{76} - 34 q^{77} + 2 q^{78} - 10 q^{81} + 18 q^{82} - 6 q^{84} - 36 q^{86} - 16 q^{87} + 10 q^{88} - 8 q^{90} - 10 q^{91} + 16 q^{92} - 16 q^{94} - 80 q^{95} - 96 q^{97} - 12 q^{98}+O(q^{100}) $ 20 * q - 10 * q^3 - 20 * q^4 - 10 * q^9 + 4 * q^10 + 6 * q^11 + 10 * q^12 + 8 * q^13 + 4 * q^14 + 20 * q^16 - 8 * q^17 - 12 * q^19 + 6 * q^21 - 10 * q^22 - 16 * q^23 + 6 * q^25 + 8 * q^26 + 20 * q^27 + 8 * q^29 + 4 * q^30 + 12 * q^31 - 6 * q^33 + 10 * q^35 + 10 * q^36 + 6 * q^38 - 10 * q^39 - 4 * q^40 - 18 * q^41 - 2 * q^42 + 18 * q^43 - 6 * q^44 - 6 * q^47 - 10 * q^48 - 20 * q^49 + 12 * q^50 + 4 * q^51 - 8 * q^52 + 18 * q^53 - 12 * q^55 - 4 * q^56 + 24 * q^58 - 6 * q^61 - 6 * q^63 - 20 * q^64 - 6 * q^65 - 10 * q^66 + 24 * q^67 + 8 * q^68 + 8 * q^69 + 42 * q^70 - 6 * q^71 + 24 * q^73 + 36 * q^74 - 12 * q^75 + 12 * q^76 - 34 * q^77 + 2 * q^78 - 10 * q^81 + 18 * q^82 - 6 * q^84 - 36 * q^86 - 16 * q^87 + 10 * q^88 - 8 * q^90 - 10 * q^91 + 16 * q^92 - 16 * q^94 - 80 * q^95 - 96 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−1.00000			−0.500000
$5$	0.0451302	+	0.0260560i	0.0201829	+	0.0116526i	0.510057	−	0.860140i	$-0.329624\pi$
$5$	0.0451302	+	0.0260560i	0.0201829	+	0.0116526i	−0.489875	+	0.871793i	$0.662957\pi$
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	−1.11788	+	2.39799i	−0.422520	+	0.906353i
$7$	−1.11788	+	2.39799i	−0.422520	+	0.906353i
$8$			1.00000i			0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.0260560	−	0.0451302i	0.00823962	−	0.0142714i
$11$	−3.79791	−	2.19272i	−1.14511	−	0.661131i	−0.197421	−	0.980319i	$-0.563257\pi$
$11$	−3.79791	−	2.19272i	−1.14511	−	0.661131i	−0.947692	+	0.319188i	$0.896590\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	1.30825	−	3.35983i	0.362844	−	0.931850i
$13$	1.30825	−	3.35983i	0.362844	−	0.931850i
$14$	2.39799	+	1.11788i	0.640889	+	0.298767i
$15$	−0.0451302	+	0.0260560i	−0.0116526	+	0.00672762i
$16$	1.00000			0.250000
$17$	−4.44977			−1.07923			−0.539613	−	0.841913i	$-0.681430\pi$
$17$	−4.44977			−1.07923			−0.539613	+	0.841913i	$0.681430\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	−1.86685	+	1.07783i	−0.428285	+	0.247271i	−0.698616	−	0.715497i	$-0.746200\pi$
$19$	−1.86685	+	1.07783i	−0.428285	+	0.247271i	0.270331	+	0.962768i	$0.412867\pi$
$20$	−0.0451302	−	0.0260560i	−0.0100914	−	0.00582629i
$21$	−1.51777	−	2.16711i	−0.331206	−	0.472902i
$22$	−2.19272	+	3.79791i	−0.467490	+	0.809717i
$23$	−4.70483			−0.981025			−0.490512	−	0.871434i	$-0.663190\pi$
$23$	−4.70483			−0.981025			−0.490512	+	0.871434i	$0.663190\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	−2.49864	−	4.32778i	−0.499728	−	0.865555i
$26$	−3.35983	−	1.30825i	−0.658917	−	0.256569i
$27$	1.00000			0.192450
$28$	1.11788	−	2.39799i	0.211260	−	0.453177i
$29$	−1.37847	−	2.38758i	−0.255976	−	0.443363i	0.709184	−	0.705023i	$-0.249063\pi$
$29$	−1.37847	−	2.38758i	−0.255976	−	0.443363i	−0.965160	+	0.261660i	$0.915730\pi$
$30$	0.0260560	+	0.0451302i	0.00475715	+	0.00823962i
$31$	0.373728	−	0.215772i	0.0671235	−	0.0387538i	−0.466063	−	0.884752i	$-0.654328\pi$
$31$	0.373728	−	0.215772i	0.0671235	−	0.0387538i	0.533186	+	0.845998i	$0.320995\pi$
$32$		−	1.00000i		−	0.176777i
$33$	3.79791	−	2.19272i	0.661131	−	0.381704i
$34$			4.44977i			0.763128i
$35$	−0.112932	+	0.0790941i	−0.0190890	+	0.0133694i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$			5.68921i			0.935301i	0.883914	+	0.467650i	$0.154899\pi$
$37$			5.68921i			0.935301i	−0.883914	+	0.467650i	$0.845101\pi$
$38$	1.07783	+	1.86685i	0.174847	+	0.302844i
$39$	2.25557	+	2.81290i	0.361181	+	0.450424i
$40$	−0.0260560	+	0.0451302i	−0.00411981	+	0.00713572i
$41$	0.0861982	−	0.0497666i	0.0134619	−	0.00777223i	−0.493254	−	0.869885i	$-0.664193\pi$
$41$	0.0861982	−	0.0497666i	0.0134619	−	0.00777223i	0.506716	+	0.862113i	$0.330859\pi$
$42$	−2.16711	+	1.51777i	−0.334392	+	0.234198i
$43$	−5.18663	+	8.98351i	−0.790954	+	1.36997i	0.134423	+	0.990924i	$0.457082\pi$
$43$	−5.18663	+	8.98351i	−0.790954	+	1.36997i	−0.925377	+	0.379049i	$0.876251\pi$
$44$	3.79791	+	2.19272i	0.572556	+	0.330566i
$45$		−	0.0521119i		−	0.00776839i
$46$			4.70483i			0.693689i
$47$	0.0347347	+	0.0200541i	0.00506658	+	0.00292519i	0.502531	−	0.864559i	$-0.332402\pi$
$47$	0.0347347	+	0.0200541i	0.00506658	+	0.00292519i	−0.497465	+	0.867484i	$0.665736\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−4.50067	−	5.36134i	−0.642953	−	0.765906i
$50$	−4.32778	+	2.49864i	−0.612040	+	0.353361i
$51$	2.22488	−	3.85361i	0.311546	−	0.539613i
$52$	−1.30825	+	3.35983i	−0.181422	+	0.465925i
$53$	−0.481787	−	0.834479i	−0.0661785	−	0.114625i	0.831038	−	0.556216i	$-0.187747\pi$
$53$	−0.481787	−	0.834479i	−0.0661785	−	0.114625i	−0.897216	+	0.441592i	$0.854414\pi$
$54$		−	1.00000i		−	0.136083i
$55$	−0.114267	−	0.197916i	−0.0154078	−	0.0266870i
$56$	−2.39799	−	1.11788i	−0.320444	−	0.149384i
$57$		−	2.15566i		−	0.285524i
$58$	−2.38758	+	1.37847i	−0.313505	+	0.181002i
$59$		−	4.88264i		−	0.635666i	−0.948147	−	0.317833i	$-0.897045\pi$
$59$		−	4.88264i		−	0.635666i	0.948147	−	0.317833i	$-0.102955\pi$
$60$	0.0451302	−	0.0260560i	0.00582629	−	0.00336381i
$61$	2.04213	+	3.53707i	0.261468	+	0.452876i	0.966632	−	0.256168i	$-0.0824601\pi$
$61$	2.04213	+	3.53707i	0.261468	+	0.452876i	−0.705164	+	0.709044i	$0.749127\pi$
$62$	−0.215772	−	0.373728i	−0.0274031	−	0.0474635i
$63$	2.63566	−	0.230877i	0.332062	−	0.0290877i
$64$	−1.00000			−0.125000
$65$	0.146585	−	0.117542i	0.0181817	−	0.0145793i
$66$	−2.19272	−	3.79791i	−0.269906	−	0.467490i
$67$	5.76483	+	3.32833i	0.704286	+	0.406620i	0.808942	−	0.587889i	$-0.200041\pi$
$67$	5.76483	+	3.32833i	0.704286	+	0.406620i	−0.104656	+	0.994509i	$0.533374\pi$
$68$	4.44977			0.539613
$69$	2.35241	−	4.07450i	0.283197	−	0.490512i
$70$	0.0790941	+	0.112932i	0.00945356	+	0.0134980i
$71$	−4.23255	−	2.44366i	−0.502311	−	0.290009i	0.227356	−	0.973812i	$-0.426992\pi$
$71$	−4.23255	−	2.44366i	−0.502311	−	0.290009i	−0.729667	+	0.683802i	$0.760325\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	1.34197	−	0.774785i	0.157065	−	0.0906817i	−0.419407	−	0.907798i	$-0.637762\pi$
$73$	1.34197	−	0.774785i	0.157065	−	0.0906817i	0.576473	+	0.817116i	$0.304429\pi$
$74$	5.68921			0.661357
$75$	4.99728			0.577037
$76$	1.86685	−	1.07783i	0.214143	−	0.123635i
$77$	9.50374	−	6.65612i	1.08305	−	0.758535i
$78$	2.81290	−	2.25557i	0.318498	−	0.255394i
$79$	−8.28968	+	14.3582i	−0.932662	+	1.61542i	−0.153912	+	0.988085i	$0.549187\pi$
$79$	−8.28968	+	14.3582i	−0.932662	+	1.61542i	−0.778750	+	0.627334i	$0.784146\pi$
$80$	0.0451302	+	0.0260560i	0.00504571	+	0.00291314i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.0497666	−	0.0861982i	−0.00549580	−	0.00951900i
$83$		−	10.7018i		−	1.17467i	−0.809343	−	0.587336i	$-0.800177\pi$
$83$		−	10.7018i		−	1.17467i	0.809343	−	0.587336i	$-0.199823\pi$
$84$	1.51777	+	2.16711i	0.165603	+	0.236451i
$85$	−0.200819	−	0.115943i	−0.0217819	−	0.0125758i
$86$	8.98351	+	5.18663i	0.968717	+	0.559289i
$87$	2.75694			0.295575
$88$	2.19272	−	3.79791i	0.233745	−	0.404859i
$89$		−	6.67156i		−	0.707184i	−0.935400	−	0.353592i	$-0.884960\pi$
$89$		−	6.67156i		−	0.707184i	0.935400	−	0.353592i	$-0.115040\pi$
$90$	−0.0521119			−0.00549308
$91$	6.59436	+	6.89307i	0.691277	+	0.722590i
$92$	4.70483			0.490512
$93$			0.431544i			0.0447490i
$94$	0.0200541	−	0.0347347i	0.00206842	−	0.00358261i
$95$	−0.112335			−0.0115254
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	3.77317	+	2.17844i	0.383108	+	0.221187i	0.679170	−	0.733981i	$-0.262340\pi$
$97$	3.77317	+	2.17844i	0.383108	+	0.221187i	−0.296062	+	0.955169i	$0.595673\pi$
$98$	−5.36134	+	4.50067i	−0.541577	+	0.454636i
$99$			4.38545i			0.440754i
$100$	2.49864	+	4.32778i	0.249864	+	0.432778i
$101$	−0.656966	+	1.13790i	−0.0653706	+	0.113225i	−0.896858	−	0.442318i	$-0.854156\pi$
$101$	−0.656966	+	1.13790i	−0.0653706	+	0.113225i	0.831488	+	0.555543i	$0.187490\pi$
$102$	−3.85361	−	2.22488i	−0.381564	−	0.220296i
$103$	4.74350	−	8.21598i	0.467391	−	0.809545i	−0.531915	−	0.846798i	$-0.678527\pi$
$103$	4.74350	−	8.21598i	0.467391	−	0.809545i	0.999306	+	0.0372530i	$0.0118607\pi$
$104$	3.35983	+	1.30825i	0.329459	+	0.128285i
$105$	−0.0120314	−	0.137349i	−0.00117415	−	0.0134039i
$106$	−0.834479	+	0.481787i	−0.0810518	+	0.0467953i
$107$	6.60217			0.638256			0.319128	−	0.947712i	$-0.396610\pi$
$107$	6.60217			0.638256			0.319128	+	0.947712i	$0.396610\pi$
$108$	−1.00000			−0.0962250
$109$	7.94365	−	4.58627i	0.760864	−	0.439285i	−0.0687418	−	0.997634i	$-0.521898\pi$
$109$	7.94365	−	4.58627i	0.760864	−	0.439285i	0.829606	+	0.558349i	$0.188565\pi$
$110$	−0.197916	+	0.114267i	−0.0188706	+	0.0108949i
$111$	−4.92700	−	2.84461i	−0.467650	−	0.269998i
$112$	−1.11788	+	2.39799i	−0.105630	+	0.226588i
$113$	−6.32805	+	10.9605i	−0.595293	+	1.03108i	0.398213	+	0.917293i	$0.369631\pi$
$113$	−6.32805	+	10.9605i	−0.595293	+	1.03108i	−0.993505	+	0.113784i	$0.963703\pi$
$114$	−2.15566			−0.201896
$115$	−0.212330	−	0.122589i	−0.0197999	−	0.0114315i
$116$	1.37847	+	2.38758i	0.127988	+	0.221681i
$117$	−3.56383	+	0.546937i	−0.329476	+	0.0505644i
$118$	−4.88264			−0.449484
$119$	4.97432	−	10.6705i	0.455995	−	0.978161i
$120$	−0.0260560	−	0.0451302i	−0.00237857	−	0.00411981i
$121$	4.11608	+	7.12926i	0.374189	+	0.648114i
$122$	3.53707	−	2.04213i	0.320232	−	0.184886i
$123$			0.0995332i			0.00897460i
$124$	−0.373728	+	0.215772i	−0.0335618	+	0.0193769i
$125$		−	0.520978i		−	0.0465977i
$126$	−0.230877	−	2.63566i	−0.0205681	−	0.234803i
$127$	6.91510	+	11.9773i	0.613616	+	1.06281i	0.990626	+	0.136604i	$0.0436188\pi$
$127$	6.91510	+	11.9773i	0.613616	+	1.06281i	−0.377010	+	0.926209i	$0.623048\pi$
$128$			1.00000i			0.0883883i
$129$	−5.18663	−	8.98351i	−0.456658	−	0.790954i
$130$	−0.117542	−	0.146585i	−0.0103091	−	0.0128564i
$131$	−4.49191	+	7.78021i	−0.392460	+	0.679760i	−0.992773	−	0.120005i	$-0.961709\pi$
$131$	−4.49191	+	7.78021i	−0.392460	+	0.679760i	0.600314	+	0.799765i	$0.295042\pi$
$132$	−3.79791	+	2.19272i	−0.330566	+	0.190852i
$133$	−0.497691	−	5.68157i	−0.0431553	−	0.492655i
$134$	3.32833	−	5.76483i	0.287524	−	0.498005i
$135$	0.0451302	+	0.0260560i	0.00388419	+	0.00224254i
$136$		−	4.44977i		−	0.381564i
$137$		−	11.1355i		−	0.951368i	−0.879616	−	0.475684i	$-0.842201\pi$
$137$		−	11.1355i		−	0.951368i	0.879616	−	0.475684i	$-0.157799\pi$
$138$	−4.07450	−	2.35241i	−0.346845	−	0.200251i
$139$	8.83267	−	15.2986i	0.749177	−	1.29761i	−0.199040	−	0.979991i	$-0.563783\pi$
$139$	8.83267	−	15.2986i	0.749177	−	1.29761i	0.948218	−	0.317622i	$-0.102884\pi$
$140$	0.112932	−	0.0790941i	0.00954451	−	0.00668468i
$141$	−0.0347347	+	0.0200541i	−0.00292519	+	0.00168886i
$142$	−2.44366	+	4.23255i	−0.205068	+	0.355188i
$143$	−12.3358	+	9.89171i	−1.03157	+	0.827186i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$		−	0.143670i		−	0.0119311i
$146$	−0.774785	−	1.34197i	−0.0641217	−	0.111062i
$147$	6.89339	−	1.21703i	0.568557	−	0.100379i
$148$		−	5.68921i		−	0.467650i
$149$	11.0581	−	6.38440i	0.905915	−	0.523030i	0.0268002	−	0.999641i	$-0.491468\pi$
$149$	11.0581	−	6.38440i	0.905915	−	0.523030i	0.879114	+	0.476611i	$0.158135\pi$
$150$		−	4.99728i		−	0.408027i
$151$	11.7710	−	6.79597i	0.957908	−	0.553048i	0.0623793	−	0.998053i	$-0.480131\pi$
$151$	11.7710	−	6.79597i	0.957908	−	0.553048i	0.895528	+	0.445004i	$0.146798\pi$
$152$	−1.07783	−	1.86685i	−0.0874234	−	0.151422i
$153$	2.22488	+	3.85361i	0.179871	+	0.311546i
$154$	−6.65612	−	9.50374i	−0.536366	−	0.765834i
$155$	0.0224886			0.00180633
$156$	−2.25557	−	2.81290i	−0.180591	−	0.225212i
$157$	0.471406	+	0.816499i	0.0376223	+	0.0651637i	0.884223	−	0.467064i	$-0.154688\pi$
$157$	0.471406	+	0.816499i	0.0376223	+	0.0651637i	−0.846601	+	0.532228i	$0.821355\pi$
$158$	14.3582	+	8.28968i	1.14227	+	0.659492i
$159$	0.963573			0.0764163
$160$	0.0260560	−	0.0451302i	0.00205990	−	0.00356786i
$161$	5.25945	−	11.2821i	0.414503	−	0.889155i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	−22.0403	+	12.7250i	−1.72633	+	0.996697i	−0.822559	+	0.568680i	$0.807454\pi$
$163$	−22.0403	+	12.7250i	−1.72633	+	0.996697i	−0.903771	+	0.428017i	$0.859212\pi$
$164$	−0.0861982	+	0.0497666i	−0.00673095	+	0.00388612i
$165$	0.228534			0.0177914
$166$	−10.7018			−0.830619
$167$	11.5885	−	6.69063i	0.896746	−	0.517737i	0.0206031	−	0.999788i	$-0.493441\pi$
$167$	11.5885	−	6.69063i	0.896746	−	0.517737i	0.876143	+	0.482051i	$0.160108\pi$
$168$	2.16711	−	1.51777i	0.167196	−	0.117099i
$169$	−9.57696	−	8.79101i	−0.736689	−	0.676232i
$170$	−0.115943	+	0.200819i	−0.00889242	+	0.0154021i
$171$	1.86685	+	1.07783i	0.142762	+	0.0824236i
$172$	5.18663	−	8.98351i	0.395477	−	0.684986i
$173$	1.06170	+	1.83891i	0.0807194	+	0.139810i	0.903559	−	0.428463i	$-0.140945\pi$
$173$	1.06170	+	1.83891i	0.0807194	+	0.139810i	−0.822840	+	0.568273i	$0.807612\pi$
$174$		−	2.75694i		−	0.209003i
$175$	13.1711	−	1.15376i	0.995644	−	0.0872159i
$176$	−3.79791	−	2.19272i	−0.286278	−	0.165283i
$177$	4.22849	+	2.44132i	0.317833	+	0.183501i
$178$	−6.67156			−0.500055
$179$	−12.0434	+	20.8597i	−0.900164	+	1.55913i	−0.0728841	+	0.997340i	$0.523220\pi$
$179$	−12.0434	+	20.8597i	−0.900164	+	1.55913i	−0.827280	+	0.561790i	$0.810113\pi$
$180$			0.0521119i			0.00388419i
$181$	−9.06625			−0.673889			−0.336945	−	0.941524i	$-0.609394\pi$
$181$	−9.06625			−0.673889			−0.336945	+	0.941524i	$0.609394\pi$
$182$	6.89307	−	6.59436i	0.510949	−	0.488806i
$183$	−4.08426			−0.301917
$184$		−	4.70483i		−	0.346845i
$185$	−0.148238	+	0.256756i	−0.0108987	+	0.0188770i
$186$	0.431544			0.0316423
$187$	16.8998	+	9.75711i	1.23584	+	0.713510i
$188$	−0.0347347	−	0.0200541i	−0.00253329	−	0.00146260i
$189$	−1.11788	+	2.39799i	−0.0813141	+	0.174428i
$190$			0.112335i			0.00814966i
$191$	1.45963	+	2.52815i	0.105615	+	0.182931i	0.913989	−	0.405738i	$-0.132986\pi$
$191$	1.45963	+	2.52815i	0.105615	+	0.182931i	−0.808374	+	0.588669i	$0.799652\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−21.3521	−	12.3276i	−1.53696	−	0.887363i	−0.999015	−	0.0443825i	$-0.985868\pi$
$193$	−21.3521	−	12.3276i	−1.53696	−	0.887363i	−0.537944	−	0.842981i	$-0.680799\pi$
$194$	2.17844	−	3.77317i	0.156403	−	0.270898i
$195$	0.0285020	+	0.185718i	0.00204107	+	0.0132995i
$196$	4.50067	+	5.36134i	0.321476	+	0.382953i
$197$	−18.9687	+	10.9516i	−1.35146	+	0.780266i	−0.988454	−	0.151521i	$-0.951583\pi$
$197$	−18.9687	+	10.9516i	−1.35146	+	0.780266i	−0.363006	+	0.931787i	$0.618250\pi$
$198$	4.38545			0.311660
$199$	−25.9657			−1.84066			−0.920329	−	0.391145i	$-0.872079\pi$
$199$	−25.9657			−1.84066			−0.920329	+	0.391145i	$0.872079\pi$
$200$	4.32778	−	2.49864i	0.306020	−	0.176681i
$201$	−5.76483	+	3.32833i	−0.406620	+	0.234762i
$202$	1.13790	+	0.656966i	0.0800623	+	0.0462240i
$203$	7.26636	−	0.636514i	0.509998	−	0.0446745i
$204$	−2.22488	+	3.85361i	−0.155773	+	0.269807i
$205$	0.00518686			0.000362266
$206$	−8.21598	−	4.74350i	−0.572435	−	0.330495i
$207$	2.35241	+	4.07450i	0.163504	+	0.283197i
$208$	1.30825	−	3.35983i	0.0907109	−	0.232963i
$209$	9.45352			0.653914
$210$	−0.137349	+	0.0120314i	−0.00947800	+	0.000830248i
$211$	4.29055	+	7.43146i	0.295374	+	0.511603i	0.975072	−	0.221890i	$-0.0712224\pi$
$211$	4.29055	+	7.43146i	0.295374	+	0.511603i	−0.679698	+	0.733492i	$0.737889\pi$
$212$	0.481787	+	0.834479i	0.0330892	+	0.0573123i
$213$	4.23255	−	2.44366i	0.290009	−	0.167437i
$214$		−	6.60217i		−	0.451315i
$215$	−0.468148	+	0.270285i	−0.0319274	+	0.0184333i
$216$			1.00000i			0.0680414i
$217$	0.0996335	+	1.13740i	0.00676356	+	0.0772119i
$218$	−4.58627	−	7.94365i	−0.310621	−	0.538012i
$219$			1.54957i			0.104710i
$220$	0.114267	+	0.197916i	0.00770388	+	0.0133435i
$221$	−5.82141	+	14.9505i	−0.391591	+	1.00568i
$222$	−2.84461	+	4.92700i	−0.190917	+	0.330679i
$223$	19.6277	−	11.3321i	1.31437	−	0.758851i	0.331552	−	0.943437i	$-0.392428\pi$
$223$	19.6277	−	11.3321i	1.31437	−	0.758851i	0.982816	+	0.184586i	$0.0590943\pi$
$224$	2.39799	+	1.11788i	0.160222	+	0.0746918i
$225$	−2.49864	+	4.32778i	−0.166576	+	0.288518i
$226$	10.9605	+	6.32805i	0.729082	+	0.420936i
$227$			23.4086i			1.55368i	0.629695	+	0.776842i	$0.283180\pi$
$227$			23.4086i			1.55368i	−0.629695	+	0.776842i	$0.716820\pi$
$228$			2.15566i			0.142762i
$229$	−1.19337	−	0.688991i	−0.0788600	−	0.0455298i	0.460052	−	0.887892i	$-0.347831\pi$
$229$	−1.19337	−	0.688991i	−0.0788600	−	0.0455298i	−0.538911	+	0.842362i	$0.681164\pi$
$230$	−0.122589	+	0.212330i	−0.00808327	+	0.0140006i
$231$	1.01250	+	11.5585i	0.0666175	+	0.760496i
$232$	2.38758	−	1.37847i	0.156752	−	0.0905010i
$233$	7.56218	−	13.0981i	0.495415	−	0.858084i	−0.504571	−	0.863370i	$-0.668349\pi$
$233$	7.56218	−	13.0981i	0.495415	−	0.858084i	0.999986	+	0.00528619i	$0.00168265\pi$
$234$	0.546937	+	3.56383i	0.0357544	+	0.232975i
$235$	0.00104506	+	0.00181009i	6.81720e−5	+	0.000118077i
$236$			4.88264i			0.317833i
$237$	−8.28968	−	14.3582i	−0.538473	−	0.932662i
$238$	−10.6705	−	4.97432i	−0.691664	−	0.322437i
$239$		−	18.2045i		−	1.17755i	−0.808297	−	0.588775i	$-0.799610\pi$
$239$		−	18.2045i		−	1.17755i	0.808297	−	0.588775i	$-0.200390\pi$
$240$	−0.0451302	+	0.0260560i	−0.00291314	+	0.00168190i
$241$			14.8693i			0.957819i	0.877864	+	0.478909i	$0.158968\pi$
$241$			14.8693i			0.957819i	−0.877864	+	0.478909i	$0.841032\pi$
$242$	7.12926	−	4.11608i	0.458286	−	0.264592i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−2.04213	−	3.53707i	−0.130734	−	0.226438i
$245$	−0.0634215	−	0.359228i	−0.00405185	−	0.0229502i
$246$	0.0995332			0.00634600
$247$	1.17901	+	7.68238i	0.0750185	+	0.488818i
$248$	0.215772	+	0.373728i	0.0137015	+	0.0237318i
$249$	9.26801	+	5.35089i	0.587336	+	0.339099i
$250$	−0.520978			−0.0329495
$251$	−13.1750	+	22.8198i	−0.831598	+	1.44037i	0.0651724	+	0.997874i	$0.479240\pi$
$251$	−13.1750	+	22.8198i	−0.831598	+	1.44037i	−0.896770	+	0.442496i	$0.854093\pi$
$252$	−2.63566	+	0.230877i	−0.166031	+	0.0145439i
$253$	17.8685	+	10.3164i	1.12338	+	0.648586i
$254$	11.9773	−	6.91510i	0.751522	−	0.433892i
$255$	0.200819	−	0.115943i	0.0125758	−	0.00726063i
$256$	1.00000			0.0625000
$257$	21.2561			1.32592			0.662960	−	0.748655i	$-0.269300\pi$
$257$	21.2561			1.32592			0.662960	+	0.748655i	$0.269300\pi$
$258$	−8.98351	+	5.18663i	−0.559289	+	0.322906i
$259$	−13.6426	−	6.35988i	−0.847713	−	0.395184i
$260$	−0.146585	+	0.117542i	−0.00909084	+	0.00728967i
$261$	−1.37847	+	2.38758i	−0.0853252	+	0.147788i
$262$	7.78021	+	4.49191i	0.480663	+	0.277511i
$263$	−12.2755	+	21.2618i	−0.756940	+	1.31106i	0.187464	+	0.982271i	$0.439973\pi$
$263$	−12.2755	+	21.2618i	−0.756940	+	1.31106i	−0.944404	+	0.328787i	$0.893360\pi$
$264$	2.19272	+	3.79791i	0.134953	+	0.233745i
$265$		−	0.0502137i		−	0.00308460i
$266$	−5.68157	+	0.497691i	−0.348360	+	0.0305154i
$267$	5.77774	+	3.33578i	0.353592	+	0.204147i
$268$	−5.76483	−	3.32833i	−0.352143	−	0.203310i
$269$	−31.1622			−1.89999			−0.949997	−	0.312259i	$-0.898914\pi$
$269$	−31.1622			−1.89999			−0.949997	+	0.312259i	$0.898914\pi$
$270$	0.0260560	−	0.0451302i	0.00158572	−	0.00274654i
$271$		−	14.7019i		−	0.893078i	−0.894764	−	0.446539i	$-0.852656\pi$
$271$		−	14.7019i		−	0.893078i	0.894764	−	0.446539i	$-0.147344\pi$
$272$	−4.44977			−0.269807
$273$	−9.26675	+	2.26435i	−0.560849	+	0.137044i
$274$	−11.1355			−0.672718
$275$			21.9153i			1.32154i
$276$	−2.35241	+	4.07450i	−0.141599	+	0.245256i
$277$	−8.28819			−0.497989			−0.248994	−	0.968505i	$-0.580100\pi$
$277$	−8.28819			−0.497989			−0.248994	+	0.968505i	$0.580100\pi$
$278$	−15.2986	−	8.83267i	−0.917551	−	0.529748i
$279$	−0.373728	−	0.215772i	−0.0223745	−	0.0129179i
$280$	−0.0790941	−	0.112932i	−0.00472678	−	0.00674899i
$281$			6.15162i			0.366975i	0.983022	+	0.183487i	$0.0587387\pi$
$281$			6.15162i			0.366975i	−0.983022	+	0.183487i	$0.941261\pi$
$282$	0.0200541	+	0.0347347i	0.00119420	+	0.00206842i
$283$	−4.94543	+	8.56574i	−0.293975	+	0.509180i	−0.974746	−	0.223316i	$-0.928312\pi$
$283$	−4.94543	+	8.56574i	−0.293975	+	0.509180i	0.680771	+	0.732497i	$0.261645\pi$
$284$	4.23255	+	2.44366i	0.251156	+	0.145005i
$285$	0.0561677	−	0.0972853i	0.00332709	−	0.00576268i
$286$	9.89171	+	12.3358i	0.584909	+	0.729432i
$287$	0.0229799	+	0.262335i	0.00135646	+	0.0154852i
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	2.80041			0.164730
$290$	−0.143670			−0.00843656
$291$	−3.77317	+	2.17844i	−0.221187	+	0.127703i
$292$	−1.34197	+	0.774785i	−0.0785327	+	0.0453409i
$293$	−3.86698	−	2.23260i	−0.225911	−	0.130430i	0.382773	−	0.923842i	$-0.374969\pi$
$293$	−3.86698	−	2.23260i	−0.225911	−	0.130430i	−0.608684	+	0.793412i	$0.708302\pi$
$294$	−1.21703	−	6.89339i	−0.0709783	−	0.402031i
$295$	0.127222	−	0.220355i	0.00740715	−	0.0128296i
$296$	−5.68921			−0.330679
$297$	−3.79791	−	2.19272i	−0.220377	−	0.127235i
$298$	−6.38440	−	11.0581i	−0.369838	−	0.640578i
$299$	−6.15510	+	15.8074i	−0.355959	+	0.914168i
$300$	−4.99728			−0.288518
$301$	−15.7443	−	22.4800i	−0.907485	−	1.29573i
$302$	−6.79597	−	11.7710i	−0.391064	−	0.677343i
$303$	−0.656966	−	1.13790i	−0.0377417	−	0.0653706i
$304$	−1.86685	+	1.07783i	−0.107071	+	0.0618177i
$305$			0.212839i			0.0121871i
$306$	3.85361	−	2.22488i	0.220296	−	0.127188i
$307$			5.17881i			0.295570i	0.989019	+	0.147785i	$0.0472144\pi$
$307$			5.17881i			0.295570i	−0.989019	+	0.147785i	$0.952786\pi$
$308$	−9.50374	+	6.65612i	−0.541526	+	0.379268i
$309$	4.74350	+	8.21598i	0.269848	+	0.467391i
$310$		−	0.0224886i		−	0.00127727i
$311$	−17.4989	−	30.3089i	−0.992269	−	1.71866i	−0.603613	−	0.797278i	$-0.706273\pi$
$311$	−17.4989	−	30.3089i	−0.992269	−	1.71866i	−0.388656	−	0.921383i	$-0.627061\pi$
$312$	−2.81290	+	2.25557i	−0.159249	+	0.127697i
$313$	3.92239	−	6.79378i	0.221707	−	0.384007i	−0.733620	−	0.679560i	$-0.762171\pi$
$313$	3.92239	−	6.79378i	0.221707	−	0.384007i	0.955326	+	0.295553i	$0.0955039\pi$
$314$	0.816499	−	0.471406i	0.0460777	−	0.0266030i
$315$	0.124964	+	0.0582551i	0.00704090	+	0.00328230i
$316$	8.28968	−	14.3582i	0.466331	−	0.807709i
$317$	17.6606	+	10.1964i	0.991921	+	0.572686i	0.905848	−	0.423603i	$-0.139235\pi$
$317$	17.6606	+	10.1964i	0.991921	+	0.572686i	0.0860728	+	0.996289i	$0.472568\pi$
$318$		−	0.963573i		−	0.0540345i
$319$			12.0904i			0.676934i
$320$	−0.0451302	−	0.0260560i	−0.00252286	−	0.00145657i
$321$	−3.30108	+	5.71764i	−0.184249	+	0.319128i
$322$	−11.2821	−	5.25945i	−0.628728	−	0.293098i
$323$	8.30706	−	4.79608i	0.462217	−	0.266861i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−17.8095	+	2.73320i	−0.987891	+	0.151611i
$326$	12.7250	+	22.0403i	0.704771	+	1.22070i
$327$			9.17254i			0.507243i
$328$	0.0497666	+	0.0861982i	0.00274790	+	0.00475950i
$329$	−0.0869188	+	0.0608752i	−0.00479199	+	0.00335616i
$330$		−	0.228534i		−	0.0125804i
$331$	−1.03196	+	0.595804i	−0.0567219	+	0.0327484i	−0.528093	−	0.849187i	$-0.677093\pi$
$331$	−1.03196	+	0.595804i	−0.0567219	+	0.0327484i	0.471371	+	0.881935i	$0.343759\pi$
$332$			10.7018i			0.587336i
$333$	4.92700	−	2.84461i	0.269998	−	0.155883i
$334$	−6.69063	−	11.5885i	−0.366095	−	0.634095i
$335$	0.173445	+	0.300416i	0.00947634	+	0.0164135i
$336$	−1.51777	−	2.16711i	−0.0828014	−	0.118225i
$337$	−1.46143			−0.0796089			−0.0398045	−	0.999207i	$-0.512674\pi$
$337$	−1.46143			−0.0796089			−0.0398045	+	0.999207i	$0.512674\pi$
$338$	−8.79101	+	9.57696i	−0.478168	+	0.520918i
$339$	−6.32805	−	10.9605i	−0.343692	−	0.595293i
$340$	0.200819	+	0.115943i	0.0108909	+	0.00628789i
$341$	−1.89251			−0.102485
$342$	1.07783	−	1.86685i	0.0582823	−	0.100948i
$343$	17.8876	−	4.79919i	0.965842	−	0.259132i
$344$	−8.98351	−	5.18663i	−0.484358	−	0.279644i
$345$	0.212330	−	0.122589i	0.0114315	−	0.00659996i
$346$	1.83891	−	1.06170i	0.0988606	−	0.0570772i
$347$	15.1772			0.814754			0.407377	−	0.913260i	$-0.366443\pi$
$347$	15.1772			0.814754			0.407377	+	0.913260i	$0.366443\pi$
$348$	−2.75694			−0.147788
$349$	23.6760	−	13.6693i	1.26735	−	0.731703i	0.292861	−	0.956155i	$-0.405393\pi$
$349$	23.6760	−	13.6693i	1.26735	−	0.731703i	0.974485	+	0.224452i	$0.0720593\pi$
$350$	−1.15376	−	13.1711i	−0.0616709	−	0.704027i
$351$	1.30825	−	3.35983i	0.0698293	−	0.179335i
$352$	−2.19272	+	3.79791i	−0.116873	+	0.202429i
$353$	16.4117	+	9.47528i	0.873505	+	0.504318i	0.868511	−	0.495669i	$-0.165077\pi$
$353$	16.4117	+	9.47528i	0.873505	+	0.504318i	0.00499373	+	0.999988i	$0.498410\pi$
$354$	2.44132	−	4.22849i	0.129755	−	0.224742i
$355$	−0.127344	−	0.220566i	−0.00675872	−	0.0117064i
$356$			6.67156i			0.353592i
$357$	6.75374	+	9.64313i	0.357446	+	0.510368i
$358$	20.8597	+	12.0434i	1.10247	+	0.636512i
$359$	−25.4931	−	14.7184i	−1.34547	−	0.776810i	−0.357869	−	0.933772i	$-0.616497\pi$
$359$	−25.4931	−	14.7184i	−1.34547	−	0.776810i	−0.987605	+	0.156962i	$0.949830\pi$
$360$	0.0521119			0.00274654
$361$	−7.17657	+	12.4302i	−0.377714	+	0.654221i
$362$			9.06625i			0.476512i
$363$	−8.23216			−0.432076
$364$	−6.59436	−	6.89307i	−0.345638	−	0.361295i
$365$	0.0807511			0.00422670
$366$			4.08426i			0.213488i
$367$	17.1347	−	29.6782i	0.894424	−	1.54919i	0.0599091	−	0.998204i	$-0.480919\pi$
$367$	17.1347	−	29.6782i	0.894424	−	1.54919i	0.834515	−	0.550985i	$-0.185748\pi$
$368$	−4.70483			−0.245256
$369$	−0.0861982	−	0.0497666i	−0.00448730	−	0.00259074i
$370$	0.256756	+	0.148238i	0.0133481	+	0.00770652i
$371$	2.53965	−	0.222467i	0.131852	−	0.0115499i
$372$		−	0.431544i		−	0.0223745i
$373$	−11.9282	−	20.6603i	−0.617619	−	1.06975i	−0.989919	−	0.141635i	$-0.954764\pi$
$373$	−11.9282	−	20.6603i	−0.617619	−	1.06975i	0.372300	−	0.928113i	$-0.378569\pi$
$374$	9.75711	−	16.8998i	0.504528	−	0.873868i
$375$	0.451180	+	0.260489i	0.0232988	+	0.0134516i
$376$	−0.0200541	+	0.0347347i	−0.00103421	+	0.00179131i
$377$	−9.82526	+	1.50787i	−0.506027	+	0.0776595i
$378$	2.39799	+	1.11788i	0.123339	+	0.0574978i
$379$	19.0619	−	11.0054i	0.979142	−	0.565308i	0.0771307	−	0.997021i	$-0.475424\pi$
$379$	19.0619	−	11.0054i	0.979142	−	0.565308i	0.902011	+	0.431713i	$0.142091\pi$
$380$	0.112335			0.00576268
$381$	−13.8302			−0.708542
$382$	2.52815	−	1.45963i	0.129351	−	0.0746811i
$383$	−23.5657	+	13.6056i	−1.20415	+	0.695216i	−0.961475	−	0.274892i	$-0.911358\pi$
$383$	−23.5657	+	13.6056i	−1.20415	+	0.695216i	−0.242674	+	0.970108i	$0.578024\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$	0.602338	−	0.0527632i	0.0306980	−	0.00268906i
$386$	−12.3276	+	21.3521i	−0.627461	+	1.08679i
$387$	10.3733			0.527303
$388$	−3.77317	−	2.17844i	−0.191554	−	0.110594i
$389$	−13.6396	−	23.6246i	−0.691558	−	1.19781i	−0.971327	−	0.237746i	$-0.923591\pi$
$389$	−13.6396	−	23.6246i	−0.691558	−	1.19781i	0.279770	−	0.960067i	$-0.409742\pi$
$390$	0.185718	−	0.0285020i	0.00940419	−	0.00144325i
$391$	20.9354			1.05875
$392$	5.36134	−	4.50067i	0.270789	−	0.227318i
$393$	−4.49191	−	7.78021i	−0.226587	−	0.392460i
$394$	10.9516	+	18.9687i	0.551731	+	0.955627i
$395$	−0.748231	+	0.431991i	−0.0376476	+	0.0217358i
$396$		−	4.38545i		−	0.220377i
$397$	0.769755	−	0.444418i	0.0386329	−	0.0223047i	−0.480559	−	0.876962i	$-0.659566\pi$
$397$	0.769755	−	0.444418i	0.0386329	−	0.0223047i	0.519192	+	0.854658i	$0.326233\pi$
$398$			25.9657i			1.30154i
$399$	5.16923	+	2.40977i	0.258785	+	0.120640i
$400$	−2.49864	−	4.32778i	−0.124932	−	0.216389i
$401$		−	8.67074i		−	0.432996i	−0.976283	−	0.216498i	$-0.930537\pi$
$401$		−	8.67074i		−	0.432996i	0.976283	−	0.216498i	$-0.0694635\pi$
$402$	3.32833	+	5.76483i	0.166002	+	0.287524i
$403$	−0.236028	−	1.53795i	−0.0117574	−	0.0766107i
$404$	0.656966	−	1.13790i	0.0326853	−	0.0566126i
$405$	−0.0451302	+	0.0260560i	−0.00224254	+	0.00129473i
$406$	−0.636514	−	7.26636i	−0.0315897	−	0.360623i
$407$	12.4749	−	21.6071i	0.618356	−	1.07102i
$408$	3.85361	+	2.22488i	0.190782	+	0.110148i
$409$			5.48497i			0.271214i	0.990763	+	0.135607i	$0.0432985\pi$
$409$			5.48497i			0.271214i	−0.990763	+	0.135607i	$0.956702\pi$
$410$		−	0.00518686i		−	0.000256161i
$411$	9.64360	+	5.56774i	0.475684	+	0.274636i
$412$	−4.74350	+	8.21598i	−0.233695	+	0.404772i
$413$	11.7085	+	5.45823i	0.576138	+	0.268582i
$414$	4.07450	−	2.35241i	0.200251	−	0.115615i
$415$	0.278845	−	0.482974i	0.0136880	−	0.0237082i
$416$	−3.35983	−	1.30825i	−0.164729	−	0.0641423i
$417$	8.83267	+	15.2986i	0.432538	+	0.749177i
$418$		−	9.45352i		−	0.462387i
$419$	−11.1825	−	19.3686i	−0.546300	−	0.946220i	−0.998524	−	0.0543152i	$-0.982702\pi$
$419$	−11.1825	−	19.3686i	−0.546300	−	0.946220i	0.452224	−	0.891905i	$-0.350631\pi$
$420$	0.0120314	+	0.137349i	0.000587074	+	0.00670196i
$421$			4.08927i			0.199299i	0.995023	+	0.0996494i	$0.0317721\pi$
$421$			4.08927i			0.199299i	−0.995023	+	0.0996494i	$0.968228\pi$
$422$	7.43146	−	4.29055i	0.361758	−	0.208861i
$423$		−	0.0401082i		−	0.00195013i
$424$	0.834479	−	0.481787i	0.0405259	−	0.0233976i
$425$	11.1184	+	19.2576i	0.539320	+	0.934130i
$426$	−2.44366	−	4.23255i	−0.118396	−	0.205068i
$427$	−10.7647	+	0.942961i	−0.520941	+	0.0456331i
$428$	−6.60217			−0.319128
$429$	−2.39857	−	15.6290i	−0.115804	−	0.754574i
$430$	0.270285	+	0.468148i	0.0130343	+	0.0225761i
$431$	−21.8476	−	12.6137i	−1.05236	−	0.607580i	−0.129051	−	0.991638i	$-0.541193\pi$
$431$	−21.8476	−	12.6137i	−1.05236	−	0.607580i	−0.923309	+	0.384058i	$0.874526\pi$
$432$	1.00000			0.0481125
$433$	11.2634	−	19.5088i	0.541286	−	0.937535i	−0.457544	−	0.889187i	$-0.651271\pi$
$433$	11.2634	−	19.5088i	0.541286	−	0.937535i	0.998831	−	0.0483483i	$-0.0153957\pi$
$434$	1.13740	−	0.0996335i	0.0545971	−	0.00478256i
$435$	0.124421	+	0.0718348i	0.00596555	+	0.00344421i
$436$	−7.94365	+	4.58627i	−0.380432	+	0.219643i
$437$	8.78322	−	5.07100i	0.420159	−	0.242579i
$438$	1.54957			0.0740413
$439$	−20.3955			−0.973426			−0.486713	−	0.873562i	$-0.661804\pi$
$439$	−20.3955			−0.973426			−0.486713	+	0.873562i	$0.661804\pi$
$440$	0.197916	−	0.114267i	0.00943529	−	0.00544747i
$441$	−2.39272	+	6.57836i	−0.113939	+	0.313255i
$442$	14.9505	+	5.82141i	0.711121	+	0.276896i
$443$	14.2431	−	24.6697i	0.676708	−	1.17209i	−0.299259	−	0.954172i	$-0.596739\pi$
$443$	14.2431	−	24.6697i	0.676708	−	1.17209i	0.975967	−	0.217921i	$-0.0699274\pi$
$444$	4.92700	+	2.84461i	0.233825	+	0.134999i
$445$	0.173834	−	0.301089i	0.00824052	−	0.0142730i
$446$	−11.3321	−	19.6277i	−0.536589	−	0.929399i
$447$			12.7688i			0.603943i
$448$	1.11788	−	2.39799i	0.0528151	−	0.113294i
$449$	0.181880	+	0.105008i	0.00858343	+	0.00495564i	0.504286	−	0.863537i	$-0.331756\pi$
$449$	0.181880	+	0.105008i	0.00858343	+	0.00495564i	−0.495702	+	0.868493i	$0.665089\pi$
$450$	4.32778	+	2.49864i	0.204013	+	0.117787i
$451$	−0.436498			−0.0205539
$452$	6.32805	−	10.9605i	0.297646	−	0.515539i
$453$			13.5919i			0.638605i
$454$	23.4086			1.09862
$455$	0.117999	+	0.482908i	0.00553190	+	0.0226391i
$456$	2.15566			0.100948
$457$		−	11.5201i		−	0.538889i	−0.963016	−	0.269444i	$-0.913160\pi$
$457$		−	11.5201i		−	0.538889i	0.963016	−	0.269444i	$-0.0868401\pi$
$458$	−0.688991	+	1.19337i	−0.0321944	+	0.0557624i
$459$	−4.44977			−0.207697
$460$	0.212330	+	0.122589i	0.00989994	+	0.00571573i
$461$	−30.7468	−	17.7517i	−1.43202	−	0.826778i	−0.434746	−	0.900553i	$-0.643162\pi$
$461$	−30.7468	−	17.7517i	−1.43202	−	0.826778i	−0.997275	+	0.0737750i	$0.976495\pi$
$462$	11.5585	−	1.01250i	0.537752	−	0.0471057i
$463$		−	7.89303i		−	0.366820i	−0.983036	−	0.183410i	$-0.941286\pi$
$463$		−	7.89303i		−	0.366820i	0.983036	−	0.183410i	$-0.0587136\pi$
$464$	−1.37847	−	2.38758i	−0.0639939	−	0.110841i
$465$	−0.0112443	+	0.0194757i	−0.000521442	+	0.000903163i
$466$	−13.0981	−	7.56218i	−0.606757	−	0.350311i
$467$	−16.2808	+	28.1992i	−0.753386	+	1.30490i	0.192787	+	0.981241i	$0.438248\pi$
$467$	−16.2808	+	28.1992i	−0.753386	+	1.30490i	−0.946173	+	0.323662i	$0.895086\pi$
$468$	3.56383	−	0.546937i	0.164738	−	0.0252822i
$469$	−14.4257	+	10.1033i	−0.666116	+	0.466527i
$470$	0.00181009	−	0.00104506i	8.34933e−5	−	4.82049e-5i
$471$	−0.942812			−0.0434425
$472$	4.88264			0.224742
$473$	39.3967	−	22.7457i	1.81146	−	1.04585i
$474$	−14.3582	+	8.28968i	−0.659492	+	0.380758i
$475$	9.32919	+	5.38621i	0.428053	+	0.247136i
$476$	−4.97432	+	10.6705i	−0.227998	+	0.489080i
$477$	−0.481787	+	0.834479i	−0.0220595	+	0.0382082i
$478$	−18.2045			−0.832653
$479$	−0.986205	−	0.569385i	−0.0450608	−	0.0260159i	0.477300	−	0.878740i	$-0.341615\pi$
$479$	−0.986205	−	0.569385i	−0.0450608	−	0.0260159i	−0.522361	+	0.852724i	$0.674949\pi$
$480$	0.0260560	+	0.0451302i	0.00118929	+	0.00205990i
$481$	19.1148	+	7.44292i	0.871560	+	0.339368i
$482$	14.8693			0.677280
$483$	7.14087	+	10.1959i	0.324921	+	0.463929i
$484$	−4.11608	−	7.12926i	−0.187094	−	0.324057i
$485$	0.113523	+	0.196627i	0.00515481	+	0.00892839i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$		−	3.30285i		−	0.149666i	−0.997196	−	0.0748332i	$-0.976158\pi$
$487$		−	3.30285i		−	0.149666i	0.997196	−	0.0748332i	$-0.0238424\pi$
$488$	−3.53707	+	2.04213i	−0.160116	+	0.0924429i
$489$		−	25.4499i		−	1.15089i
$490$	−0.359228	+	0.0634215i	−0.0162283	+	0.00286509i
$491$	−8.73997	−	15.1381i	−0.394429	−	0.683172i	0.598599	−	0.801049i	$-0.295724\pi$
$491$	−8.73997	−	15.1381i	−0.394429	−	0.683172i	−0.993028	+	0.117877i	$0.962391\pi$
$492$		−	0.0995332i		−	0.00448730i
$493$	6.13387	+	10.6242i	0.276256	+	0.478489i
$494$	7.68238	−	1.17901i	0.345647	−	0.0530461i
$495$	−0.114267	+	0.197916i	−0.00513592	+	0.00889568i
$496$	0.373728	−	0.215772i	0.0167809	−	0.00968845i
$497$	10.5914	−	7.41786i	0.475088	−	0.332736i
$498$	5.35089	−	9.26801i	0.239779	−	0.415309i
$499$	0.808340	+	0.466695i	0.0361863	+	0.0208921i	0.517984	−	0.855390i	$-0.326683\pi$
$499$	0.808340	+	0.466695i	0.0361863	+	0.0208921i	−0.481798	+	0.876282i	$0.660016\pi$
$500$			0.520978i			0.0232988i
$501$			13.3813i			0.597831i
$502$	22.8198	+	13.1750i	1.01850	+	0.588029i
$503$	8.90322	−	15.4208i	0.396975	−	0.687581i	−0.596376	−	0.802705i	$-0.703393\pi$
$503$	8.90322	−	15.4208i	0.396975	−	0.687581i	0.993351	+	0.115124i	$0.0367267\pi$
$504$	0.230877	+	2.63566i	0.0102841	+	0.117402i
$505$	−0.0592981	+	0.0342358i	−0.00263873	+	0.00152347i
$506$	10.3164	−	17.8685i	0.458620	−	0.794353i
$507$	12.4017	−	3.89838i	0.550780	−	0.173133i
$508$	−6.91510	−	11.9773i	−0.306808	−	0.531407i
$509$			39.6424i			1.75712i	0.477633	+	0.878560i	$0.341495\pi$
$509$			39.6424i			1.75712i	−0.477633	+	0.878560i	$0.658505\pi$
$510$	−0.115943	−	0.200819i	−0.00513404	−	0.00889242i
$511$	0.357760	+	4.08414i	0.0158264	+	0.180672i
$512$		−	1.00000i		−	0.0441942i
$513$	−1.86685	+	1.07783i	−0.0824236	+	0.0475873i
$514$		−	21.2561i		−	0.937566i
$515$	0.428151	−	0.247193i	0.0188666	−	0.0108926i
$516$	5.18663	+	8.98351i	0.228329	+	0.395477i
$517$	−0.0879462	−	0.152327i	−0.00386787	−	0.00669935i
$518$	−6.35988	+	13.6426i	−0.279437	+	0.599424i
$519$	−2.12340			−0.0932067
$520$	0.117542	+	0.146585i	0.00515457	+	0.00642819i
$521$	10.8983	+	18.8765i	0.477465	+	0.826993i	0.999666	−	0.0258290i	$-0.00822253\pi$
$521$	10.8983	+	18.8765i	0.477465	+	0.826993i	−0.522202	+	0.852822i	$0.674889\pi$
$522$	2.38758	+	1.37847i	0.104502	+	0.0603340i
$523$	41.5093			1.81507			0.907537	−	0.419973i	$-0.137960\pi$
$523$	41.5093			1.81507			0.907537	+	0.419973i	$0.137960\pi$
$524$	4.49191	−	7.78021i	0.196230	−	0.339880i
$525$	−5.58638	+	11.9834i	−0.243810	+	0.522999i
$526$	21.2618	+	12.2755i	0.927058	+	0.535237i
$527$	−1.66300	+	0.960135i	−0.0724415	+	0.0418241i
$528$	3.79791	−	2.19272i	0.165283	−	0.0954261i
$529$	−0.864578			−0.0375903
$530$	−0.0502137			−0.00218114
$531$	−4.22849	+	2.44132i	−0.183501	+	0.105944i
$532$	0.497691	+	5.68157i	0.0215776	+	0.246327i
$533$	−0.0544384	−	0.354719i	−0.00235799	−	0.0153646i
$534$	3.33578	−	5.77774i	0.144353	−	0.250027i
$535$	0.297957	+	0.172026i	0.0128818	+	0.00743732i
$536$	−3.32833	+	5.76483i	−0.143762	+	0.249003i
$537$	−12.0434	−	20.8597i	−0.519710	−	0.900164i
$538$			31.1622i			1.34350i
$539$	5.33720	+	30.2306i	0.229890	+	1.30212i
$540$	−0.0451302	−	0.0260560i	−0.00194210	−	0.00112127i
$541$	−9.59172	−	5.53778i	−0.412380	−	0.238088i	0.279432	−	0.960166i	$-0.409854\pi$
$541$	−9.59172	−	5.53778i	−0.412380	−	0.238088i	−0.691812	+	0.722078i	$0.743187\pi$
$542$	−14.7019			−0.631501
$543$	4.53313	−	7.85161i	0.194535	−	0.336945i
$544$			4.44977i			0.190782i
$545$	0.477999			0.0204752
$546$	2.26435	+	9.26675i	0.0969050	+	0.396580i
$547$	−31.6610			−1.35373			−0.676863	−	0.736109i	$-0.736661\pi$
$547$	−31.6610			−1.35373			−0.676863	+	0.736109i	$0.736661\pi$
$548$			11.1355i			0.475684i
$549$	2.04213	−	3.53707i	0.0871560	−	0.150959i
$550$	21.9153			0.934473
$551$	5.14680	+	2.97151i	0.219261	+	0.126591i
$552$	4.07450	+	2.35241i	0.173422	+	0.100125i
$553$	−25.1637	−	35.9293i	−1.07007	−	1.52787i
$554$			8.28819i			0.352131i
$555$	−0.148238	−	0.256756i	−0.00629235	−	0.0108987i
$556$	−8.83267	+	15.2986i	−0.374589	+	0.648806i
$557$	6.18967	+	3.57361i	0.262265	+	0.151419i	0.625367	−	0.780331i	$-0.284949\pi$
$557$	6.18967	+	3.57361i	0.262265	+	0.151419i	−0.363102	+	0.931749i	$0.618283\pi$
$558$	−0.215772	+	0.373728i	−0.00913436	+	0.0158212i
$559$	23.3977	+	29.1789i	0.989616	+	1.23414i
$560$	−0.112932	+	0.0790941i	−0.00477226	+	0.00334234i
$561$	−16.8998	+	9.75711i	−0.713510	+	0.411945i
$562$	6.15162			0.259490
$563$	37.9083			1.59764			0.798822	−	0.601567i	$-0.205457\pi$
$563$	37.9083			1.59764			0.798822	+	0.601567i	$0.205457\pi$
$564$	0.0347347	−	0.0200541i	0.00146260	−	0.000844430i
$565$	−0.571173	+	0.329767i	−0.0240294	+	0.0138734i
$566$	8.56574	+	4.94543i	0.360045	+	0.207872i
$567$	−1.51777	−	2.16711i	−0.0637405	−	0.0910100i
$568$	2.44366	−	4.23255i	0.102534	−	0.177594i
$569$	8.07494			0.338519			0.169259	−	0.985572i	$-0.445862\pi$
$569$	8.07494			0.338519			0.169259	+	0.985572i	$0.445862\pi$
$570$	−0.0972853	−	0.0561677i	−0.00407483	−	0.00235261i
$571$	−6.39328	−	11.0735i	−0.267551	−	0.463411i	0.700678	−	0.713477i	$-0.252881\pi$
$571$	−6.39328	−	11.0735i	−0.267551	−	0.463411i	−0.968229	+	0.250066i	$0.919548\pi$
$572$	12.3358	−	9.89171i	0.515786	−	0.413593i
$573$	−2.91926			−0.121954
$574$	0.262335	−	0.0229799i	0.0109497	−	0.000959163i
$575$	11.7557	+	20.3614i	0.490246	+	0.849131i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	32.1077	−	18.5374i	1.33666	−	0.771722i	0.350350	−	0.936619i	$-0.386062\pi$
$577$	32.1077	−	18.5374i	1.33666	−	0.771722i	0.986311	+	0.164897i	$0.0527291\pi$
$578$		−	2.80041i		−	0.116482i
$579$	21.3521	−	12.3276i	0.887363	−	0.512319i
$580$			0.143670i			0.00596555i
$581$	25.6627	+	11.9633i	1.06467	+	0.496323i
$582$	2.17844	+	3.77317i	0.0902994	+	0.156403i
$583$			4.22570i			0.175011i
$584$	0.774785	+	1.34197i	0.0320608	+	0.0555310i
$585$	−0.175087	−	0.0681755i	−0.00723897	−	0.00281871i
$586$	−2.23260	+	3.86698i	−0.0922278	+	0.159743i
$587$	−24.7273	+	14.2763i	−1.02060	+	0.589246i	−0.914279	−	0.405086i	$-0.867242\pi$
$587$	−24.7273	+	14.2763i	−1.02060	+	0.589246i	−0.106325	+	0.994331i	$0.533908\pi$
$588$	−6.89339	+	1.21703i	−0.284279	+	0.0501893i
$589$	−0.465130	+	0.805629i	−0.0191654	+	0.0331954i
$590$	−0.220355	−	0.127222i	−0.00907187	−	0.00523764i
$591$		−	21.9031i		−	0.900974i
$592$			5.68921i			0.233825i
$593$	−14.4152	−	8.32262i	−0.591961	−	0.341769i	0.173911	−	0.984761i	$-0.444359\pi$
$593$	−14.4152	−	8.32262i	−0.591961	−	0.341769i	−0.765873	+	0.642992i	$0.777693\pi$
$594$	−2.19272	+	3.79791i	−0.0899686	+	0.155830i
$595$	0.502522	−	0.351950i	0.0206014	−	0.0144286i
$596$	−11.0581	+	6.38440i	−0.452957	+	0.261515i
$597$	12.9828	−	22.4869i	0.531352	−	0.920329i
$598$	15.8074	+	6.15510i	0.646414	+	0.251701i
$599$	0.518738	+	0.898481i	0.0211951	+	0.0367110i	0.876428	−	0.481532i	$-0.159920\pi$
$599$	0.518738	+	0.898481i	0.0211951	+	0.0367110i	−0.855233	+	0.518243i	$0.826586\pi$
$600$			4.99728i			0.204013i
$601$	−9.82464	−	17.0168i	−0.400755	−	0.694129i	0.593062	−	0.805157i	$-0.297919\pi$
$601$	−9.82464	−	17.0168i	−0.400755	−	0.694129i	−0.993817	+	0.111028i	$0.964586\pi$
$602$	−22.4800	+	15.7443i	−0.916216	+	0.641689i
$603$		−	6.65665i		−	0.271080i
$604$	−11.7710	+	6.79597i	−0.478954	+	0.276524i
$605$			0.428994i			0.0174411i
$606$	−1.13790	+	0.656966i	−0.0462240	+	0.0266874i
$607$	−20.2310	−	35.0412i	−0.821152	−	1.42228i	−0.904825	−	0.425784i	$-0.859998\pi$
$607$	−20.2310	−	35.0412i	−0.821152	−	1.42228i	0.0836722	−	0.996493i	$-0.473335\pi$
$608$	1.07783	+	1.86685i	0.0437117	+	0.0757109i
$609$	−3.08194	+	6.61111i	−0.124887	+	0.267896i
$610$	0.212839			0.00861759
$611$	0.112820	−	0.0904670i	0.00456421	−	0.00365990i
$612$	−2.22488	−	3.85361i	−0.0899356	−	0.155773i
$613$	−10.5990	−	6.11935i	−0.428090	−	0.247158i	0.270442	−	0.962736i	$-0.412830\pi$
$613$	−10.5990	−	6.11935i	−0.428090	−	0.247158i	−0.698533	+	0.715578i	$0.746163\pi$
$614$	5.17881			0.209000
$615$	−0.00259343	+	0.00449196i	−0.000104577	+	0.000181133i
$616$	6.65612	+	9.50374i	0.268183	+	0.382917i
$617$	29.2035	+	16.8607i	1.17569	+	0.678784i	0.955013	−	0.296563i	$-0.0958404\pi$
$617$	29.2035	+	16.8607i	1.17569	+	0.678784i	0.220676	+	0.975347i	$0.429174\pi$
$618$	8.21598	−	4.74350i	0.330495	−	0.190812i
$619$	11.3245	−	6.53822i	0.455171	−	0.262793i	−0.254841	−	0.966983i	$-0.582023\pi$
$619$	11.3245	−	6.53822i	0.455171	−	0.262793i	0.710012	+	0.704190i	$0.248690\pi$
$620$	−0.0224886			−0.000903163
$621$	−4.70483			−0.188798
$622$	−30.3089	+	17.4989i	−1.21528	+	0.701640i
$623$	15.9983	+	7.45804i	0.640959	+	0.298800i
$624$	2.25557	+	2.81290i	0.0902953	+	0.112606i
$625$	−12.4796	+	21.6154i	−0.499185	+	0.864615i
$626$	−6.79378	−	3.92239i	−0.271534	−	0.156770i
$627$	−4.72676	+	8.18699i	−0.188769	+	0.326957i
$628$	−0.471406	−	0.816499i	−0.0188111	−	0.0325819i
$629$		−	25.3157i		−	1.00940i
$630$	0.0582551	−	0.124964i	0.00232094	−	0.00497867i
$631$	−15.8280	−	9.13827i	−0.630101	−	0.363789i	0.150690	−	0.988581i	$-0.451850\pi$
$631$	−15.8280	−	9.13827i	−0.630101	−	0.363789i	−0.780791	+	0.624792i	$0.785184\pi$
$632$	−14.3582	−	8.28968i	−0.571137	−	0.329746i
$633$	−8.58111			−0.341068
$634$	10.1964	−	17.6606i	0.404950	−	0.701394i
$635$			0.720718i			0.0286008i
$636$	−0.963573			−0.0382082
$637$	−23.9012	+	8.10752i	−0.947001	+	0.321232i
$638$	12.0904			0.478665
$639$			4.88733i			0.193340i
$640$	−0.0260560	+	0.0451302i	−0.00102995	+	0.00178393i
$641$	−11.2574			−0.444640			−0.222320	−	0.974974i	$-0.571363\pi$
$641$	−11.2574			−0.444640			−0.222320	+	0.974974i	$0.571363\pi$
$642$	5.71764	+	3.30108i	0.225657	+	0.130283i
$643$	11.9401	+	6.89361i	0.470871	+	0.271858i	0.716604	−	0.697480i	$-0.245695\pi$
$643$	11.9401	+	6.89361i	0.470871	+	0.271858i	−0.245733	+	0.969337i	$0.579029\pi$
$644$	−5.25945	+	11.2821i	−0.207252	+	0.444578i
$645$		−	0.540571i		−	0.0212850i
$646$	−4.79608	−	8.30706i	−0.188699	−	0.326837i
$647$	6.24090	−	10.8095i	0.245355	−	0.424967i	−0.716876	−	0.697200i	$-0.754429\pi$
$647$	6.24090	−	10.8095i	0.245355	−	0.424967i	0.962231	+	0.272233i	$0.0877622\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−10.7063	+	18.5438i	−0.420259	+	0.727909i
$650$	2.73320	+	17.8095i	0.107205	+	0.698544i
$651$	−1.03484	−	0.482416i	−0.0405584	−	0.0189074i
$652$	22.0403	−	12.7250i	0.863165	−	0.498348i
$653$	12.8218			0.501754			0.250877	−	0.968019i	$-0.419281\pi$
$653$	12.8218			0.501754			0.250877	+	0.968019i	$0.419281\pi$
$654$	9.17254			0.358675
$655$	−0.405442	+	0.234082i	−0.0158419	+	0.00914633i
$656$	0.0861982	−	0.0497666i	0.00336548	−	0.00194306i
$657$	−1.34197	−	0.774785i	−0.0523551	−	0.0302272i
$658$	0.0608752	+	0.0869188i	0.00237316	+	0.00338845i
$659$	−0.105070	+	0.181986i	−0.00409294	+	0.00708918i	−0.868065	−	0.496451i	$-0.834636\pi$
$659$	−0.105070	+	0.181986i	−0.00409294	+	0.00708918i	0.863972	+	0.503540i	$0.167969\pi$
$660$	−0.228534			−0.00889568
$661$	36.8736	+	21.2890i	1.43422	+	0.828045i	0.997439	−	0.0715252i	$-0.0227866\pi$
$661$	36.8736	+	21.2890i	1.43422	+	0.828045i	0.436777	+	0.899570i	$0.356120\pi$
$662$	0.595804	+	1.03196i	0.0231566	+	0.0401084i
$663$	−10.0368	−	12.5167i	−0.389796	−	0.486109i
$664$	10.7018			0.415309
$665$	0.125578	−	0.269379i	0.00486970	−	0.0104461i
$666$	−2.84461	−	4.92700i	−0.110226	−	0.190917i
$667$	6.48547	+	11.2332i	0.251118	+	0.434950i
$668$	−11.5885	+	6.69063i	−0.448373	+	0.258868i
$669$			22.6641i			0.876246i
$670$	0.300416	−	0.173445i	0.0116061	−	0.00670078i
$671$		−	17.9113i		−	0.691459i
$672$	−2.16711	+	1.51777i	−0.0835980	+	0.0585494i
$673$	−1.00829	−	1.74642i	−0.0388668	−	0.0673194i	0.845938	−	0.533282i	$-0.179041\pi$
$673$	−1.00829	−	1.74642i	−0.0388668	−	0.0673194i	−0.884804	+	0.465963i	$0.845708\pi$
$674$			1.46143i			0.0562920i
$675$	−2.49864	−	4.32778i	−0.0961728	−	0.166576i
$676$	9.57696	+	8.79101i	0.368344	+	0.338116i
$677$	7.37573	−	12.7751i	0.283472	−	0.490988i	−0.688765	−	0.724984i	$-0.741847\pi$
$677$	7.37573	−	12.7751i	0.283472	−	0.490988i	0.972238	+	0.233996i	$0.0751803\pi$
$678$	−10.9605	+	6.32805i	−0.420936	+	0.243027i
$679$	−9.44184	+	6.61277i	−0.362345	+	0.253775i
$680$	0.115943	−	0.200819i	0.00444621	−	0.00770106i
$681$	−20.2725	−	11.7043i	−0.776842	−	0.448510i
$682$			1.89251i			0.0724681i
$683$		−	2.37992i		−	0.0910652i	−0.998963	−	0.0455326i	$-0.985502\pi$
$683$		−	2.37992i		−	0.0910652i	0.998963	−	0.0455326i	$-0.0144985\pi$
$684$	−1.86685	−	1.07783i	−0.0713809	−	0.0412118i
$685$	0.290145	−	0.502547i	0.0110859	−	0.0192013i
$686$	−4.79919	−	17.8876i	−0.183234	−	0.682953i
$687$	1.19337	−	0.688991i	0.0455298	−	0.0262867i
$688$	−5.18663	+	8.98351i	−0.197739	+	0.342493i
$689$	−3.43401	+	0.527014i	−0.130825	+	0.0200777i
$690$	−0.122589	−	0.212330i	−0.00466688	−	0.00808327i
$691$		−	10.5707i		−	0.402128i	−0.979578	−	0.201064i	$-0.935560\pi$
$691$		−	10.5707i		−	0.402128i	0.979578	−	0.201064i	$-0.0644399\pi$
$692$	−1.06170	−	1.83891i	−0.0403597	−	0.0699050i
$693$	−10.5162	−	4.90242i	−0.399479	−	0.186228i
$694$		−	15.1772i		−	0.576118i
$695$	0.797241	−	0.460287i	0.0302411	−	0.0174597i
$696$			2.75694i			0.104502i
$697$	−0.383562	+	0.221450i	−0.0145284	+	0.00838800i
$698$	−13.6693	−	23.6760i	−0.517392	−	0.896149i
$699$	7.56218	+	13.0981i	0.286028	+	0.495415i
$700$	−13.1711	+	1.15376i	−0.497822	+	0.0436079i
$701$	6.16242			0.232751			0.116376	−	0.993205i	$-0.462872\pi$
$701$	6.16242			0.232751			0.116376	+	0.993205i	$0.462872\pi$
$702$	−3.35983	−	1.30825i	−0.126809	−	0.0493768i
$703$	−6.13199	−	10.6209i	−0.231272	−	0.400576i
$704$	3.79791	+	2.19272i	0.143139	+	0.0826414i
$705$	−0.00209011			−7.87183e−5
$706$	9.47528	−	16.4117i	0.356607	−	0.617661i
$707$	−1.99425	−	2.84743i	−0.0750016	−	0.107089i
$708$	−4.22849	−	2.44132i	−0.158916	−	0.0917505i
$709$	−18.4621	+	10.6591i	−0.693359	+	0.400311i	−0.804869	−	0.593452i	$-0.797765\pi$
$709$	−18.4621	+	10.6591i	−0.693359	+	0.400311i	0.111510	+	0.993763i	$0.464431\pi$
$710$	−0.220566	+	0.127344i	−0.00827770	+	0.00477913i
$711$	16.5794			0.621775
$712$	6.67156			0.250027
$713$	−1.75833	+	1.01517i	−0.0658499	+	0.0380184i
$714$	9.64313	−	6.75374i	0.360885	−	0.252752i
$715$	−0.814456	+	0.124994i	−0.0304589	+	0.00467451i
$716$	12.0434	−	20.8597i	0.450082	−	0.779565i
$717$	15.7655	+	9.10224i	0.588775	+	0.339929i
$718$	−14.7184	+	25.4931i	−0.549287	+	0.951394i
$719$	−15.6899	−	27.1756i	−0.585133	−	1.01348i	−0.994859	−	0.101272i	$-0.967709\pi$
$719$	−15.6899	−	27.1756i	−0.585133	−	1.01348i	0.409726	−	0.912209i	$-0.365624\pi$
$720$		−	0.0521119i		−	0.00194210i
$721$	14.3991	+	20.5594i	0.536251	+	0.765671i
$722$	12.4302	+	7.17657i	0.462604	+	0.267084i
$723$	−12.8772	−	7.43467i	−0.478909	−	0.276498i
$724$	9.06625			0.336945
$725$	−6.88861	+	11.9314i	−0.255837	+	0.443122i
$726$			8.23216i			0.305524i
$727$	−42.2847			−1.56825			−0.784127	−	0.620600i	$-0.786889\pi$
$727$	−42.2847			−1.56825			−0.784127	+	0.620600i	$0.786889\pi$
$728$	−6.89307	+	6.59436i	−0.255474	+	0.244403i
$729$	1.00000			0.0370370
$730$		−	0.0807511i		−	0.00298873i
$731$	23.0793	−	39.9745i	0.853619	−	1.47851i
$732$	4.08426			0.150959
$733$	1.98907	+	1.14839i	0.0734681	+	0.0424169i	0.536284	−	0.844038i	$-0.319828\pi$
$733$	1.98907	+	1.14839i	0.0734681	+	0.0424169i	−0.462816	+	0.886454i	$0.653161\pi$
$734$	−29.6782	−	17.1347i	−1.09544	−	0.632454i
$735$	0.342811	+	0.124689i	0.0126448	+	0.00459923i
$736$			4.70483i			0.173422i
$737$	−14.5962	−	25.2814i	−0.537658	−	0.931251i
$738$	−0.0497666	+	0.0861982i	−0.00183193	+	0.00317300i
$739$	−36.7926	−	21.2422i	−1.35344	−	0.781407i	−0.364708	−	0.931122i	$-0.618831\pi$
$739$	−36.7926	−	21.2422i	−1.35344	−	0.781407i	−0.988729	+	0.149714i	$0.952165\pi$
$740$	0.148238	−	0.256756i	0.00544933	−	0.00943852i
$741$	−7.24264	−	2.82014i	−0.266065	−	0.103600i
$742$	−0.222467	−	2.53965i	−0.00816701	−	0.0932335i
$743$	9.91595	−	5.72498i	0.363781	−	0.210029i	−0.306957	−	0.951723i	$-0.599311\pi$
$743$	9.91595	−	5.72498i	0.363781	−	0.210029i	0.670738	+	0.741694i	$0.265977\pi$
$744$	−0.431544			−0.0158212
$745$	0.665406			0.0243786
$746$	−20.6603	+	11.9282i	−0.756426	+	0.436723i
$747$	−9.26801	+	5.35089i	−0.339099	+	0.195779i
$748$	−16.8998	−	9.75711i	−0.617918	−	0.356755i
$749$	−7.38046	+	15.8319i	−0.269676	+	0.578485i
$750$	0.260489	−	0.451180i	0.00951171	−	0.0164748i
$751$	−31.9597			−1.16623			−0.583113	−	0.812391i	$-0.698165\pi$
$751$	−31.9597			−1.16623			−0.583113	+	0.812391i	$0.698165\pi$
$752$	0.0347347	+	0.0200541i	0.00126664	+	0.000731298i
$753$	−13.1750	−	22.8198i	−0.480123	−	0.831598i
$754$	1.50787	+	9.82526i	0.0549136	+	0.357815i
$755$	0.708302			0.0257778
$756$	1.11788	−	2.39799i	0.0406570	−	0.0872139i
$757$	6.49630	+	11.2519i	0.236112	+	0.408958i	0.959595	−	0.281384i	$-0.0907934\pi$
$757$	6.49630	+	11.2519i	0.236112	+	0.408958i	−0.723483	+	0.690342i	$0.757460\pi$
$758$	−11.0054	−	19.0619i	−0.399733	−	0.692358i
$759$	−17.8685	+	10.3164i	−0.648586	+	0.374461i
$760$		−	0.112335i		−	0.00407483i
$761$	32.3065	−	18.6522i	1.17111	−	0.676140i	0.217168	−	0.976134i	$-0.430318\pi$
$761$	32.3065	−	18.6522i	1.17111	−	0.676140i	0.953941	+	0.299994i	$0.0969846\pi$
$762$			13.8302i			0.501015i
$763$	2.11773	+	24.1757i	0.0766669	+	0.875219i
$764$	−1.45963	−	2.52815i	−0.0528075	−	0.0914653i
$765$			0.231886i			0.00838385i
$766$	13.6056	+	23.5657i	0.491592	+	0.851462i
$767$	−16.4049	−	6.38773i	−0.592345	−	0.230647i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	−13.6906	+	7.90425i	−0.493694	+	0.285035i	−0.726106	−	0.687583i	$-0.758672\pi$
$769$	−13.6906	+	7.90425i	−0.493694	+	0.285035i	0.232411	+	0.972618i	$0.425338\pi$
$770$	−0.0527632	−	0.602338i	−0.00190146	−	0.0217068i
$771$	−10.6281	+	18.4083i	−0.382760	+	0.662960i
$772$	21.3521	+	12.3276i	0.768479	+	0.443682i
$773$			15.6090i			0.561416i	0.959793	+	0.280708i	$0.0905692\pi$
$773$			15.6090i			0.561416i	−0.959793	+	0.280708i	$0.909431\pi$
$774$		−	10.3733i		−	0.372859i
$775$	−1.86763	−	1.07827i	−0.0670871	−	0.0387328i
$776$	−2.17844	+	3.77317i	−0.0782015	+	0.135449i
$777$	12.3291	−	8.63494i	0.442305	−	0.309777i
$778$	−23.6246	+	13.6396i	−0.846982	+	0.489005i
$779$	−0.107280	+	0.185814i	−0.00384369	+	0.00665747i
$780$	−0.0285020	−	0.185718i	−0.00102053	−	0.00664977i
$781$	10.7166	+	18.5616i	0.383469	+	0.664187i
$782$		−	20.9354i		−	0.748648i
$783$	−1.37847	−	2.38758i	−0.0492625	−	0.0853252i
$784$	−4.50067	−	5.36134i	−0.160738	−	0.191476i
$785$			0.0491317i			0.00175359i
$786$	−7.78021	+	4.49191i	−0.277511	+	0.160221i
$787$			7.43020i			0.264858i	0.991192	+	0.132429i	$0.0422777\pi$
$787$			7.43020i			0.264858i	−0.991192	+	0.132429i	$0.957722\pi$
$788$	18.9687	−	10.9516i	0.675730	−	0.390133i
$789$	−12.2755	−	21.2618i	−0.437019	−	0.756940i
$790$	0.431991	+	0.748231i	0.0153696	+	0.0266209i
$791$	−19.2091	−	27.4271i	−0.682997	−	0.975197i
$792$	−4.38545			−0.155830
$793$	14.5556	−	2.23384i	0.516885	−	0.0793258i
$794$	−0.444418	−	0.769755i	−0.0157718	−	0.0273176i
$795$	0.0434863	+	0.0251068i	0.00154230	+	0.000890448i
$796$	25.9657			0.920329
$797$	−21.9177	+	37.9625i	−0.776363	+	1.34470i	0.157662	+	0.987493i	$0.449604\pi$
$797$	−21.9177	+	37.9625i	−0.776363	+	1.34470i	−0.934025	+	0.357208i	$0.883729\pi$
$798$	2.40977	−	5.16923i	0.0853051	−	0.182989i
$799$	−0.154561	−	0.0892360i	−0.00546799	−	0.00315694i
$800$	−4.32778	+	2.49864i	−0.153010	+	0.0883403i
$801$	−5.77774	+	3.33578i	−0.204147	+	0.117864i
$802$	−8.67074			−0.306174
$803$	−6.79556			−0.239810
$804$	5.76483	−	3.32833i	0.203310	−	0.117381i
$805$	0.531327	−	0.372124i	0.0187268	−	0.0131157i
$806$	−1.53795	+	0.236028i	−0.0541719	+	0.00831372i
$807$	15.5811	−	26.9873i	0.548481	−	0.949997i
$808$	−1.13790	−	0.656966i	−0.0400311	−	0.0231120i
$809$	−24.6336	+	42.6666i	−0.866071	+	1.50008i	−9.13533e−5		1.00000i	$0.500029\pi$
$809$	−24.6336	+	42.6666i	−0.866071	+	1.50008i	−0.865980	+	0.500079i	$0.833304\pi$
$810$	0.0260560	+	0.0451302i	0.000915513	+	0.00158572i
$811$			38.6075i			1.35569i	0.735204	+	0.677846i	$0.237087\pi$
$811$			38.6075i			1.35569i	−0.735204	+	0.677846i	$0.762913\pi$
$812$	−7.26636	+	0.636514i	−0.254999	+	0.0223373i
$813$	12.7322	+	7.35096i	0.446539	+	0.257809i
$814$	−21.6071	−	12.4749i	−0.757329	−	0.437244i
$815$	−1.32625			−0.0464564
$816$	2.22488	−	3.85361i	0.0778865	−	0.134903i
$817$		−	22.3612i		−	0.782319i
$818$	5.48497			0.191777
$819$	2.67240	−	9.15742i	0.0933811	−	0.319986i
$820$	−0.00518686			−0.000181133
$821$		−	2.59773i		−	0.0906613i	−0.998972	−	0.0453306i	$-0.985566\pi$
$821$		−	2.59773i		−	0.0906613i	0.998972	−	0.0453306i	$-0.0144341\pi$
$822$	5.56774	−	9.64360i	0.194197	−	0.336359i
$823$	2.46005			0.0857519			0.0428760	−	0.999080i	$-0.486348\pi$
$823$	2.46005			0.0857519			0.0428760	+	0.999080i	$0.486348\pi$
$824$	8.21598	+	4.74350i	0.286217	+	0.165248i
$825$	−18.9792	−	10.9577i	−0.660772	−	0.381497i
$826$	5.45823	−	11.7085i	0.189916	−	0.407391i
$827$			2.35563i			0.0819132i	0.999161	+	0.0409566i	$0.0130405\pi$
$827$			2.35563i			0.0819132i	−0.999161	+	0.0409566i	$0.986959\pi$
$828$	−2.35241	−	4.07450i	−0.0817521	−	0.141599i
$829$	−22.3260	+	38.6698i	−0.775414	+	1.34306i	0.159147	+	0.987255i	$0.449126\pi$
$829$	−22.3260	+	38.6698i	−0.775414	+	1.34306i	−0.934561	+	0.355802i	$0.884208\pi$
$830$	−0.482974	−	0.278845i	−0.0167643	−	0.00967885i
$831$	4.14409	−	7.17778i	0.143757	−	0.248994i
$832$	−1.30825	+	3.35983i	−0.0453555	+	0.116481i
$833$	20.0269	+	23.8567i	0.693892	+	0.826586i
$834$	15.2986	−	8.83267i	0.529748	−	0.305850i
$835$	0.697323			0.0241319
$836$	−9.45352			−0.326957
$837$	0.373728	−	0.215772i	0.0129179	−	0.00745817i
$838$	−19.3686	+	11.1825i	−0.669078	+	0.386293i
$839$	−2.38033	−	1.37428i	−0.0821781	−	0.0474456i	0.458348	−	0.888773i	$-0.348441\pi$
$839$	−2.38033	−	1.37428i	−0.0821781	−	0.0474456i	−0.540526	+	0.841327i	$0.681775\pi$
$840$	0.137349	−	0.0120314i	0.00473900	−	0.000415124i
$841$	10.6996	−	18.5323i	0.368953	−	0.639045i
$842$	4.08927			0.140925
$843$	−5.32746	−	3.07581i	−0.183487	−	0.105937i
$844$	−4.29055	−	7.43146i	−0.147687	−	0.255801i
$845$	−0.203152	−	0.646277i	−0.00698864	−	0.0222326i
$846$	−0.0401082			−0.00137895
$847$	−21.6972	+	1.90061i	−0.745523	+	0.0653059i
$848$	−0.481787	−	0.834479i	−0.0165446	−	0.0286561i
$849$	−4.94543	−	8.56574i	−0.169727	−	0.293975i
$850$	19.2576	−	11.1184i	0.660530	−	0.381357i
$851$		−	26.7668i		−	0.917553i
$852$	−4.23255	+	2.44366i	−0.145005	+	0.0837185i
$853$		−	7.77483i		−	0.266205i	−0.991102	−	0.133103i	$-0.957506\pi$
$853$		−	7.77483i		−	0.266205i	0.991102	−	0.133103i	$-0.0424940\pi$
$854$	0.942961	+	10.7647i	0.0322675	+	0.368361i
$855$	0.0561677	+	0.0972853i	0.00192089	+	0.00332709i
$856$			6.60217i			0.225657i
$857$	28.8728	+	50.0091i	0.986275	+	1.70828i	0.636125	+	0.771586i	$0.280536\pi$
$857$	28.8728	+	50.0091i	0.986275	+	1.70828i	0.350150	+	0.936694i	$0.386131\pi$
$858$	−15.6290	+	2.39857i	−0.533564	+	0.0818857i
$859$	0.309869	−	0.536709i	0.0105726	−	0.0183123i	−0.860691	−	0.509128i	$-0.829968\pi$
$859$	0.309869	−	0.536709i	0.0105726	−	0.0183123i	0.871263	+	0.490816i	$0.163301\pi$
$860$	0.468148	−	0.270285i	0.0159637	−	0.00921665i
$861$	−0.238679	−	0.111267i	−0.00813416	−	0.00379195i
$862$	−12.6137	+	21.8476i	−0.429624	+	0.744131i
$863$	−44.9667	−	25.9616i	−1.53069	−	0.883741i	−0.999330	−	0.0365922i	$-0.988350\pi$
$863$	−44.9667	−	25.9616i	−1.53069	−	0.883741i	−0.531355	−	0.847149i	$-0.678317\pi$
$864$		−	1.00000i		−	0.0340207i
$865$			0.110654i			0.00376236i
$866$	−19.5088	−	11.2634i	−0.662937	−	0.382747i
$867$	−1.40021	+	2.42523i	−0.0475535	+	0.0823651i
$868$	−0.0996335	−	1.13740i	−0.00338178	−	0.0386060i
$869$	62.9670	−	36.3540i	2.13601	−	1.23322i
$870$	0.0718348	−	0.124421i	0.00243543	−	0.00421828i
$871$	18.7245	−	15.0146i	0.634454	−	0.508750i
$872$	4.58627	+	7.94365i	0.155311	+	0.269006i
$873$		−	4.35689i		−	0.147458i
$874$	−5.07100	−	8.78322i	−0.171529	−	0.297097i
$875$	1.24930	+	0.582393i	0.0422339	+	0.0196885i
$876$		−	1.54957i		−	0.0523551i
$877$	6.49223	−	3.74829i	0.219227	−	0.126571i	−0.386365	−	0.922346i	$-0.626270\pi$
$877$	6.49223	−	3.74829i	0.219227	−	0.126571i	0.605592	+	0.795775i	$0.292936\pi$
$878$			20.3955i			0.688316i
$879$	3.86698	−	2.23260i	0.130430	−	0.0753037i
$880$	−0.114267	−	0.197916i	−0.00385194	−	0.00667176i
$881$	26.2962	+	45.5463i	0.885940	+	1.53449i	0.844632	+	0.535347i	$0.179819\pi$
$881$	26.2962	+	45.5463i	0.885940	+	1.53449i	0.0413084	+	0.999146i	$0.486847\pi$
$882$	6.57836	+	2.39272i	0.221505	+	0.0805671i
$883$	−37.7063			−1.26892			−0.634458	−	0.772957i	$-0.718777\pi$
$883$	−37.7063			−1.26892			−0.634458	+	0.772957i	$0.718777\pi$
$884$	5.82141	−	14.9505i	0.195795	−	0.502839i
$885$	0.127222	+	0.220355i	0.00427652	+	0.00740715i
$886$	−24.6697	−	14.2431i	−0.828795	−	0.478505i
$887$	25.4857			0.855725			0.427863	−	0.903844i	$-0.359267\pi$
$887$	25.4857			0.855725			0.427863	+	0.903844i	$0.359267\pi$
$888$	2.84461	−	4.92700i	0.0954587	−	0.165339i
$889$	−36.4517	+	3.19307i	−1.22255	+	0.107092i
$890$	−0.301089	−	0.173834i	−0.0100925	−	0.00582693i
$891$	3.79791	−	2.19272i	0.127235	−	0.0734590i
$892$	−19.6277	+	11.3321i	−0.657184	+	0.379426i
$893$	−0.0864595			−0.00289326
$894$	12.7688			0.427052
$895$	−1.08704	+	0.627603i	−0.0363358	+	0.0209785i
$896$	−2.39799	−	1.11788i	−0.0801111	−	0.0373459i
$897$	−10.6121	−	13.2342i	−0.354328	−	0.441877i
$898$	0.105008	−	0.181880i	0.00350417	−	0.00606940i
$899$	−1.03035	−	0.594871i	−0.0343640	−	0.0198401i
$900$	2.49864	−	4.32778i	0.0832881	−	0.144259i
$901$	2.14384	+	3.71324i	0.0714216	+	0.123706i
$902$			0.436498i			0.0145338i
$903$	27.3404	−	2.39495i	0.909831	−	0.0796988i
$904$	−10.9605	−	6.32805i	−0.364541	−	0.210468i
$905$	−0.409162	−	0.236230i	−0.0136010	−	0.00785255i
$906$	13.5919			0.451562
$907$	−10.3953	+	18.0052i	−0.345170	+	0.597852i	−0.985385	−	0.170344i	$-0.945512\pi$
$907$	−10.3953	+	18.0052i	−0.345170	+	0.597852i	0.640214	+	0.768196i	$0.278845\pi$
$908$		−	23.4086i		−	0.776842i
$909$	1.31393			0.0435804
$910$	0.482908	−	0.117999i	0.0160083	−	0.00391164i
$911$	−3.17234			−0.105104			−0.0525522	−	0.998618i	$-0.516736\pi$
$911$	−3.17234			−0.105104			−0.0525522	+	0.998618i	$0.516736\pi$
$912$		−	2.15566i		−	0.0713809i
$913$	−23.4660	+	40.6444i	−0.776612	+	1.34513i
$914$	−11.5201			−0.381052
$915$	−0.184324	−	0.106419i	−0.00609355	−	0.00351812i
$916$	1.19337	+	0.688991i	0.0394300	+	0.0227649i
$917$	−13.6354	−	19.4689i	−0.450281	−	0.642920i
$918$			4.44977i			0.146864i
$919$	−25.0071	−	43.3135i	−0.824907	−	1.42878i	−0.901991	−	0.431756i	$-0.857894\pi$
$919$	−25.0071	−	43.3135i	−0.824907	−	1.42878i	0.0770839	−	0.997025i	$-0.475439\pi$
$920$	0.122589	−	0.212330i	0.00404163	−	0.00700032i
$921$	−4.48498	−	2.58941i	−0.147785	−	0.0853238i
$922$	−17.7517	+	30.7468i	−0.584620	+	1.01259i
$923$	−13.7475	+	11.0237i	−0.452506	+	0.362850i
$924$	−1.01250	−	11.5585i	−0.0333088	−	0.380248i
$925$	24.6216	−	14.2153i	0.809554	−	0.467396i
$926$	−7.89303			−0.259381
$927$	−9.48700			−0.311594
$928$	−2.38758	+	1.37847i	−0.0783762	+	0.0452505i
$929$	2.42097	−	1.39775i	0.0794296	−	0.0458587i	−0.459759	−	0.888044i	$-0.652064\pi$
$929$	2.42097	−	1.39775i	0.0794296	−	0.0458587i	0.539189	+	0.842185i	$0.318731\pi$
$930$	0.0194757	+	0.0112443i	0.000638633	+	0.000368715i
$931$	14.1807	+	5.15788i	0.464753	+	0.169043i
$932$	−7.56218	+	13.0981i	−0.247708	+	0.429042i
$933$	34.9977			1.14577
$934$	28.1992	+	16.2808i	0.922706	+	0.532724i
$935$	0.508462	+	0.880681i	0.0166285	+	0.0288014i
$936$	−0.546937	−	3.56383i	−0.0178772	−	0.116487i
$937$	−18.8527			−0.615890			−0.307945	−	0.951404i	$-0.599641\pi$
$937$	−18.8527			−0.615890			−0.307945	+	0.951404i	$0.599641\pi$
$938$	10.1033	+	14.4257i	0.329884	+	0.471015i
$939$	3.92239	+	6.79378i	0.128002	+	0.221707i
$940$	−0.00104506	−	0.00181009i	−3.40860e−5	−	5.90387e-5i
$941$	33.1581	−	19.1438i	1.08092	−	0.624071i	0.149778	−	0.988720i	$-0.452144\pi$
$941$	33.1581	−	19.1438i	1.08092	−	0.624071i	0.931145	+	0.364648i	$0.118811\pi$
$942$			0.942812i			0.0307185i
$943$	−0.405548	+	0.234143i	−0.0132065	+	0.00762475i
$944$		−	4.88264i		−	0.158916i
$945$	−0.112932	+	0.0790941i	−0.00367368	+	0.00257293i
$946$	−22.7457	−	39.3967i	−0.739527	−	1.28090i
$947$			60.0547i			1.95152i	0.218852	+	0.975758i	$0.429769\pi$
$947$			60.0547i			1.95152i	−0.218852	+	0.975758i	$0.570231\pi$
$948$	8.28968	+	14.3582i	0.269236	+	0.466331i
$949$	−0.847518	−	5.52240i	−0.0275116	−	0.179265i
$950$	5.38621	−	9.32919i	0.174752	−	0.302679i
$951$	−17.6606	+	10.1964i	−0.572686	+	0.330640i
$952$	10.6705	+	4.97432i	0.345832	+	0.161219i
$953$	−11.8752	+	20.5684i	−0.384675	+	0.666277i	−0.991724	−	0.128387i	$-0.959020\pi$
$953$	−11.8752	+	20.5684i	−0.384675	+	0.666277i	0.607049	+	0.794665i	$0.292353\pi$
$954$	0.834479	+	0.481787i	0.0270173	+	0.0155984i
$955$			0.152128i			0.00492275i
$956$			18.2045i			0.588775i
$957$	−10.4706	−	6.04521i	−0.338467	−	0.195414i
$958$	−0.569385	+	0.986205i	−0.0183960	+	0.0318628i
$959$	26.7027	+	12.4482i	0.862275	+	0.401972i
$960$	0.0451302	−	0.0260560i	0.00145657	−	0.000840952i
$961$	−15.4069	+	26.6855i	−0.496996	+	0.860823i
$962$	7.44292	−	19.1148i	0.239969	−	0.616286i
$963$	−3.30108	−	5.71764i	−0.106376	−	0.184249i
$964$		−	14.8693i		−	0.478909i
$965$	−0.642417	−	1.11270i	−0.0206801	−	0.0358191i
$966$	10.1959	−	7.14087i	0.328047	−	0.229754i
$967$			32.1318i			1.03329i	0.856200	+	0.516645i	$0.172819\pi$
$967$			32.1318i			1.03329i	−0.856200	+	0.516645i	$0.827181\pi$
$968$	−7.12926	+	4.11608i	−0.229143	+	0.132296i
$969$			9.59216i			0.308145i
$970$	0.196627	−	0.113523i	0.00631332	−	0.00364500i
$971$	−17.3758	−	30.0958i	−0.557617	−	0.965821i	−0.997695	−	0.0678611i	$-0.978383\pi$
$971$	−17.3758	−	30.0958i	−0.557617	−	0.965821i	0.440078	−	0.897960i	$-0.354951\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	26.8120	+	38.2827i	0.859553	+	1.22729i
$974$	−3.30285			−0.105830
$975$	6.53770	−	16.7900i	0.209374	−	0.537712i
$976$	2.04213	+	3.53707i	0.0653670	+	0.113219i
$977$	9.92835	+	5.73214i	0.317636	+	0.183387i	0.650338	−	0.759645i	$-0.274627\pi$
$977$	9.92835	+	5.73214i	0.317636	+	0.183387i	−0.332702	+	0.943032i	$0.607960\pi$
$978$	−25.4499			−0.813800
$979$	−14.6289	+	25.3380i	−0.467542	+	0.809806i
$980$	0.0634215	+	0.359228i	0.00202593	+	0.0114751i
$981$	−7.94365	−	4.58627i	−0.253621	−	0.146428i
$982$	−15.1381	+	8.73997i	−0.483075	+	0.278904i
$983$	37.1123	−	21.4268i	1.18370	−	0.683408i	0.226830	−	0.973934i	$-0.427164\pi$
$983$	37.1123	−	21.4268i	1.18370	−	0.683408i	0.956867	+	0.290526i	$0.0938304\pi$
$984$	−0.0995332			−0.00317300
$985$	−1.14141			−0.0363684
$986$	10.6242	−	6.13387i	0.338343	−	0.195342i
$987$	−0.00926005	−	0.105711i	−0.000294751	−	0.00336483i
$988$	−1.17901	−	7.68238i	−0.0375093	−	0.244409i
$989$	24.4022	−	42.2659i	0.775946	−	1.34398i
$990$	0.197916	+	0.114267i	0.00629020	+	0.00363165i
$991$	−2.45984	+	4.26057i	−0.0781395	+	0.135342i	−0.902447	−	0.430800i	$-0.858231\pi$
$991$	−2.45984	+	4.26057i	−0.0781395	+	0.135342i	0.824308	+	0.566142i	$0.191565\pi$
$992$	−0.215772	−	0.373728i	−0.00685077	−	0.0118659i
$993$		−	1.19161i		−	0.0378146i
$994$	−7.41786	−	10.5914i	−0.235280	−	0.335938i
$995$	−1.17184	−	0.676561i	−0.0371497	−	0.0214484i
$996$	−9.26801	−	5.35089i	−0.293668	−	0.169549i
$997$	−10.3760			−0.328612			−0.164306	−	0.986409i	$-0.552538\pi$
$997$	−10.3760			−0.328612			−0.164306	+	0.986409i	$0.552538\pi$
$998$	0.466695	−	0.808340i	0.0147730	−	0.0255875i
$999$			5.68921i			0.179999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bm.b.205.3	yes	20
3.2	odd	2		1638.2.dt.b.1297.8		20
7.4	even	3		546.2.bd.b.361.8	yes	20
13.4	even	6		546.2.bd.b.121.8	✓	20
21.11	odd	6		1638.2.cr.b.361.3		20
39.17	odd	6		1638.2.cr.b.667.3		20
91.4	even	6	inner	546.2.bm.b.277.8	yes	20
273.95	odd	6		1638.2.dt.b.1369.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.b.121.8	✓	20	13.4	even	6
546.2.bd.b.361.8	yes	20	7.4	even	3
546.2.bm.b.205.3	yes	20	1.1	even	1	trivial
546.2.bm.b.277.8	yes	20	91.4	even	6	inner
1638.2.cr.b.361.3		20	21.11	odd	6
1638.2.cr.b.667.3		20	39.17	odd	6
1638.2.dt.b.1297.8		20	3.2	odd	2
1638.2.dt.b.1369.3		20	273.95	odd	6

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.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +(0.0451302 + 0.0260560i) q^{5} +(0.866025 + 0.500000i) q^{6} +(-1.11788 + 2.39799i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +(0.0451302 + 0.0260560i) q^{5} +(0.866025 + 0.500000i) q^{6} +(-1.11788 + 2.39799i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.0260560 - 0.0451302i) q^{10} +(-3.79791 - 2.19272i) q^{11} +(0.500000 - 0.866025i) q^{12} +(1.30825 - 3.35983i) q^{13} +(2.39799 + 1.11788i) q^{14} +(-0.0451302 + 0.0260560i) q^{15} +1.00000 q^{16} -4.44977 q^{17} +(-0.866025 + 0.500000i) q^{18} +(-1.86685 + 1.07783i) q^{19} +(-0.0451302 - 0.0260560i) q^{20} +(-1.51777 - 2.16711i) q^{21} +(-2.19272 + 3.79791i) q^{22} -4.70483 q^{23} +(-0.866025 - 0.500000i) q^{24} +(-2.49864 - 4.32778i) q^{25} +(-3.35983 - 1.30825i) q^{26} +1.00000 q^{27} +(1.11788 - 2.39799i) q^{28} +(-1.37847 - 2.38758i) q^{29} +(0.0260560 + 0.0451302i) q^{30} +(0.373728 - 0.215772i) q^{31} -1.00000i q^{32} +(3.79791 - 2.19272i) q^{33} +4.44977i q^{34} +(-0.112932 + 0.0790941i) q^{35} +(0.500000 + 0.866025i) q^{36} +5.68921i q^{37} +(1.07783 + 1.86685i) q^{38} +(2.25557 + 2.81290i) q^{39} +(-0.0260560 + 0.0451302i) q^{40} +(0.0861982 - 0.0497666i) q^{41} +(-2.16711 + 1.51777i) q^{42} +(-5.18663 + 8.98351i) q^{43} +(3.79791 + 2.19272i) q^{44} -0.0521119i q^{45} +4.70483i q^{46} +(0.0347347 + 0.0200541i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(-4.50067 - 5.36134i) q^{49} +(-4.32778 + 2.49864i) q^{50} +(2.22488 - 3.85361i) q^{51} +(-1.30825 + 3.35983i) q^{52} +(-0.481787 - 0.834479i) q^{53} -1.00000i q^{54} +(-0.114267 - 0.197916i) q^{55} +(-2.39799 - 1.11788i) q^{56} -2.15566i q^{57} +(-2.38758 + 1.37847i) q^{58} -4.88264i q^{59} +(0.0451302 - 0.0260560i) q^{60} +(2.04213 + 3.53707i) q^{61} +(-0.215772 - 0.373728i) q^{62} +(2.63566 - 0.230877i) q^{63} -1.00000 q^{64} +(0.146585 - 0.117542i) q^{65} +(-2.19272 - 3.79791i) q^{66} +(5.76483 + 3.32833i) q^{67} +4.44977 q^{68} +(2.35241 - 4.07450i) q^{69} +(0.0790941 + 0.112932i) q^{70} +(-4.23255 - 2.44366i) q^{71} +(0.866025 - 0.500000i) q^{72} +(1.34197 - 0.774785i) q^{73} +5.68921 q^{74} +4.99728 q^{75} +(1.86685 - 1.07783i) q^{76} +(9.50374 - 6.65612i) q^{77} +(2.81290 - 2.25557i) q^{78} +(-8.28968 + 14.3582i) q^{79} +(0.0451302 + 0.0260560i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.0497666 - 0.0861982i) q^{82} -10.7018i q^{83} +(1.51777 + 2.16711i) q^{84} +(-0.200819 - 0.115943i) q^{85} +(8.98351 + 5.18663i) q^{86} +2.75694 q^{87} +(2.19272 - 3.79791i) q^{88} -6.67156i q^{89} -0.0521119 q^{90} +(6.59436 + 6.89307i) q^{91} +4.70483 q^{92} +0.431544i q^{93} +(0.0200541 - 0.0347347i) q^{94} -0.112335 q^{95} +(0.866025 + 0.500000i) q^{96} +(3.77317 + 2.17844i) q^{97} +(-5.36134 + 4.50067i) q^{98} +4.38545i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 10 q^{3} - 20 q^{4} - 10 q^{9}+O(q^{10}) \) 20 * q - 10 * q^3 - 20 * q^4 - 10 * q^9	\( 20 q - 10 q^{3} - 20 q^{4} - 10 q^{9} + 4 q^{10} + 6 q^{11} + 10 q^{12} + 8 q^{13} + 4 q^{14} + 20 q^{16} - 8 q^{17} - 12 q^{19} + 6 q^{21} - 10 q^{22} - 16 q^{23} + 6 q^{25} + 8 q^{26} + 20 q^{27} + 8 q^{29} + 4 q^{30} + 12 q^{31} - 6 q^{33} + 10 q^{35} + 10 q^{36} + 6 q^{38} - 10 q^{39} - 4 q^{40} - 18 q^{41} - 2 q^{42} + 18 q^{43} - 6 q^{44} - 6 q^{47} - 10 q^{48} - 20 q^{49} + 12 q^{50} + 4 q^{51} - 8 q^{52} + 18 q^{53} - 12 q^{55} - 4 q^{56} + 24 q^{58} - 6 q^{61} - 6 q^{63} - 20 q^{64} - 6 q^{65} - 10 q^{66} + 24 q^{67} + 8 q^{68} + 8 q^{69} + 42 q^{70} - 6 q^{71} + 24 q^{73} + 36 q^{74} - 12 q^{75} + 12 q^{76} - 34 q^{77} + 2 q^{78} - 10 q^{81} + 18 q^{82} - 6 q^{84} - 36 q^{86} - 16 q^{87} + 10 q^{88} - 8 q^{90} - 10 q^{91} + 16 q^{92} - 16 q^{94} - 80 q^{95} - 96 q^{97} - 12 q^{98}+O(q^{100}) \) 20 * q - 10 * q^3 - 20 * q^4 - 10 * q^9 + 4 * q^10 + 6 * q^11 + 10 * q^12 + 8 * q^13 + 4 * q^14 + 20 * q^16 - 8 * q^17 - 12 * q^19 + 6 * q^21 - 10 * q^22 - 16 * q^23 + 6 * q^25 + 8 * q^26 + 20 * q^27 + 8 * q^29 + 4 * q^30 + 12 * q^31 - 6 * q^33 + 10 * q^35 + 10 * q^36 + 6 * q^38 - 10 * q^39 - 4 * q^40 - 18 * q^41 - 2 * q^42 + 18 * q^43 - 6 * q^44 - 6 * q^47 - 10 * q^48 - 20 * q^49 + 12 * q^50 + 4 * q^51 - 8 * q^52 + 18 * q^53 - 12 * q^55 - 4 * q^56 + 24 * q^58 - 6 * q^61 - 6 * q^63 - 20 * q^64 - 6 * q^65 - 10 * q^66 + 24 * q^67 + 8 * q^68 + 8 * q^69 + 42 * q^70 - 6 * q^71 + 24 * q^73 + 36 * q^74 - 12 * q^75 + 12 * q^76 - 34 * q^77 + 2 * q^78 - 10 * q^81 + 18 * q^82 - 6 * q^84 - 36 * q^86 - 16 * q^87 + 10 * q^88 - 8 * q^90 - 10 * q^91 + 16 * q^92 - 16 * q^94 - 80 * q^95 - 96 * q^97 - 12 * q^98

Introduction

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