LMFDB - Embedded newform 546.2.bd.b.361.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(121,546)]

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, 1]))

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

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

chi := DirichletCharacter("546.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bd (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			361.8
Root			$0.0521119i$ of defining polynomial
Character	$\chi$	$=$	546.361
Dual form			546.2.bd.b.121.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.0451302 + 0.0260560i) q^{5} +(0.866025 + 0.500000i) q^{6} +(1.51777 - 2.16711i) q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.0451302 + 0.0260560i) q^{5} +(0.866025 + 0.500000i) q^{6} +(1.51777 - 2.16711i) q^{7} +1.00000i q^{8} +1.00000 q^{9} -0.0521119 q^{10} +4.38545i 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} +(-0.500000 + 0.866025i) q^{16} +(2.22488 + 3.85361i) q^{17} +(0.866025 + 0.500000i) q^{18} -2.15566i q^{19} +(-0.0451302 - 0.0260560i) q^{20} +(1.51777 - 2.16711i) q^{21} +(-2.19272 + 3.79791i) q^{22} +(2.35241 - 4.07450i) q^{23} +1.00000i q^{24} +(-2.49864 + 4.32778i) q^{25} +(2.81290 - 2.25557i) q^{26} +1.00000 q^{27} +(2.63566 + 0.230877i) q^{28} +(-1.37847 - 2.38758i) q^{29} -0.0521119 q^{30} +(-0.373728 - 0.215772i) q^{31} +(-0.866025 + 0.500000i) q^{32} +4.38545i q^{33} +4.44977i q^{34} +(-0.0120314 + 0.137349i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-4.92700 - 2.84461i) q^{37} +(1.07783 - 1.86685i) q^{38} +(1.30825 - 3.35983i) q^{39} +(-0.0260560 - 0.0451302i) q^{40} +(0.0861982 - 0.0497666i) q^{41} +(2.39799 - 1.11788i) q^{42} +(-5.18663 + 8.98351i) q^{43} +(-3.79791 + 2.19272i) q^{44} +(-0.0451302 + 0.0260560i) q^{45} +(4.07450 - 2.35241i) q^{46} +(-0.0347347 + 0.0200541i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(-2.39272 - 6.57836i) q^{49} +(-4.32778 + 2.49864i) q^{50} +(2.22488 + 3.85361i) q^{51} +(3.56383 - 0.546937i) q^{52} +(-0.481787 + 0.834479i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-0.114267 - 0.197916i) q^{55} +(2.16711 + 1.51777i) q^{56} -2.15566i q^{57} -2.75694i q^{58} +(-4.22849 + 2.44132i) q^{59} +(-0.0451302 - 0.0260560i) q^{60} -4.08426 q^{61} +(-0.215772 - 0.373728i) q^{62} +(1.51777 - 2.16711i) q^{63} -1.00000 q^{64} +(0.0285020 + 0.185718i) q^{65} +(-2.19272 + 3.79791i) q^{66} -6.65665i q^{67} +(-2.22488 + 3.85361i) q^{68} +(2.35241 - 4.07450i) q^{69} +(-0.0790941 + 0.112932i) q^{70} +(-4.23255 - 2.44366i) q^{71} +1.00000i q^{72} +(-1.34197 - 0.774785i) q^{73} +(-2.84461 - 4.92700i) q^{74} +(-2.49864 + 4.32778i) 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} -0.0521119i q^{80} +1.00000 q^{81} +0.0995332 q^{82} -10.7018i q^{83} +(2.63566 + 0.230877i) q^{84} +(-0.200819 - 0.115943i) q^{85} +(-8.98351 + 5.18663i) q^{86} +(-1.37847 - 2.38758i) q^{87} -4.38545 q^{88} +(5.77774 + 3.33578i) q^{89} -0.0521119 q^{90} +(-5.29549 - 7.93459i) q^{91} +4.70483 q^{92} +(-0.373728 - 0.215772i) q^{93} -0.0401082 q^{94} +(0.0561677 + 0.0972853i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(3.77317 + 2.17844i) q^{97} +(1.21703 - 6.89339i) q^{98} +4.38545i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9}+O(q^{10}) $ 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9	$ 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9} - 8 q^{10} + 10 q^{12} + 8 q^{13} + 4 q^{14} - 10 q^{16} + 4 q^{17} - 6 q^{21} - 10 q^{22} + 8 q^{23} + 6 q^{25} + 2 q^{26} + 20 q^{27} - 6 q^{28} + 8 q^{29} - 8 q^{30} - 12 q^{31} + 4 q^{35} + 10 q^{36} + 6 q^{38} + 8 q^{39} - 4 q^{40} - 18 q^{41} + 4 q^{42} + 18 q^{43} + 6 q^{44} - 24 q^{46} + 6 q^{47} - 10 q^{48} + 4 q^{49} + 12 q^{50} + 4 q^{51} - 2 q^{52} + 18 q^{53} - 12 q^{55} + 2 q^{56} + 36 q^{59} + 12 q^{61} - 6 q^{63} - 20 q^{64} - 10 q^{66} - 4 q^{68} + 8 q^{69} - 42 q^{70} - 6 q^{71} - 24 q^{73} - 18 q^{74} + 6 q^{75} + 12 q^{76} - 34 q^{77} + 2 q^{78} + 20 q^{81} - 36 q^{82} - 6 q^{84} + 36 q^{86} + 8 q^{87} - 20 q^{88} + 18 q^{89} - 8 q^{90} - 94 q^{91} + 16 q^{92} - 12 q^{93} + 32 q^{94} + 40 q^{95} - 96 q^{97} - 12 q^{98}+O(q^{100}) $ 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9 - 8 * q^10 + 10 * q^12 + 8 * q^13 + 4 * q^14 - 10 * q^16 + 4 * q^17 - 6 * q^21 - 10 * q^22 + 8 * q^23 + 6 * q^25 + 2 * q^26 + 20 * q^27 - 6 * q^28 + 8 * q^29 - 8 * q^30 - 12 * q^31 + 4 * q^35 + 10 * q^36 + 6 * q^38 + 8 * q^39 - 4 * q^40 - 18 * q^41 + 4 * q^42 + 18 * q^43 + 6 * q^44 - 24 * q^46 + 6 * q^47 - 10 * q^48 + 4 * q^49 + 12 * q^50 + 4 * q^51 - 2 * q^52 + 18 * q^53 - 12 * q^55 + 2 * q^56 + 36 * q^59 + 12 * q^61 - 6 * q^63 - 20 * q^64 - 10 * q^66 - 4 * q^68 + 8 * q^69 - 42 * q^70 - 6 * q^71 - 24 * q^73 - 18 * q^74 + 6 * q^75 + 12 * q^76 - 34 * q^77 + 2 * q^78 + 20 * q^81 - 36 * q^82 - 6 * q^84 + 36 * q^86 + 8 * q^87 - 20 * q^88 + 18 * q^89 - 8 * q^90 - 94 * q^91 + 16 * q^92 - 12 * q^93 + 32 * q^94 + 40 * q^95 - 96 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.0451302	+	0.0260560i	−0.0201829	+	0.0116526i	−0.510057	−	0.860140i	$-0.670376\pi$
$5$	−0.0451302	+	0.0260560i	−0.0201829	+	0.0116526i	0.489875	+	0.871793i	$0.337043\pi$
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	1.51777	−	2.16711i	0.573665	−	0.819090i
$7$	1.51777	−	2.16711i	0.573665	−	0.819090i
$8$			1.00000i			0.353553i
$9$	1.00000			0.333333
$10$	−0.0521119			−0.0164792
$11$			4.38545i			1.32226i	0.750270	+	0.661131i	$0.229923\pi$
$11$			4.38545i			1.32226i	−0.750270	+	0.661131i	$0.770077\pi$
$12$	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
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.22488	+	3.85361i	0.539613	+	0.934638i	0.998925	+	0.0463623i	$0.0147629\pi$
$17$	2.22488	+	3.85361i	0.539613	+	0.934638i	−0.459311	+	0.888275i	$0.651904\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$		−	2.15566i		−	0.494541i	−0.968946	−	0.247271i	$-0.920466\pi$
$19$		−	2.15566i		−	0.494541i	0.968946	−	0.247271i	$-0.0795337\pi$
$20$	−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
$23$	2.35241	−	4.07450i	0.490512	−	0.849592i	−0.509428	−	0.860513i	$-0.670143\pi$
$23$	2.35241	−	4.07450i	0.490512	−	0.849592i	0.999940	+	0.0109209i	$0.00347630\pi$
$24$			1.00000i			0.204124i
$25$	−2.49864	+	4.32778i	−0.499728	+	0.865555i
$26$	2.81290	−	2.25557i	0.551654	−	0.442355i
$27$	1.00000			0.192450
$28$	2.63566	+	0.230877i	0.498093	+	0.0436316i
$29$	−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	$0.915730\pi$
$30$	−0.0521119			−0.00951429
$31$	−0.373728	−	0.215772i	−0.0671235	−	0.0387538i	0.466063	−	0.884752i	$-0.345672\pi$
$31$	−0.373728	−	0.215772i	−0.0671235	−	0.0387538i	−0.533186	+	0.845998i	$0.679005\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$			4.38545i			0.763409i
$34$			4.44977i			0.763128i
$35$	−0.0120314	+	0.137349i	−0.00203368	+	0.0232163i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−4.92700	−	2.84461i	−0.809994	−	0.467650i	0.0369597	−	0.999317i	$-0.488233\pi$
$37$	−4.92700	−	2.84461i	−0.809994	−	0.467650i	−0.846954	+	0.531666i	$0.821566\pi$
$38$	1.07783	−	1.86685i	0.174847	−	0.302844i
$39$	1.30825	−	3.35983i	0.209488	−	0.538004i
$40$	−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	$0.330859\pi$
$42$	2.39799	−	1.11788i	0.370017	−	0.172493i
$43$	−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
$45$	−0.0451302	+	0.0260560i	−0.00672762	+	0.00388419i
$46$	4.07450	−	2.35241i	0.600753	−	0.346845i
$47$	−0.0347347	+	0.0200541i	−0.00506658	+	0.00292519i	−0.502531	−	0.864559i	$-0.667598\pi$
$47$	−0.0347347	+	0.0200541i	−0.00506658	+	0.00292519i	0.497465	+	0.867484i	$0.334264\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−2.39272	−	6.57836i	−0.341817	−	0.939766i
$50$	−4.32778	+	2.49864i	−0.612040	+	0.353361i
$51$	2.22488	+	3.85361i	0.311546	+	0.539613i
$52$	3.56383	−	0.546937i	0.494214	−	0.0758466i
$53$	−0.481787	+	0.834479i	−0.0661785	+	0.114625i	−0.897216	−	0.441592i	$-0.854414\pi$
$53$	−0.481787	+	0.834479i	−0.0661785	+	0.114625i	0.831038	+	0.556216i	$0.187747\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	−0.114267	−	0.197916i	−0.0154078	−	0.0266870i
$56$	2.16711	+	1.51777i	0.289592	+	0.202821i
$57$		−	2.15566i		−	0.285524i
$58$		−	2.75694i		−	0.362004i
$59$	−4.22849	+	2.44132i	−0.550503	+	0.317833i	−0.749325	−	0.662203i	$-0.769622\pi$
$59$	−4.22849	+	2.44132i	−0.550503	+	0.317833i	0.198822	+	0.980036i	$0.436288\pi$
$60$	−0.0451302	−	0.0260560i	−0.00582629	−	0.00336381i
$61$	−4.08426			−0.522936			−0.261468	−	0.965212i	$-0.584207\pi$
$61$	−4.08426			−0.522936			−0.261468	+	0.965212i	$0.584207\pi$
$62$	−0.215772	−	0.373728i	−0.0274031	−	0.0474635i
$63$	1.51777	−	2.16711i	0.191222	−	0.273030i
$64$	−1.00000			−0.125000
$65$	0.0285020	+	0.185718i	0.00353523	+	0.0230355i
$66$	−2.19272	+	3.79791i	−0.269906	+	0.467490i
$67$		−	6.65665i		−	0.813239i	−0.913597	−	0.406620i	$-0.866707\pi$
$67$		−	6.65665i		−	0.813239i	0.913597	−	0.406620i	$-0.133293\pi$
$68$	−2.22488	+	3.85361i	−0.269807	+	0.467319i
$69$	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	$0.760325\pi$
$72$			1.00000i			0.117851i
$73$	−1.34197	−	0.774785i	−0.157065	−	0.0906817i	0.419407	−	0.907798i	$-0.362238\pi$
$73$	−1.34197	−	0.774785i	−0.157065	−	0.0906817i	−0.576473	+	0.817116i	$0.695571\pi$
$74$	−2.84461	−	4.92700i	−0.330679	−	0.572752i
$75$	−2.49864	+	4.32778i	−0.288518	+	0.499728i
$76$	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	−0.778750	−	0.627334i	$-0.784146\pi$
$79$	−8.28968	−	14.3582i	−0.932662	−	1.61542i	−0.153912	−	0.988085i	$-0.549187\pi$
$80$		−	0.0521119i		−	0.00582629i
$81$	1.00000			0.111111
$82$	0.0995332			0.0109916
$83$		−	10.7018i		−	1.17467i	−0.809343	−	0.587336i	$-0.800177\pi$
$83$		−	10.7018i		−	1.17467i	0.809343	−	0.587336i	$-0.199823\pi$
$84$	2.63566	+	0.230877i	0.287574	+	0.0251907i
$85$	−0.200819	−	0.115943i	−0.0217819	−	0.0125758i
$86$	−8.98351	+	5.18663i	−0.968717	+	0.559289i
$87$	−1.37847	−	2.38758i	−0.147788	−	0.255976i
$88$	−4.38545			−0.467490
$89$	5.77774	+	3.33578i	0.612440	+	0.353592i	0.773920	−	0.633284i	$-0.218293\pi$
$89$	5.77774	+	3.33578i	0.612440	+	0.353592i	−0.161480	+	0.986876i	$0.551627\pi$
$90$	−0.0521119			−0.00549308
$91$	−5.29549	−	7.93459i	−0.555118	−	0.831771i
$92$	4.70483			0.490512
$93$	−0.373728	−	0.215772i	−0.0387538	−	0.0223745i
$94$	−0.0401082			−0.00413684
$95$	0.0561677	+	0.0972853i	0.00576268	+	0.00998126i
$96$	−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	$0.595673\pi$
$98$	1.21703	−	6.89339i	0.122938	−	0.696338i
$99$			4.38545i			0.440754i
$100$	−4.99728			−0.499728
$101$	1.31393			0.130741			0.0653706	−	0.997861i	$-0.479177\pi$
$101$	1.31393			0.130741			0.0653706	+	0.997861i	$0.479177\pi$
$102$			4.44977i			0.440592i
$103$	4.74350	+	8.21598i	0.467391	+	0.809545i	0.999306	−	0.0372530i	$-0.0118607\pi$
$103$	4.74350	+	8.21598i	0.467391	+	0.809545i	−0.531915	+	0.846798i	$0.678527\pi$
$104$	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
$107$	−3.30108	+	5.71764i	−0.319128	+	0.552746i	−0.980306	−	0.197483i	$-0.936723\pi$
$107$	−3.30108	+	5.71764i	−0.319128	+	0.552746i	0.661179	+	0.750229i	$0.270057\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−7.94365	−	4.58627i	−0.760864	−	0.439285i	0.0687418	−	0.997634i	$-0.478102\pi$
$109$	−7.94365	−	4.58627i	−0.760864	−	0.439285i	−0.829606	+	0.558349i	$0.811435\pi$
$110$		−	0.228534i		−	0.0217899i
$111$	−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	$0.963703\pi$
$114$	1.07783	−	1.86685i	0.100948	−	0.174847i
$115$			0.245178i			0.0228629i
$116$	1.37847	−	2.38758i	0.127988	−	0.221681i
$117$	1.30825	−	3.35983i	0.120948	−	0.310617i
$118$	−4.88264			−0.449484
$119$	11.7281	+	1.02735i	1.07511	+	0.0941768i
$120$	−0.0260560	−	0.0451302i	−0.00237857	−	0.00411981i
$121$	−8.23216			−0.748378
$122$	−3.53707	−	2.04213i	−0.320232	−	0.184886i
$123$	0.0861982	−	0.0497666i	0.00777223	−	0.00448730i
$124$		−	0.431544i		−	0.0387538i
$125$		−	0.520978i		−	0.0465977i
$126$	2.39799	−	1.11788i	0.213630	−	0.0995890i
$127$	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	$0.623048\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−5.18663	+	8.98351i	−0.456658	+	0.790954i
$130$	−0.0681755	+	0.175087i	−0.00597939	+	0.0153562i
$131$	−4.49191	−	7.78021i	−0.392460	−	0.679760i	0.600314	−	0.799765i	$-0.295042\pi$
$131$	−4.49191	−	7.78021i	−0.392460	−	0.679760i	−0.992773	+	0.120005i	$0.961709\pi$
$132$	−3.79791	+	2.19272i	−0.330566	+	0.190852i
$133$	−4.67154	−	3.27180i	−0.405074	−	0.283701i
$134$	3.32833	−	5.76483i	0.287524	−	0.498005i
$135$	−0.0451302	+	0.0260560i	−0.00388419	+	0.00224254i
$136$	−3.85361	+	2.22488i	−0.330444	+	0.190782i
$137$	−9.64360	+	5.56774i	−0.823908	+	0.475684i	−0.851762	−	0.523928i	$-0.824466\pi$
$137$	−9.64360	+	5.56774i	−0.823908	+	0.475684i	0.0278540	+	0.999612i	$0.491133\pi$
$138$	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	$-0.102884\pi$
$140$	−0.124964	+	0.0582551i	−0.0105614	+	0.00492345i
$141$	−0.0347347	+	0.0200541i	−0.00292519	+	0.00168886i
$142$	−2.44366	−	4.23255i	−0.205068	−	0.355188i
$143$	14.7344	+	5.73727i	1.23215	+	0.479775i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	0.124421	+	0.0718348i	0.0103326	+	0.00596555i
$146$	−0.774785	−	1.34197i	−0.0641217	−	0.111062i
$147$	−2.39272	−	6.57836i	−0.197348	−	0.542574i
$148$		−	5.68921i		−	0.467650i
$149$			12.7688i			1.04606i	0.852314	+	0.523030i	$0.175198\pi$
$149$			12.7688i			1.04606i	−0.852314	+	0.523030i	$0.824802\pi$
$150$	−4.32778	+	2.49864i	−0.353361	+	0.204013i
$151$	−11.7710	−	6.79597i	−0.957908	−	0.553048i	−0.0623793	−	0.998053i	$-0.519869\pi$
$151$	−11.7710	−	6.79597i	−0.957908	−	0.553048i	−0.895528	+	0.445004i	$0.853202\pi$
$152$	2.15566			0.174847
$153$	2.22488	+	3.85361i	0.179871	+	0.311546i
$154$	4.90242	+	10.5162i	0.395048	+	0.847423i
$155$	0.0224886			0.00180633
$156$	3.56383	−	0.546937i	0.285334	−	0.0437900i
$157$	0.471406	−	0.816499i	0.0376223	−	0.0651637i	−0.846601	−	0.532228i	$-0.821355\pi$
$157$	0.471406	−	0.816499i	0.0376223	−	0.0651637i	0.884223	+	0.467064i	$0.154688\pi$
$158$		−	16.5794i		−	1.31898i
$159$	−0.481787	+	0.834479i	−0.0382082	+	0.0661785i
$160$	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
$163$		−	25.4499i		−	1.99339i	−0.0812115	−	0.996697i	$-0.525879\pi$
$163$		−	25.4499i		−	1.99339i	0.0812115	−	0.996697i	$-0.474121\pi$
$164$	0.0861982	+	0.0497666i	0.00673095	+	0.00388612i
$165$	−0.114267	−	0.197916i	−0.00889568	−	0.0154078i
$166$	5.35089	−	9.26801i	0.415309	−	0.719337i
$167$	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
$171$		−	2.15566i		−	0.164847i
$172$	−10.3733			−0.790954
$173$	−2.12340			−0.161439			−0.0807194	−	0.996737i	$-0.525722\pi$
$173$	−2.12340			−0.161439			−0.0807194	+	0.996737i	$0.525722\pi$
$174$		−	2.75694i		−	0.209003i
$175$	5.58638	+	11.9834i	0.422291	+	0.905861i
$176$	−3.79791	−	2.19272i	−0.286278	−	0.165283i
$177$	−4.22849	+	2.44132i	−0.317833	+	0.183501i
$178$	3.33578	+	5.77774i	0.250027	+	0.433060i
$179$	24.0868			1.80033			0.900164	−	0.435551i	$-0.143446\pi$
$179$	24.0868			1.80033			0.900164	+	0.435551i	$0.143446\pi$
$180$	−0.0451302	−	0.0260560i	−0.00336381	−	0.00194210i
$181$	−9.06625			−0.673889			−0.336945	−	0.941524i	$-0.609394\pi$
$181$	−9.06625			−0.673889			−0.336945	+	0.941524i	$0.609394\pi$
$182$	−0.618735	−	9.51930i	−0.0458637	−	0.705618i
$183$	−4.08426			−0.301917
$184$	4.07450	+	2.35241i	0.300376	+	0.173422i
$185$	0.296476			0.0217973
$186$	−0.215772	−	0.373728i	−0.0158212	−	0.0274031i
$187$	−16.8998	+	9.75711i	−1.23584	+	0.713510i
$188$	−0.0347347	−	0.0200541i	−0.00253329	−	0.00146260i
$189$	1.51777	−	2.16711i	0.110402	−	0.157634i
$190$			0.112335i			0.00814966i
$191$	−2.91926			−0.211230			−0.105615	−	0.994407i	$-0.533681\pi$
$191$	−2.91926			−0.211230			−0.105615	+	0.994407i	$0.533681\pi$
$192$	−1.00000			−0.0721688
$193$			24.6553i			1.77473i	0.461071	+	0.887363i	$0.347465\pi$
$193$			24.6553i			1.77473i	−0.461071	+	0.887363i	$0.652535\pi$
$194$	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	$0.618250\pi$
$198$	−2.19272	+	3.79791i	−0.155830	+	0.269906i
$199$	12.9828	+	22.4869i	0.920329	+	1.59406i	0.798906	+	0.601456i	$0.205412\pi$
$199$	12.9828	+	22.4869i	0.920329	+	1.59406i	0.121423	+	0.992601i	$0.461254\pi$
$200$	−4.32778	−	2.49864i	−0.306020	−	0.176681i
$201$		−	6.65665i		−	0.469524i
$202$	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
$205$	−0.00259343	+	0.00449196i	−0.000181133	+	0.000313732i
$206$			9.48700i			0.660991i
$207$	2.35241	−	4.07450i	0.163504	−	0.283197i
$208$	2.25557	+	2.81290i	0.156396	+	0.195039i
$209$	9.45352			0.653914
$210$	−0.0790941	+	0.112932i	−0.00545801	+	0.00779306i
$211$	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	$0.737889\pi$
$212$	−0.963573			−0.0661785
$213$	−4.23255	−	2.44366i	−0.290009	−	0.167437i
$214$	−5.71764	+	3.30108i	−0.390850	+	0.225657i
$215$		−	0.540571i		−	0.0368666i
$216$			1.00000i			0.0680414i
$217$	−1.03484	+	0.482416i	−0.0702493	+	0.0327485i
$218$	−4.58627	−	7.94365i	−0.310621	−	0.538012i
$219$	−1.34197	−	0.774785i	−0.0906817	−	0.0523551i
$220$	0.114267	−	0.197916i	0.00770388	−	0.0133435i
$221$	15.8582	−	2.43374i	1.06674	−	0.163711i
$222$	−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	$0.0590943\pi$
$224$	−0.230877	+	2.63566i	−0.0154261	+	0.176102i
$225$	−2.49864	+	4.32778i	−0.166576	+	0.288518i
$226$	−10.9605	+	6.32805i	−0.729082	+	0.420936i
$227$	20.2725	−	11.7043i	1.34553	−	0.776842i	0.357917	−	0.933753i	$-0.383487\pi$
$227$	20.2725	−	11.7043i	1.34553	−	0.776842i	0.987613	+	0.156911i	$0.0501536\pi$
$228$	1.86685	−	1.07783i	0.123635	−	0.0713809i
$229$	1.19337	−	0.688991i	0.0788600	−	0.0455298i	−0.460052	−	0.887892i	$-0.652169\pi$
$229$	1.19337	−	0.688991i	0.0788600	−	0.0455298i	0.538911	+	0.842362i	$0.318836\pi$
$230$	−0.122589	+	0.212330i	−0.00808327	+	0.0140006i
$231$	9.50374	+	6.65612i	0.625300	+	0.437941i
$232$	2.38758	−	1.37847i	0.156752	−	0.0905010i
$233$	7.56218	+	13.0981i	0.495415	+	0.858084i	0.999986	−	0.00528619i	$-0.00168265\pi$
$233$	7.56218	+	13.0981i	0.495415	+	0.858084i	−0.504571	+	0.863370i	$0.668349\pi$
$234$	2.81290	−	2.25557i	0.183885	−	0.147452i
$235$	0.00104506	−	0.00181009i	6.81720e−5	−	0.000118077i
$236$	−4.22849	−	2.44132i	−0.275251	−	0.158916i
$237$	−8.28968	−	14.3582i	−0.538473	−	0.932662i
$238$	9.64313	+	6.75374i	0.625071	+	0.437780i
$239$		−	18.2045i		−	1.17755i	−0.808297	−	0.588775i	$-0.799610\pi$
$239$		−	18.2045i		−	1.17755i	0.808297	−	0.588775i	$-0.200390\pi$
$240$		−	0.0521119i		−	0.00336381i
$241$	12.8772	−	7.43467i	0.829495	−	0.478909i	−0.0241845	−	0.999708i	$-0.507699\pi$
$241$	12.8772	−	7.43467i	0.829495	−	0.478909i	0.853680	+	0.520798i	$0.174366\pi$
$242$	−7.12926	−	4.11608i	−0.458286	−	0.264592i
$243$	1.00000			0.0641500
$244$	−2.04213	−	3.53707i	−0.130734	−	0.226438i
$245$	0.279390	+	0.234539i	0.0178496	+	0.0149841i
$246$	0.0995332			0.00634600
$247$	−7.24264	−	2.82014i	−0.460838	−	0.179441i
$248$	0.215772	−	0.373728i	0.0137015	−	0.0237318i
$249$		−	10.7018i		−	0.678197i
$250$	0.260489	−	0.451180i	0.0164748	−	0.0285351i
$251$	−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
$254$			13.8302i			0.867783i
$255$	−0.200819	−	0.115943i	−0.0125758	−	0.00726063i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.6281	+	18.4083i	−0.662960	+	1.14828i	0.316875	+	0.948467i	$0.397367\pi$
$257$	−10.6281	+	18.4083i	−0.662960	+	1.14828i	−0.979834	+	0.199812i	$0.935967\pi$
$258$	−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
$262$		−	8.98381i		−	0.555022i
$263$	24.5510			1.51388			0.756940	−	0.653484i	$-0.226694\pi$
$263$	24.5510			1.51388			0.756940	+	0.653484i	$0.226694\pi$
$264$	−4.38545			−0.269906
$265$		−	0.0502137i		−	0.00308460i
$266$	−2.40977	−	5.16923i	−0.147753	−	0.316946i
$267$	5.77774	+	3.33578i	0.353592	+	0.204147i
$268$	5.76483	−	3.32833i	0.352143	−	0.203310i
$269$	15.5811	+	26.9873i	0.949997	+	1.64544i	0.745423	+	0.666592i	$0.232248\pi$
$269$	15.5811	+	26.9873i	0.949997	+	1.64544i	0.204574	+	0.978851i	$0.434419\pi$
$270$	−0.0521119			−0.00317143
$271$	12.7322	+	7.35096i	0.773428	+	0.446539i	0.834096	−	0.551619i	$-0.185990\pi$
$271$	12.7322	+	7.35096i	0.773428	+	0.446539i	−0.0606681	+	0.998158i	$0.519323\pi$
$272$	−4.44977			−0.269807
$273$	−5.29549	−	7.93459i	−0.320498	−	0.480223i
$274$	−11.1355			−0.672718
$275$	−18.9792	−	10.9577i	−1.14449	−	0.660772i
$276$	4.70483			0.283197
$277$	4.14409	+	7.17778i	0.248994	+	0.431271i	0.963247	−	0.268617i	$-0.0865666\pi$
$277$	4.14409	+	7.17778i	0.248994	+	0.431271i	−0.714253	+	0.699888i	$0.753233\pi$
$278$	15.2986	−	8.83267i	0.917551	−	0.529748i
$279$	−0.373728	−	0.215772i	−0.0223745	−	0.0129179i
$280$	−0.137349	−	0.0120314i	−0.00820819	−	0.000719016i
$281$			6.15162i			0.366975i	0.983022	+	0.183487i	$0.0587387\pi$
$281$			6.15162i			0.366975i	−0.983022	+	0.183487i	$0.941261\pi$
$282$	−0.0401082			−0.00238841
$283$	9.89086			0.587951			0.293975	−	0.955813i	$-0.405022\pi$
$283$	9.89086			0.587951			0.293975	+	0.955813i	$0.405022\pi$
$284$		−	4.88733i		−	0.290009i
$285$	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
$289$	−1.40021	+	2.42523i	−0.0823651	+	0.142660i
$290$	0.0718348	+	0.124421i	0.00421828	+	0.00730628i
$291$	3.77317	+	2.17844i	0.221187	+	0.127703i
$292$		−	1.54957i		−	0.0906817i
$293$	−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
$296$	2.84461	−	4.92700i	0.165339	−	0.286376i
$297$			4.38545i			0.254470i
$298$	−6.38440	+	11.0581i	−0.369838	+	0.640578i
$299$	−10.6121	−	13.2342i	−0.613713	−	0.765353i
$300$	−4.99728			−0.288518
$301$	11.5961	+	24.8749i	0.668389	+	1.43377i
$302$	−6.79597	−	11.7710i	−0.391064	−	0.677343i
$303$	1.31393			0.0754834
$304$	1.86685	+	1.07783i	0.107071	+	0.0618177i
$305$	0.184324	−	0.106419i	0.0105543	−	0.00609355i
$306$			4.44977i			0.254376i
$307$			5.17881i			0.295570i	0.989019	+	0.147785i	$0.0472144\pi$
$307$			5.17881i			0.295570i	−0.989019	+	0.147785i	$0.952786\pi$
$308$	−1.01250	+	11.5585i	−0.0576925	+	0.658609i
$309$	4.74350	+	8.21598i	0.269848	+	0.467391i
$310$	0.0194757	+	0.0112443i	0.00110614	+	0.000638633i
$311$	−17.4989	+	30.3089i	−0.992269	+	1.71866i	−0.388656	+	0.921383i	$0.627061\pi$
$311$	−17.4989	+	30.3089i	−0.992269	+	1.71866i	−0.603613	+	0.797278i	$0.706273\pi$
$312$	3.35983	+	1.30825i	0.190213	+	0.0740652i
$313$	3.92239	+	6.79378i	0.221707	+	0.384007i	0.955326	−	0.295553i	$-0.0955039\pi$
$313$	3.92239	+	6.79378i	0.221707	+	0.384007i	−0.733620	+	0.679560i	$0.762171\pi$
$314$	0.816499	−	0.471406i	0.0460777	−	0.0266030i
$315$	−0.0120314	+	0.137349i	−0.000677895	+	0.00773875i
$316$	8.28968	−	14.3582i	0.466331	−	0.807709i
$317$	−17.6606	+	10.1964i	−0.991921	+	0.572686i	−0.905848	−	0.423603i	$-0.860765\pi$
$317$	−17.6606	+	10.1964i	−0.991921	+	0.572686i	−0.0860728	+	0.996289i	$0.527432\pi$
$318$	−0.834479	+	0.481787i	−0.0467953	+	0.0270173i
$319$	10.4706	−	6.04521i	0.586242	−	0.338467i
$320$	0.0451302	−	0.0260560i	0.00252286	−	0.00145657i
$321$	−3.30108	+	5.71764i	−0.184249	+	0.319128i
$322$	1.08624	−	12.4003i	0.0605336	−	0.691043i
$323$	8.30706	−	4.79608i	0.462217	−	0.266861i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	11.2717	+	14.0568i	0.625244	+	0.779733i
$326$	12.7250	−	22.0403i	0.704771	−	1.22070i
$327$	−7.94365	−	4.58627i	−0.439285	−	0.253621i
$328$	0.0497666	+	0.0861982i	0.00274790	+	0.00475950i
$329$	−0.00926005	+	0.105711i	−0.000510523	+	0.00582806i
$330$		−	0.228534i		−	0.0125804i
$331$		−	1.19161i		−	0.0654968i	−0.999464	−	0.0327484i	$-0.989574\pi$
$331$		−	1.19161i		−	0.0654968i	0.999464	−	0.0327484i	$-0.0104260\pi$
$332$	9.26801	−	5.35089i	0.508648	−	0.293668i
$333$	−4.92700	−	2.84461i	−0.269998	−	0.155883i
$334$	13.3813			0.732190
$335$	0.173445	+	0.300416i	0.00947634	+	0.0164135i
$336$	1.11788	+	2.39799i	0.0609856	+	0.130821i
$337$	−1.46143			−0.0796089			−0.0398045	−	0.999207i	$-0.512674\pi$
$337$	−1.46143			−0.0796089			−0.0398045	+	0.999207i	$0.512674\pi$
$338$	−3.89838	−	12.4017i	−0.212044	−	0.674565i
$339$	−6.32805	+	10.9605i	−0.343692	+	0.595293i
$340$		−	0.231886i		−	0.0125758i
$341$	0.946257	−	1.63897i	0.0512427	−	0.0887549i
$342$	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
$345$			0.245178i			0.0131999i
$346$	−1.83891	−	1.06170i	−0.0988606	−	0.0570772i
$347$	−7.58859	−	13.1438i	−0.407377	−	0.705598i	0.587218	−	0.809429i	$-0.300223\pi$
$347$	−7.58859	−	13.1438i	−0.407377	−	0.705598i	−0.994595	+	0.103831i	$0.966890\pi$
$348$	1.37847	−	2.38758i	0.0738938	−	0.127988i
$349$	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
$353$		−	18.9506i		−	1.00864i	−0.863518	−	0.504318i	$-0.831744\pi$
$353$		−	18.9506i		−	1.00864i	0.863518	−	0.504318i	$-0.168256\pi$
$354$	−4.88264			−0.259510
$355$	0.254688			0.0135174
$356$			6.67156i			0.353592i
$357$	11.7281	+	1.02735i	0.620715	+	0.0543730i
$358$	20.8597	+	12.0434i	1.10247	+	0.636512i
$359$	25.4931	−	14.7184i	1.34547	−	0.776810i	0.357869	−	0.933772i	$-0.383503\pi$
$359$	25.4931	−	14.7184i	1.34547	−	0.776810i	0.987605	+	0.156962i	$0.0501700\pi$
$360$	−0.0260560	−	0.0451302i	−0.00137327	−	0.00237857i
$361$	14.3531			0.755429
$362$	−7.85161	−	4.53313i	−0.412671	−	0.238256i
$363$	−8.23216			−0.432076
$364$	4.22381	−	8.55333i	0.221388	−	0.448316i
$365$	0.0807511			0.00422670
$366$	−3.53707	−	2.04213i	−0.184886	−	0.106744i
$367$	−34.2694			−1.78885			−0.894424	−	0.447219i	$-0.852414\pi$
$367$	−34.2694			−1.78885			−0.894424	+	0.447219i	$0.852414\pi$
$368$	2.35241	+	4.07450i	0.122628	+	0.212398i
$369$	0.0861982	−	0.0497666i	0.00448730	−	0.00259074i
$370$	0.256756	+	0.148238i	0.0133481	+	0.00770652i
$371$	1.07716	+	2.31064i	0.0559235	+	0.119962i
$372$		−	0.431544i		−	0.0223745i
$373$	23.8564			1.23524			0.617619	−	0.786477i	$-0.288097\pi$
$373$	23.8564			1.23524			0.617619	+	0.786477i	$0.288097\pi$
$374$	−19.5142			−1.00906
$375$		−	0.520978i		−	0.0269032i
$376$	−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	$0.142091\pi$
$380$	−0.0561677	+	0.0972853i	−0.00288134	+	0.00499063i
$381$	6.91510	+	11.9773i	0.354271	+	0.613616i
$382$	−2.52815	−	1.45963i	−0.129351	−	0.0746811i
$383$		−	27.2113i		−	1.39043i	−0.718801	−	0.695216i	$-0.755309\pi$
$383$		−	27.2113i		−	1.39043i	0.718801	−	0.695216i	$-0.244691\pi$
$384$	−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
$387$	−5.18663	+	8.98351i	−0.263651	+	0.456658i
$388$			4.35689i			0.221187i
$389$	−13.6396	+	23.6246i	−0.691558	+	1.19781i	0.279770	+	0.960067i	$0.409742\pi$
$389$	−13.6396	+	23.6246i	−0.691558	+	1.19781i	−0.971327	+	0.237746i	$0.923591\pi$
$390$	−0.0681755	+	0.175087i	−0.00345220	+	0.00886589i
$391$	20.9354			1.05875
$392$	6.57836	−	2.39272i	0.332258	−	0.120851i
$393$	−4.49191	−	7.78021i	−0.226587	−	0.392460i
$394$	−21.9031			−1.10346
$395$	0.748231	+	0.431991i	0.0376476	+	0.0217358i
$396$	−3.79791	+	2.19272i	−0.190852	+	0.110189i
$397$			0.888836i			0.0446094i	0.999751	+	0.0223047i	$0.00710040\pi$
$397$			0.888836i			0.0446094i	−0.999751	+	0.0223047i	$0.992900\pi$
$398$			25.9657i			1.30154i
$399$	−4.67154	−	3.27180i	−0.233870	−	0.163795i
$400$	−2.49864	−	4.32778i	−0.124932	−	0.216389i
$401$	7.50908	+	4.33537i	0.374985	+	0.216498i	0.675634	−	0.737237i	$-0.263870\pi$
$401$	7.50908	+	4.33537i	0.374985	+	0.216498i	−0.300649	+	0.953735i	$0.597203\pi$
$402$	3.32833	−	5.76483i	0.166002	−	0.287524i
$403$	−1.21389	+	0.973380i	−0.0604681	+	0.0484875i
$404$	0.656966	+	1.13790i	0.0326853	+	0.0566126i
$405$	−0.0451302	+	0.0260560i	−0.00224254	+	0.00129473i
$406$	−5.97459	−	4.18442i	−0.296514	−	0.207669i
$407$	12.4749	−	21.6071i	0.618356	−	1.07102i
$408$	−3.85361	+	2.22488i	−0.190782	+	0.110148i
$409$	4.75012	−	2.74248i	0.234878	−	0.135607i	−0.377942	−	0.925829i	$-0.623368\pi$
$409$	4.75012	−	2.74248i	0.234878	−	0.135607i	0.612821	+	0.790222i	$0.290035\pi$
$410$	−0.00449196	+	0.00259343i	−0.000221842	+	0.000128080i
$411$	−9.64360	+	5.56774i	−0.475684	+	0.274636i
$412$	−4.74350	+	8.21598i	−0.233695	+	0.404772i
$413$	−1.12729	+	12.8690i	−0.0554703	+	0.633241i
$414$	4.07450	−	2.35241i	0.200251	−	0.115615i
$415$	0.278845	+	0.482974i	0.0136880	+	0.0237082i
$416$	0.546937	+	3.56383i	0.0268158	+	0.174731i
$417$	8.83267	−	15.2986i	0.432538	−	0.749177i
$418$	8.18699	+	4.72676i	0.400439	+	0.231193i
$419$	−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	$-0.350631\pi$
$420$	−0.124964	+	0.0582551i	−0.00609760	+	0.00284256i
$421$			4.08927i			0.199299i	0.995023	+	0.0996494i	$0.0317721\pi$
$421$			4.08927i			0.199299i	−0.995023	+	0.0996494i	$0.968228\pi$
$422$			8.58111i			0.417722i
$423$	−0.0347347	+	0.0200541i	−0.00168886	+	0.000975063i
$424$	−0.834479	−	0.481787i	−0.0405259	−	0.0233976i
$425$	−22.2367			−1.07864
$426$	−2.44366	−	4.23255i	−0.118396	−	0.205068i
$427$	−6.19899	+	8.85104i	−0.299990	+	0.428332i
$428$	−6.60217			−0.319128
$429$	14.7344	+	5.73727i	0.711382	+	0.276998i
$430$	0.270285	−	0.468148i	0.0130343	−	0.0225761i
$431$			25.2274i			1.21516i	0.794258	+	0.607580i	$0.207860\pi$
$431$			25.2274i			1.21516i	−0.794258	+	0.607580i	$0.792140\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	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
$436$		−	9.17254i		−	0.439285i
$437$	−8.78322	−	5.07100i	−0.420159	−	0.242579i
$438$	−0.774785	−	1.34197i	−0.0370207	−	0.0641217i
$439$	10.1978	−	17.6631i	0.486713	−	0.843012i	−0.513170	−	0.858287i	$-0.671529\pi$
$439$	10.1978	−	17.6631i	0.486713	−	0.843012i	0.999883	+	0.0152752i	$0.00486244\pi$
$440$	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	0.975967	+	0.217921i	$0.0699274\pi$
$443$	14.2431	+	24.6697i	0.676708	+	1.17209i	−0.299259	+	0.954172i	$0.596739\pi$
$444$		−	5.68921i		−	0.269998i
$445$	−0.347668			−0.0164810
$446$	22.6641			1.07318
$447$			12.7688i			0.603943i
$448$	−1.51777	+	2.16711i	−0.0717081	+	0.102386i
$449$	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
$451$	0.218249	+	0.378018i	0.0102769	+	0.0178002i
$452$	−12.6561			−0.595293
$453$	−11.7710	−	6.79597i	−0.553048	−	0.319303i
$454$	23.4086			1.09862
$455$	0.445730	+	0.220111i	0.0208962	+	0.0103190i
$456$	2.15566			0.100948
$457$	9.97672	+	5.76006i	0.466691	+	0.269444i	0.714854	−	0.699274i	$-0.246493\pi$
$457$	9.97672	+	5.76006i	0.466691	+	0.269444i	−0.248162	+	0.968718i	$0.579827\pi$
$458$	1.37798			0.0643889
$459$	2.22488	+	3.85361i	0.103849	+	0.179871i
$460$	−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	$0.976495\pi$
$462$	4.90242	+	10.5162i	0.228081	+	0.489260i
$463$		−	7.89303i		−	0.366820i	−0.983036	−	0.183410i	$-0.941286\pi$
$463$		−	7.89303i		−	0.366820i	0.983036	−	0.183410i	$-0.0587136\pi$
$464$	2.75694			0.127988
$465$	0.0224886			0.00104288
$466$			15.1244i			0.700623i
$467$	−16.2808	−	28.1992i	−0.753386	−	1.30490i	−0.946173	−	0.323662i	$-0.895086\pi$
$467$	−16.2808	−	28.1992i	−0.753386	−	1.30490i	0.192787	−	0.981241i	$-0.438248\pi$
$468$	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
$471$	0.471406	−	0.816499i	0.0217212	−	0.0376223i
$472$	−2.44132	−	4.22849i	−0.112371	−	0.194632i
$473$	−39.3967	−	22.7457i	−1.81146	−	1.04585i
$474$		−	16.5794i		−	0.761516i
$475$	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
$478$	9.10224	−	15.7655i	0.416327	−	0.721099i
$479$			1.13877i			0.0520318i	0.999662	+	0.0260159i	$0.00828205\pi$
$479$			1.13877i			0.0520318i	−0.999662	+	0.0260159i	$0.991718\pi$
$480$	0.0260560	−	0.0451302i	0.00118929	−	0.00205990i
$481$	−16.0032	+	12.8324i	−0.729681	+	0.585109i
$482$	14.8693			0.677280
$483$	−5.25945	−	11.2821i	−0.239313	−	0.513354i
$484$	−4.11608	−	7.12926i	−0.187094	−	0.324057i
$485$	−0.227046			−0.0103096
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	−2.86035	+	1.65142i	−0.129615	+	0.0748332i	−0.563405	−	0.826181i	$-0.690509\pi$
$487$	−2.86035	+	1.65142i	−0.129615	+	0.0748332i	0.433791	+	0.901014i	$0.357176\pi$
$488$		−	4.08426i		−	0.184886i
$489$		−	25.4499i		−	1.15089i
$490$	0.124689	+	0.342811i	0.00563289	+	0.0154866i
$491$	−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	$0.962391\pi$
$492$	0.0861982	+	0.0497666i	0.00388612	+	0.00224365i
$493$	6.13387	−	10.6242i	0.276256	−	0.478489i
$494$	−4.86224	−	6.06364i	−0.218763	−	0.272816i
$495$	−0.114267	−	0.197916i	−0.00513592	−	0.00889568i
$496$	0.373728	−	0.215772i	0.0167809	−	0.00968845i
$497$	−11.7197	+	5.46346i	−0.525702	+	0.245070i
$498$	5.35089	−	9.26801i	0.239779	−	0.415309i
$499$	−0.808340	+	0.466695i	−0.0361863	+	0.0208921i	−0.517984	−	0.855390i	$-0.673317\pi$
$499$	−0.808340	+	0.466695i	−0.0361863	+	0.0208921i	0.481798	+	0.876282i	$0.339984\pi$
$500$	0.451180	−	0.260489i	0.0201774	−	0.0116494i
$501$	11.5885	−	6.69063i	0.517737	−	0.298915i
$502$	−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	$0.0367267\pi$
$504$	2.16711	+	1.51777i	0.0965307	+	0.0676070i
$505$	−0.0592981	+	0.0342358i	−0.00263873	+	0.00152347i
$506$	10.3164	+	17.8685i	0.458620	+	0.794353i
$507$	−9.57696	−	8.79101i	−0.425328	−	0.390423i
$508$	−6.91510	+	11.9773i	−0.306808	+	0.531407i
$509$	−34.3313	−	19.8212i	−1.52171	−	0.878560i	−0.999671	−	0.0256378i	$-0.991838\pi$
$509$	−34.3313	−	19.8212i	−1.52171	−	0.878560i	−0.522039	−	0.852922i	$-0.674828\pi$
$510$	−0.115943	−	0.200819i	−0.00513404	−	0.00889242i
$511$	−3.71585	+	1.73224i	−0.164379	+	0.0766298i
$512$		−	1.00000i		−	0.0441942i
$513$		−	2.15566i		−	0.0951745i
$514$	−18.4083	+	10.6281i	−0.811956	+	0.468783i
$515$	−0.428151	−	0.247193i	−0.0188666	−	0.0108926i
$516$	−10.3733			−0.456658
$517$	−0.0879462	−	0.152327i	−0.00386787	−	0.00669935i
$518$	−14.9948	−	1.31351i	−0.658835	−	0.0577122i
$519$	−2.12340			−0.0932067
$520$	−0.185718	+	0.0285020i	−0.00814427	+	0.00124989i
$521$	10.8983	−	18.8765i	0.477465	−	0.826993i	−0.522202	−	0.852822i	$-0.674889\pi$
$521$	10.8983	−	18.8765i	0.477465	−	0.826993i	0.999666	+	0.0258290i	$0.00822253\pi$
$522$		−	2.75694i		−	0.120668i
$523$	−20.7546	+	35.9481i	−0.907537	+	1.57190i	−0.0900610	+	0.995936i	$0.528706\pi$
$523$	−20.7546	+	35.9481i	−0.907537	+	1.57190i	−0.817476	+	0.575963i	$0.804627\pi$
$524$	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
$527$		−	1.92027i		−	0.0836483i
$528$	−3.79791	−	2.19272i	−0.165283	−	0.0954261i
$529$	0.432289	+	0.748746i	0.0187952	+	0.0325542i
$530$	0.0251068	−	0.0434863i	0.00109057	−	0.00188892i
$531$	−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
$535$		−	0.344052i		−	0.0148746i
$536$	6.65665			0.287524
$537$	24.0868			1.03942
$538$			31.1622i			1.34350i
$539$	28.8491	−	10.4932i	1.24262	−	0.451972i
$540$	−0.0451302	−	0.0260560i	−0.00194210	−	0.00112127i
$541$	9.59172	−	5.53778i	0.412380	−	0.238088i	−0.279432	−	0.960166i	$-0.590146\pi$
$541$	9.59172	−	5.53778i	0.412380	−	0.238088i	0.691812	+	0.722078i	$0.256813\pi$
$542$	7.35096	+	12.7322i	0.315751	+	0.546896i
$543$	−9.06625			−0.389070
$544$	−3.85361	−	2.22488i	−0.165222	−	0.0953911i
$545$	0.477999			0.0204752
$546$	−0.618735	−	9.51930i	−0.0264794	−	0.407389i
$547$	−31.6610			−1.35373			−0.676863	−	0.736109i	$-0.736661\pi$
$547$	−31.6610			−1.35373			−0.676863	+	0.736109i	$0.736661\pi$
$548$	−9.64360	−	5.56774i	−0.411954	−	0.237842i
$549$	−4.08426			−0.174312
$550$	−10.9577	−	18.9792i	−0.467236	−	0.809277i
$551$	−5.14680	+	2.97151i	−0.219261	+	0.126591i
$552$	4.07450	+	2.35241i	0.173422	+	0.100125i
$553$	−43.6976	−	3.82779i	−1.85821	−	0.162774i
$554$			8.28819i			0.352131i
$555$	0.296476			0.0125847
$556$	17.6653			0.749177
$557$		−	7.14722i		−	0.302837i	−0.988470	−	0.151419i	$-0.951616\pi$
$557$		−	7.14722i		−	0.302837i	0.988470	−	0.151419i	$-0.0483842\pi$
$558$	−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
$562$	−3.07581	+	5.32746i	−0.129745	+	0.224725i
$563$	−18.9542	−	32.8296i	−0.798822	−	1.38360i	−0.920384	−	0.391017i	$-0.872123\pi$
$563$	−18.9542	−	32.8296i	−0.798822	−	1.38360i	0.121561	−	0.992584i	$-0.461210\pi$
$564$	−0.0347347	−	0.0200541i	−0.00146260	−	0.000844430i
$565$		−	0.659534i		−	0.0277468i
$566$	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
$569$	−4.03747	+	6.99310i	−0.169259	+	0.293166i	−0.938160	−	0.346203i	$-0.887471\pi$
$569$	−4.03747	+	6.99310i	−0.169259	+	0.293166i	0.768900	+	0.639369i	$0.220804\pi$
$570$			0.112335i			0.00470521i
$571$	−6.39328	+	11.0735i	−0.267551	+	0.463411i	−0.968229	−	0.250066i	$-0.919548\pi$
$571$	−6.39328	+	11.0735i	−0.267551	+	0.463411i	0.700678	+	0.713477i	$0.252881\pi$
$572$	2.39857	+	15.6290i	0.100289	+	0.653480i
$573$	−2.91926			−0.121954
$574$	0.151069	−	0.215699i	0.00630549	−	0.00900311i
$575$	11.7557	+	20.3614i	0.490246	+	0.849131i
$576$	−1.00000			−0.0416667
$577$	−32.1077	−	18.5374i	−1.33666	−	0.771722i	−0.350350	−	0.936619i	$-0.613938\pi$
$577$	−32.1077	−	18.5374i	−1.33666	−	0.771722i	−0.986311	+	0.164897i	$0.947271\pi$
$578$	−2.42523	+	1.40021i	−0.100876	+	0.0582409i
$579$			24.6553i			1.02464i
$580$			0.143670i			0.00596555i
$581$	−23.1919	−	16.2429i	−0.962162	−	0.673868i
$582$	2.17844	+	3.77317i	0.0902994	+	0.156403i
$583$	−3.65957	−	2.11285i	−0.151564	−	0.0875053i
$584$	0.774785	−	1.34197i	0.0320608	−	0.0555310i
$585$	0.0285020	+	0.185718i	0.00117841	+	0.00767849i
$586$	−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	$0.533908\pi$
$588$	4.50067	−	5.36134i	0.185605	−	0.221098i
$589$	−0.465130	+	0.805629i	−0.0191654	+	0.0331954i
$590$	0.220355	−	0.127222i	0.00907187	−	0.00523764i
$591$	−18.9687	+	10.9516i	−0.780266	+	0.450487i
$592$	4.92700	−	2.84461i	0.202499	−	0.116913i
$593$	14.4152	−	8.32262i	0.591961	−	0.341769i	−0.173911	−	0.984761i	$-0.555641\pi$
$593$	14.4152	−	8.32262i	0.591961	−	0.341769i	0.765873	+	0.642992i	$0.222307\pi$
$594$	−2.19272	+	3.79791i	−0.0899686	+	0.155830i
$595$	−0.556059	+	0.259221i	−0.0227962	+	0.0106270i
$596$	−11.0581	+	6.38440i	−0.452957	+	0.261515i
$597$	12.9828	+	22.4869i	0.531352	+	0.920329i
$598$	−2.57325	−	16.7672i	−0.105228	−	0.685662i
$599$	0.518738	−	0.898481i	0.0211951	−	0.0367110i	−0.855233	−	0.518243i	$-0.826586\pi$
$599$	0.518738	−	0.898481i	0.0211951	−	0.0367110i	0.876428	+	0.481532i	$0.159920\pi$
$600$	−4.32778	−	2.49864i	−0.176681	−	0.102007i
$601$	−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	$0.964586\pi$
$602$	−2.39495	+	27.3404i	−0.0976107	+	1.11431i
$603$		−	6.65665i		−	0.271080i
$604$		−	13.5919i		−	0.553048i
$605$	0.371519	−	0.214497i	0.0151044	−	0.00872053i
$606$	1.13790	+	0.656966i	0.0462240	+	0.0266874i
$607$	40.4621			1.64230			0.821152	−	0.570709i	$-0.193332\pi$
$607$	40.4621			1.64230			0.821152	+	0.570709i	$0.193332\pi$
$608$	1.07783	+	1.86685i	0.0437117	+	0.0757109i
$609$	−7.26636	−	0.636514i	−0.294448	−	0.0257928i
$610$	0.212839			0.00861759
$611$	0.0219367	+	0.142939i	0.000887463	+	0.00578268i
$612$	−2.22488	+	3.85361i	−0.0899356	+	0.155773i
$613$			12.2387i			0.494316i	0.968975	+	0.247158i	$0.0794967\pi$
$613$			12.2387i			0.494316i	−0.968975	+	0.247158i	$0.920503\pi$
$614$	−2.58941	+	4.48498i	−0.104500	+	0.180999i
$615$	−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	$0.429174\pi$
$618$			9.48700i			0.381623i
$619$	−11.3245	−	6.53822i	−0.455171	−	0.262793i	0.254841	−	0.966983i	$-0.417977\pi$
$619$	−11.3245	−	6.53822i	−0.455171	−	0.262793i	−0.710012	+	0.704190i	$0.751310\pi$
$620$	0.0112443	+	0.0194757i	0.000451582	+	0.000782162i
$621$	2.35241	−	4.07450i	0.0943992	−	0.163504i
$622$	−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
$626$			7.84478i			0.313540i
$627$	9.45352			0.377537
$628$	0.942812			0.0376223
$629$		−	25.3157i		−	1.00940i
$630$	−0.0790941	+	0.112932i	−0.00315119	+	0.00449933i
$631$	−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
$633$	4.29055	+	7.43146i	0.170534	+	0.295374i
$634$	−20.3928			−0.809900
$635$	−0.624160	−	0.360359i	−0.0247690	−	0.0143004i
$636$	−0.963573			−0.0382082
$637$	−25.2325	−	0.567012i	−0.999748	−	0.0224658i
$638$	12.0904			0.478665
$639$	−4.23255	−	2.44366i	−0.167437	−	0.0966698i
$640$	0.0521119			0.00205990
$641$	5.62869	+	9.74918i	0.222320	+	0.385069i	0.955512	−	0.294952i	$-0.0953037\pi$
$641$	5.62869	+	9.74918i	0.222320	+	0.385069i	−0.733192	+	0.680022i	$0.761970\pi$
$642$	−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	$0.579029\pi$
$644$	7.14087	−	10.1959i	0.281390	−	0.401774i
$645$		−	0.540571i		−	0.0212850i
$646$	9.59216			0.377399
$647$	−12.4818			−0.490710			−0.245355	−	0.969433i	$-0.578904\pi$
$647$	−12.4818			−0.490710			−0.245355	+	0.969433i	$0.578904\pi$
$648$			1.00000i			0.0392837i
$649$	−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
$653$	−6.41088	+	11.1040i	−0.250877	+	0.434532i	−0.963768	−	0.266744i	$-0.914052\pi$
$653$	−6.41088	+	11.1040i	−0.250877	+	0.434532i	0.712890	+	0.701275i	$0.247386\pi$
$654$	−4.58627	−	7.94365i	−0.179337	−	0.310621i
$655$	0.405442	+	0.234082i	0.0158419	+	0.00914633i
$656$			0.0995332i			0.00388612i
$657$	−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	$0.167969\pi$
$660$	0.114267	−	0.197916i	0.00444784	−	0.00770388i
$661$		−	42.5779i		−	1.65609i	−0.560662	−	0.828045i	$-0.689453\pi$
$661$		−	42.5779i		−	1.65609i	0.560662	−	0.828045i	$-0.310547\pi$
$662$	0.595804	−	1.03196i	0.0231566	−	0.0401084i
$663$	15.8582	−	2.43374i	0.615881	−	0.0945188i
$664$	10.7018			0.415309
$665$	0.296078	+	0.0259356i	0.0114814	+	0.00100574i
$666$	−2.84461	−	4.92700i	−0.110226	−	0.190917i
$667$	−12.9709			−0.502237
$668$	11.5885	+	6.69063i	0.448373	+	0.258868i
$669$	19.6277	−	11.3321i	0.758851	−	0.438123i
$670$			0.346891i			0.0134016i
$671$		−	17.9113i		−	0.691459i
$672$	−0.230877	+	2.63566i	−0.00890627	+	0.101673i
$673$	−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	$0.845708\pi$
$674$	−1.26563	−	0.730713i	−0.0487503	−	0.0281460i
$675$	−2.49864	+	4.32778i	−0.0961728	+	0.166576i
$676$	2.82476	−	12.6894i	0.108645	−	0.488054i
$677$	7.37573	+	12.7751i	0.283472	+	0.490988i	0.972238	−	0.233996i	$-0.0751803\pi$
$677$	7.37573	+	12.7751i	0.283472	+	0.490988i	−0.688765	+	0.724984i	$0.741847\pi$
$678$	−10.9605	+	6.32805i	−0.420936	+	0.243027i
$679$	10.4477	−	4.87049i	0.400948	−	0.186912i
$680$	0.115943	−	0.200819i	0.00444621	−	0.00770106i
$681$	20.2725	−	11.7043i	0.776842	−	0.448510i
$682$	1.63897	−	0.946257i	0.0627592	−	0.0362341i
$683$	−2.06107	+	1.18996i	−0.0788648	+	0.0455326i	−0.538914	−	0.842361i	$-0.681165\pi$
$683$	−2.06107	+	1.18996i	−0.0788648	+	0.0455326i	0.460049	+	0.887894i	$0.347832\pi$
$684$	1.86685	−	1.07783i	0.0713809	−	0.0412118i
$685$	0.290145	−	0.502547i	0.0110859	−	0.0192013i
$686$	−13.0916	−	13.1000i	−0.499838	−	0.500162i
$687$	1.19337	−	0.688991i	0.0455298	−	0.0262867i
$688$	−5.18663	−	8.98351i	−0.197739	−	0.342493i
$689$	2.17341	+	2.71043i	0.0828004	+	0.103259i
$690$	−0.122589	+	0.212330i	−0.00466688	+	0.00808327i
$691$	9.15448	+	5.28534i	0.348253	+	0.201064i	0.663916	−	0.747808i	$-0.268893\pi$
$691$	9.15448	+	5.28534i	0.348253	+	0.201064i	−0.315663	+	0.948871i	$0.602227\pi$
$692$	−1.06170	−	1.83891i	−0.0403597	−	0.0699050i
$693$	9.50374	+	6.65612i	0.361017	+	0.252845i
$694$		−	15.1772i		−	0.576118i
$695$			0.920575i			0.0349194i
$696$	2.38758	−	1.37847i	0.0905010	−	0.0522508i
$697$	0.383562	+	0.221450i	0.0145284	+	0.00838800i
$698$	27.3387			1.03478
$699$	7.56218	+	13.0981i	0.286028	+	0.495415i
$700$	−7.58475	+	10.8297i	−0.286677	+	0.409323i
$701$	6.16242			0.232751			0.116376	−	0.993205i	$-0.462872\pi$
$701$	6.16242			0.232751			0.116376	+	0.993205i	$0.462872\pi$
$702$	2.81290	−	2.25557i	0.106166	−	0.0851312i
$703$	−6.13199	+	10.6209i	−0.231272	+	0.400576i
$704$		−	4.38545i		−	0.165283i
$705$	0.00104506	−	0.00181009i	3.93591e−5	−	6.81720e-5i
$706$	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
$709$		−	21.3182i		−	0.800622i	−0.916379	−	0.400311i	$-0.868902\pi$
$709$		−	21.3182i		−	0.800622i	0.916379	−	0.400311i	$-0.131098\pi$
$710$	0.220566	+	0.127344i	0.00827770	+	0.00477913i
$711$	−8.28968	−	14.3582i	−0.310887	−	0.538473i
$712$	−3.33578	+	5.77774i	−0.125014	+	0.216530i
$713$	−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
$717$		−	18.2045i		−	0.679859i
$718$	29.4369			1.09857
$719$	31.3797			1.17027			0.585133	−	0.810937i	$-0.301042\pi$
$719$	31.3797			1.17027			0.585133	+	0.810937i	$0.301042\pi$
$720$		−	0.0521119i		−	0.00194210i
$721$	25.0045	+	2.19033i	0.931216	+	0.0815721i
$722$	12.4302	+	7.17657i	0.462604	+	0.267084i
$723$	12.8772	−	7.43467i	0.478909	−	0.276498i
$724$	−4.53313	−	7.85161i	−0.168472	−	0.291803i
$725$	13.7772			0.511673
$726$	−7.12926	−	4.11608i	−0.264592	−	0.152762i
$727$	−42.2847			−1.56825			−0.784127	−	0.620600i	$-0.786889\pi$
$727$	−42.2847			−1.56825			−0.784127	+	0.620600i	$0.786889\pi$
$728$	7.93459	−	5.29549i	0.294076	−	0.196264i
$729$	1.00000			0.0370370
$730$	0.0699325	+	0.0403755i	0.00258832	+	0.00149437i
$731$	−46.1586			−1.70724
$732$	−2.04213	−	3.53707i	−0.0754793	−	0.130734i
$733$	−1.98907	+	1.14839i	−0.0734681	+	0.0424169i	−0.536284	−	0.844038i	$-0.680172\pi$
$733$	−1.98907	+	1.14839i	−0.0734681	+	0.0424169i	0.462816	+	0.886454i	$0.346839\pi$
$734$	−29.6782	−	17.1347i	−1.09544	−	0.632454i
$735$	0.279390	+	0.234539i	0.0103054	+	0.00865109i
$736$			4.70483i			0.173422i
$737$	29.1924			1.07532
$738$	0.0995332			0.00366387
$739$			42.4844i			1.56281i	0.624021	+	0.781407i	$0.285498\pi$
$739$			42.4844i			1.56281i	−0.624021	+	0.781407i	$0.714502\pi$
$740$	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	$0.265977\pi$
$744$	0.215772	−	0.373728i	0.00791059	−	0.0137015i
$745$	−0.332703	−	0.576259i	−0.0121893	−	0.0211125i
$746$	20.6603	+	11.9282i	0.756426	+	0.436723i
$747$		−	10.7018i		−	0.391557i
$748$	−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
$751$	15.9798	−	27.6779i	0.583113	−	1.00998i	−0.411995	−	0.911186i	$-0.635168\pi$
$751$	15.9798	−	27.6779i	0.583113	−	1.00998i	0.995108	−	0.0987946i	$-0.0314987\pi$
$752$		−	0.0401082i		−	0.00146260i
$753$	−13.1750	+	22.8198i	−0.480123	+	0.831598i
$754$	−9.26286	−	3.60677i	−0.337334	−	0.131351i
$755$	0.708302			0.0257778
$756$	2.63566	+	0.230877i	0.0958580	+	0.00839691i
$757$	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	$0.757460\pi$
$758$	22.0107			0.799466
$759$	17.8685	+	10.3164i	0.648586	+	0.374461i
$760$	−0.0972853	+	0.0561677i	−0.00352891	+	0.00203742i
$761$			37.3043i			1.35228i	0.736773	+	0.676140i	$0.236349\pi$
$761$			37.3043i			1.35228i	−0.736773	+	0.676140i	$0.763651\pi$
$762$			13.8302i			0.501015i
$763$	−21.9956	+	10.2538i	−0.796295	+	0.371214i
$764$	−1.45963	−	2.52815i	−0.0528075	−	0.0914653i
$765$	−0.200819	−	0.115943i	−0.00726063	−	0.00419192i
$766$	13.6056	−	23.5657i	0.491592	−	0.851462i
$767$	2.67050	+	17.4009i	0.0964262	+	0.628310i
$768$	−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	$0.425338\pi$
$770$	−0.495258	−	0.346863i	−0.0178479	−	0.0125001i
$771$	−10.6281	+	18.4083i	−0.382760	+	0.662960i
$772$	−21.3521	+	12.3276i	−0.768479	+	0.443682i
$773$	13.5178	−	7.80449i	0.486201	−	0.280708i	−0.236796	−	0.971559i	$-0.576097\pi$
$773$	13.5178	−	7.80449i	0.486201	−	0.280708i	0.722997	+	0.690851i	$0.242764\pi$
$774$	−8.98351	+	5.18663i	−0.322906	+	0.186430i
$775$	1.86763	−	1.07827i	0.0670871	−	0.0387328i
$776$	−2.17844	+	3.77317i	−0.0782015	+	0.135449i
$777$	−13.6426	+	6.35988i	−0.489427	+	0.228159i
$778$	−23.6246	+	13.6396i	−0.846982	+	0.489005i
$779$	−0.107280	−	0.185814i	−0.00384369	−	0.00665747i
$780$	−0.146585	+	0.117542i	−0.00524860	+	0.00420869i
$781$	10.7166	−	18.5616i	0.383469	−	0.664187i
$782$	18.1306	+	10.4677i	0.648348	+	0.374324i
$783$	−1.37847	−	2.38758i	−0.0492625	−	0.0853252i
$784$	6.89339	+	1.21703i	0.246193	+	0.0434652i
$785$			0.0491317i			0.00175359i
$786$		−	8.98381i		−	0.320442i
$787$	6.43475	−	3.71510i	0.229374	−	0.132429i	−0.380909	−	0.924612i	$-0.624389\pi$
$787$	6.43475	−	3.71510i	0.229374	−	0.132429i	0.610283	+	0.792183i	$0.291056\pi$
$788$	−18.9687	−	10.9516i	−0.675730	−	0.390133i
$789$	24.5510			0.874039
$790$	0.431991	+	0.748231i	0.0153696	+	0.0266209i
$791$	14.1481	+	30.3491i	0.503047	+	1.07909i
$792$	−4.38545			−0.155830
$793$	−5.34324	+	13.7224i	−0.189744	+	0.487298i
$794$	−0.444418	+	0.769755i	−0.0157718	+	0.0273176i
$795$		−	0.0502137i		−	0.00178090i
$796$	−12.9828	+	22.4869i	−0.460164	+	0.797028i
$797$	−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
$800$		−	4.99728i		−	0.176681i
$801$	5.77774	+	3.33578i	0.204147	+	0.117864i
$802$	4.33537	+	7.50908i	0.153087	+	0.265155i
$803$	3.39778	−	5.88513i	0.119905	−	0.207682i
$804$	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
$808$			1.31393i			0.0462240i
$809$	49.2672			1.73214			0.866071	−	0.499921i	$-0.166638\pi$
$809$	49.2672			1.73214			0.866071	+	0.499921i	$0.166638\pi$
$810$	−0.0521119			−0.00183103
$811$			38.6075i			1.35569i	0.735204	+	0.677846i	$0.237087\pi$
$811$			38.6075i			1.35569i	−0.735204	+	0.677846i	$0.762913\pi$
$812$	−3.08194	−	6.61111i	−0.108155	−	0.232004i
$813$	12.7322	+	7.35096i	0.446539	+	0.257809i
$814$	21.6071	−	12.4749i	0.757329	−	0.437244i
$815$	0.663123	+	1.14856i	0.0232282	+	0.0402324i
$816$	−4.44977			−0.155773
$817$	19.3654	+	11.1806i	0.677508	+	0.391160i
$818$	5.48497			0.191777
$819$	−5.29549	−	7.93459i	−0.185039	−	0.277257i
$820$	−0.00518686			−0.000181133
$821$	2.24970	+	1.29886i	0.0785150	+	0.0453306i	0.538744	−	0.842470i	$-0.318899\pi$
$821$	2.24970	+	1.29886i	0.0785150	+	0.0453306i	−0.460229	+	0.887800i	$0.652233\pi$
$822$	−11.1355			−0.388394
$823$	−1.23002	−	2.13047i	−0.0428760	−	0.0742634i	0.843791	−	0.536672i	$-0.180319\pi$
$823$	−1.23002	−	2.13047i	−0.0428760	−	0.0742634i	−0.886667	+	0.462409i	$0.846985\pi$
$824$	−8.21598	+	4.74350i	−0.286217	+	0.165248i
$825$	−18.9792	−	10.9577i	−0.660772	−	0.381497i
$826$	−7.41075	+	10.5812i	−0.257853	+	0.368168i
$827$			2.35563i			0.0819132i	0.999161	+	0.0409566i	$0.0130405\pi$
$827$			2.35563i			0.0819132i	−0.999161	+	0.0409566i	$0.986959\pi$
$828$	4.70483			0.163504
$829$	44.6520			1.55083			0.775414	−	0.631453i	$-0.217541\pi$
$829$	44.6520			1.55083			0.775414	+	0.631453i	$0.217541\pi$
$830$			0.557690i			0.0193577i
$831$	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
$835$	−0.348662	+	0.603900i	−0.0120659	+	0.0208988i
$836$	4.72676	+	8.18699i	0.163478	+	0.283153i
$837$	−0.373728	−	0.215772i	−0.0129179	−	0.00745817i
$838$		−	22.3650i		−	0.772585i
$839$	−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
$842$	−2.04463	+	3.54141i	−0.0704627	+	0.122045i
$843$			6.15162i			0.211873i
$844$	−4.29055	+	7.43146i	−0.147687	+	0.255801i
$845$	0.661269	+	0.147204i	0.0227483	+	0.00506397i
$846$	−0.0401082			−0.00137895
$847$	−12.4946	+	17.8400i	−0.429318	+	0.612989i
$848$	−0.481787	−	0.834479i	−0.0165446	−	0.0286561i
$849$	9.89086			0.339453
$850$	−19.2576	−	11.1184i	−0.660530	−	0.381357i
$851$	−23.1807	+	13.3834i	−0.794624	+	0.458777i
$852$		−	4.88733i		−	0.167437i
$853$		−	7.77483i		−	0.266205i	−0.991102	−	0.133103i	$-0.957506\pi$
$853$		−	7.77483i		−	0.266205i	0.991102	−	0.133103i	$-0.0424940\pi$
$854$	−9.79400	+	4.56573i	−0.335144	+	0.156236i
$855$	0.0561677	+	0.0972853i	0.00192089	+	0.00332709i
$856$	−5.71764	−	3.30108i	−0.195425	−	0.112829i
$857$	28.8728	−	50.0091i	0.986275	−	1.70828i	0.350150	−	0.936694i	$-0.386131\pi$
$857$	28.8728	−	50.0091i	0.986275	−	1.70828i	0.636125	−	0.771586i	$-0.280536\pi$
$858$	9.89171	+	12.3358i	0.337697	+	0.421138i
$859$	0.309869	+	0.536709i	0.0105726	+	0.0183123i	0.871263	−	0.490816i	$-0.163301\pi$
$859$	0.309869	+	0.536709i	0.0105726	+	0.0183123i	−0.860691	+	0.509128i	$0.829968\pi$
$860$	0.468148	−	0.270285i	0.0159637	−	0.00921665i
$861$	0.0229799	−	0.262335i	0.000783153	−	0.00894037i
$862$	−12.6137	+	21.8476i	−0.429624	+	0.744131i
$863$	44.9667	−	25.9616i	1.53069	−	0.883741i	0.531355	−	0.847149i	$-0.321683\pi$
$863$	44.9667	−	25.9616i	1.53069	−	0.883741i	0.999330	−	0.0365922i	$-0.0116502\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	0.0958293	−	0.0553271i	0.00325830	−	0.00188118i
$866$	19.5088	−	11.2634i	0.662937	−	0.382747i
$867$	−1.40021	+	2.42523i	−0.0475535	+	0.0823651i
$868$	−0.935203	−	0.654987i	−0.0317429	−	0.0222317i
$869$	62.9670	−	36.3540i	2.13601	−	1.23322i
$870$	0.0718348	+	0.124421i	0.00243543	+	0.00421828i
$871$	−22.3652	−	8.70858i	−0.757817	−	0.295079i
$872$	4.58627	−	7.94365i	0.155311	−	0.269006i
$873$	3.77317	+	2.17844i	0.127703	+	0.0737291i
$874$	−5.07100	−	8.78322i	−0.171529	−	0.297097i
$875$	−1.12902	−	0.790727i	−0.0381677	−	0.0267314i
$876$		−	1.54957i		−	0.0523551i
$877$			7.49658i			0.253142i	0.991958	+	0.126571i	$0.0403971\pi$
$877$			7.49658i			0.253142i	−0.991958	+	0.126571i	$0.959603\pi$
$878$	17.6631	−	10.1978i	0.596099	−	0.344158i
$879$	−3.86698	−	2.23260i	−0.130430	−	0.0753037i
$880$	0.228534			0.00770388
$881$	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	$0.486847\pi$
$882$	1.21703	−	6.89339i	0.0409794	−	0.232113i
$883$	−37.7063			−1.26892			−0.634458	−	0.772957i	$-0.718777\pi$
$883$	−37.7063			−1.26892			−0.634458	+	0.772957i	$0.718777\pi$
$884$	10.0368	+	12.5167i	0.337573	+	0.420983i
$885$	0.127222	−	0.220355i	0.00427652	−	0.00740715i
$886$			28.4861i			0.957010i
$887$	−12.7428	+	22.0712i	−0.427863	+	0.741080i	−0.996683	−	0.0813821i	$-0.974067\pi$
$887$	−12.7428	+	22.0712i	−0.427863	+	0.741080i	0.568820	+	0.822462i	$0.307400\pi$
$888$	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
$891$			4.38545i			0.146918i
$892$	19.6277	+	11.3321i	0.657184	+	0.379426i
$893$	0.0432297	+	0.0748761i	0.00144663	+	0.00250563i
$894$	−6.38440	+	11.0581i	−0.213526	+	0.369838i
$895$	−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
$899$			1.18974i			0.0396801i
$900$	−4.99728			−0.166576
$901$	−4.28768			−0.142843
$902$			0.436498i			0.0145338i
$903$	11.5961	+	24.8749i	0.385894	+	0.827786i
$904$	−10.9605	−	6.32805i	−0.364541	−	0.210468i
$905$	0.409162	−	0.236230i	0.0136010	−	0.00785255i
$906$	−6.79597	−	11.7710i	−0.225781	−	0.391064i
$907$	20.7906			0.690340			0.345170	−	0.938540i	$-0.387821\pi$
$907$	20.7906			0.690340			0.345170	+	0.938540i	$0.387821\pi$
$908$	20.2725	+	11.7043i	0.672765	+	0.388421i
$909$	1.31393			0.0435804
$910$	0.275958	+	0.413487i	0.00914793	+	0.0137070i
$911$	−3.17234			−0.105104			−0.0525522	−	0.998618i	$-0.516736\pi$
$911$	−3.17234			−0.105104			−0.0525522	+	0.998618i	$0.516736\pi$
$912$	1.86685	+	1.07783i	0.0618177	+	0.0356905i
$913$	46.9321			1.55322
$914$	5.76006	+	9.97672i	0.190526	+	0.330001i
$915$	0.184324	−	0.106419i	0.00609355	−	0.00351812i
$916$	1.19337	+	0.688991i	0.0394300	+	0.0227649i
$917$	−23.6783	−	2.07415i	−0.781925	−	0.0684946i
$918$			4.44977i			0.146864i
$919$	50.0141			1.64981			0.824907	−	0.565269i	$-0.191228\pi$
$919$	50.0141			1.64981			0.824907	+	0.565269i	$0.191228\pi$
$920$	−0.245178			−0.00808327
$921$			5.17881i			0.170648i
$922$	−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
$926$	3.94651	−	6.83556i	0.129690	−	0.224631i
$927$	4.74350	+	8.21598i	0.155797	+	0.269848i
$928$	2.38758	+	1.37847i	0.0783762	+	0.0452505i
$929$			2.79550i			0.0917174i	0.998948	+	0.0458587i	$0.0146024\pi$
$929$			2.79550i			0.0917174i	−0.998948	+	0.0458587i	$0.985398\pi$
$930$	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
$933$	−17.4989	+	30.3089i	−0.572887	+	0.992269i
$934$		−	32.5616i		−	1.06545i
$935$	0.508462	−	0.880681i	0.0166285	−	0.0288014i
$936$	3.35983	+	1.30825i	0.109820	+	0.0427615i
$937$	−18.8527			−0.615890			−0.307945	−	0.951404i	$-0.599641\pi$
$937$	−18.8527			−0.615890			−0.307945	+	0.951404i	$0.599641\pi$
$938$	−7.44137	−	15.9626i	−0.242969	−	0.521196i
$939$	3.92239	+	6.79378i	0.128002	+	0.221707i
$940$	0.00209011			6.81720e−5
$941$	−33.1581	−	19.1438i	−1.08092	−	0.624071i	−0.149778	−	0.988720i	$-0.547856\pi$
$941$	−33.1581	−	19.1438i	−1.08092	−	0.624071i	−0.931145	+	0.364648i	$0.881189\pi$
$942$	0.816499	−	0.471406i	0.0266030	−	0.0153592i
$943$		−	0.468287i		−	0.0152495i
$944$		−	4.88264i		−	0.158916i
$945$	−0.0120314	+	0.137349i	−0.000391383	+	0.00446797i
$946$	−22.7457	−	39.3967i	−0.739527	−	1.28090i
$947$	−52.0089	−	30.0274i	−1.69006	−	0.975758i	−0.954457	−	0.298348i	$-0.903564\pi$
$947$	−52.0089	−	30.0274i	−1.69006	−	0.975758i	−0.735606	−	0.677410i	$-0.763102\pi$
$948$	8.28968	−	14.3582i	0.269236	−	0.466331i
$949$	−4.35878	+	3.49517i	−0.141492	+	0.113458i
$950$	5.38621	+	9.32919i	0.174752	+	0.302679i
$951$	−17.6606	+	10.1964i	−0.572686	+	0.330640i
$952$	−1.02735	+	11.7281i	−0.0332965	+	0.380109i
$953$	−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
$955$	0.131747	−	0.0760640i	0.00426323	−	0.00246137i
$956$	15.7655	−	9.10224i	0.509894	−	0.294387i
$957$	10.4706	−	6.04521i	0.338467	−	0.195414i
$958$	−0.569385	+	0.986205i	−0.0183960	+	0.0318628i
$959$	−2.57092	+	29.3493i	−0.0830194	+	0.947738i
$960$	0.0451302	−	0.0260560i	0.00145657	−	0.000840952i
$961$	−15.4069	−	26.6855i	−0.496996	−	0.860823i
$962$	−20.2754	+	3.11164i	−0.653704	+	0.100323i
$963$	−3.30108	+	5.71764i	−0.106376	+	0.184249i
$964$	12.8772	+	7.43467i	0.414748	+	0.239455i
$965$	−0.642417	−	1.11270i	−0.0206801	−	0.0358191i
$966$	1.08624	−	12.4003i	0.0349491	−	0.398974i
$967$			32.1318i			1.03329i	0.856200	+	0.516645i	$0.172819\pi$
$967$			32.1318i			1.03329i	−0.856200	+	0.516645i	$0.827181\pi$
$968$		−	8.23216i		−	0.264592i
$969$	8.30706	−	4.79608i	0.266861	−	0.154072i
$970$	−0.196627	−	0.113523i	−0.00631332	−	0.00364500i
$971$	34.7517			1.11523			0.557617	−	0.830098i	$-0.311716\pi$
$971$	34.7517			1.11523			0.557617	+	0.830098i	$0.311716\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−19.7478	−	42.3612i	−0.633085	−	1.35804i
$974$	−3.30285			−0.105830
$975$	11.2717	+	14.0568i	0.360985	+	0.450179i
$976$	2.04213	−	3.53707i	0.0653670	−	0.113219i
$977$		−	11.4643i		−	0.366775i	−0.983041	−	0.183387i	$-0.941294\pi$
$977$		−	11.4643i		−	0.366775i	0.983041	−	0.183387i	$-0.0587062\pi$
$978$	12.7250	−	22.0403i	0.406900	−	0.704771i
$979$	−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
$982$		−	17.4799i		−	0.557807i
$983$	−37.1123	−	21.4268i	−1.18370	−	0.683408i	−0.226830	−	0.973934i	$-0.572836\pi$
$983$	−37.1123	−	21.4268i	−1.18370	−	0.683408i	−0.956867	+	0.290526i	$0.906170\pi$
$984$	0.0497666	+	0.0861982i	0.00158650	+	0.00274790i
$985$	0.570707	−	0.988493i	0.0181842	−	0.0314960i
$986$	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
$990$		−	0.228534i		−	0.00726329i
$991$	4.91969			0.156279			0.0781395	−	0.996942i	$-0.475102\pi$
$991$	4.91969			0.156279			0.0781395	+	0.996942i	$0.475102\pi$
$992$	0.431544			0.0137015
$993$		−	1.19161i		−	0.0378146i
$994$	−12.8813	−	1.12837i	−0.408571	−	0.0357897i
$995$	−1.17184	−	0.676561i	−0.0371497	−	0.0214484i
$996$	9.26801	−	5.35089i	0.293668	−	0.169549i
$997$	5.18801	+	8.98590i	0.164306	+	0.284586i	0.936409	−	0.350911i	$-0.114128\pi$
$997$	5.18801	+	8.98590i	0.164306	+	0.284586i	−0.772103	+	0.635498i	$0.780795\pi$
$998$	−0.933390			−0.0295460
$999$	−4.92700	−	2.84461i	−0.155883	−	0.0899993i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.b.121.8	✓	20	91.30	even	6	inner
546.2.bd.b.361.8	yes	20	1.1	even	1	trivial
546.2.bm.b.205.3	yes	20	7.2	even	3
546.2.bm.b.277.8	yes	20	13.4	even	6
1638.2.cr.b.361.3		20	3.2	odd	2
1638.2.cr.b.667.3		20	273.212	odd	6
1638.2.dt.b.1297.8		20	21.2	odd	6
1638.2.dt.b.1369.3		20	39.17	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.bd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.0451302 + 0.0260560i) q^{5} +(0.866025 + 0.500000i) q^{6} +(1.51777 - 2.16711i) q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.0451302 + 0.0260560i) q^{5} +(0.866025 + 0.500000i) q^{6} +(1.51777 - 2.16711i) q^{7} +1.00000i q^{8} +1.00000 q^{9} -0.0521119 q^{10} +4.38545i 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} +(-0.500000 + 0.866025i) q^{16} +(2.22488 + 3.85361i) q^{17} +(0.866025 + 0.500000i) q^{18} -2.15566i q^{19} +(-0.0451302 - 0.0260560i) q^{20} +(1.51777 - 2.16711i) q^{21} +(-2.19272 + 3.79791i) q^{22} +(2.35241 - 4.07450i) q^{23} +1.00000i q^{24} +(-2.49864 + 4.32778i) q^{25} +(2.81290 - 2.25557i) q^{26} +1.00000 q^{27} +(2.63566 + 0.230877i) q^{28} +(-1.37847 - 2.38758i) q^{29} -0.0521119 q^{30} +(-0.373728 - 0.215772i) q^{31} +(-0.866025 + 0.500000i) q^{32} +4.38545i q^{33} +4.44977i q^{34} +(-0.0120314 + 0.137349i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-4.92700 - 2.84461i) q^{37} +(1.07783 - 1.86685i) q^{38} +(1.30825 - 3.35983i) q^{39} +(-0.0260560 - 0.0451302i) q^{40} +(0.0861982 - 0.0497666i) q^{41} +(2.39799 - 1.11788i) q^{42} +(-5.18663 + 8.98351i) q^{43} +(-3.79791 + 2.19272i) q^{44} +(-0.0451302 + 0.0260560i) q^{45} +(4.07450 - 2.35241i) q^{46} +(-0.0347347 + 0.0200541i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(-2.39272 - 6.57836i) q^{49} +(-4.32778 + 2.49864i) q^{50} +(2.22488 + 3.85361i) q^{51} +(3.56383 - 0.546937i) q^{52} +(-0.481787 + 0.834479i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-0.114267 - 0.197916i) q^{55} +(2.16711 + 1.51777i) q^{56} -2.15566i q^{57} -2.75694i q^{58} +(-4.22849 + 2.44132i) q^{59} +(-0.0451302 - 0.0260560i) q^{60} -4.08426 q^{61} +(-0.215772 - 0.373728i) q^{62} +(1.51777 - 2.16711i) q^{63} -1.00000 q^{64} +(0.0285020 + 0.185718i) q^{65} +(-2.19272 + 3.79791i) q^{66} -6.65665i q^{67} +(-2.22488 + 3.85361i) q^{68} +(2.35241 - 4.07450i) q^{69} +(-0.0790941 + 0.112932i) q^{70} +(-4.23255 - 2.44366i) q^{71} +1.00000i q^{72} +(-1.34197 - 0.774785i) q^{73} +(-2.84461 - 4.92700i) q^{74} +(-2.49864 + 4.32778i) 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} -0.0521119i q^{80} +1.00000 q^{81} +0.0995332 q^{82} -10.7018i q^{83} +(2.63566 + 0.230877i) q^{84} +(-0.200819 - 0.115943i) q^{85} +(-8.98351 + 5.18663i) q^{86} +(-1.37847 - 2.38758i) q^{87} -4.38545 q^{88} +(5.77774 + 3.33578i) q^{89} -0.0521119 q^{90} +(-5.29549 - 7.93459i) q^{91} +4.70483 q^{92} +(-0.373728 - 0.215772i) q^{93} -0.0401082 q^{94} +(0.0561677 + 0.0972853i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(3.77317 + 2.17844i) q^{97} +(1.21703 - 6.89339i) q^{98} +4.38545i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9}+O(q^{10}) \) 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9	\( 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9} - 8 q^{10} + 10 q^{12} + 8 q^{13} + 4 q^{14} - 10 q^{16} + 4 q^{17} - 6 q^{21} - 10 q^{22} + 8 q^{23} + 6 q^{25} + 2 q^{26} + 20 q^{27} - 6 q^{28} + 8 q^{29} - 8 q^{30} - 12 q^{31} + 4 q^{35} + 10 q^{36} + 6 q^{38} + 8 q^{39} - 4 q^{40} - 18 q^{41} + 4 q^{42} + 18 q^{43} + 6 q^{44} - 24 q^{46} + 6 q^{47} - 10 q^{48} + 4 q^{49} + 12 q^{50} + 4 q^{51} - 2 q^{52} + 18 q^{53} - 12 q^{55} + 2 q^{56} + 36 q^{59} + 12 q^{61} - 6 q^{63} - 20 q^{64} - 10 q^{66} - 4 q^{68} + 8 q^{69} - 42 q^{70} - 6 q^{71} - 24 q^{73} - 18 q^{74} + 6 q^{75} + 12 q^{76} - 34 q^{77} + 2 q^{78} + 20 q^{81} - 36 q^{82} - 6 q^{84} + 36 q^{86} + 8 q^{87} - 20 q^{88} + 18 q^{89} - 8 q^{90} - 94 q^{91} + 16 q^{92} - 12 q^{93} + 32 q^{94} + 40 q^{95} - 96 q^{97} - 12 q^{98}+O(q^{100}) \) 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9 - 8 * q^10 + 10 * q^12 + 8 * q^13 + 4 * q^14 - 10 * q^16 + 4 * q^17 - 6 * q^21 - 10 * q^22 + 8 * q^23 + 6 * q^25 + 2 * q^26 + 20 * q^27 - 6 * q^28 + 8 * q^29 - 8 * q^30 - 12 * q^31 + 4 * q^35 + 10 * q^36 + 6 * q^38 + 8 * q^39 - 4 * q^40 - 18 * q^41 + 4 * q^42 + 18 * q^43 + 6 * q^44 - 24 * q^46 + 6 * q^47 - 10 * q^48 + 4 * q^49 + 12 * q^50 + 4 * q^51 - 2 * q^52 + 18 * q^53 - 12 * q^55 + 2 * q^56 + 36 * q^59 + 12 * q^61 - 6 * q^63 - 20 * q^64 - 10 * q^66 - 4 * q^68 + 8 * q^69 - 42 * q^70 - 6 * q^71 - 24 * q^73 - 18 * q^74 + 6 * q^75 + 12 * q^76 - 34 * q^77 + 2 * q^78 + 20 * q^81 - 36 * q^82 - 6 * q^84 + 36 * q^86 + 8 * q^87 - 20 * q^88 + 18 * q^89 - 8 * q^90 - 94 * q^91 + 16 * q^92 - 12 * q^93 + 32 * q^94 + 40 * q^95 - 96 * q^97 - 12 * q^98

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