LMFDB - Embedded newform 570.2.f.d.341.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(341,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("570.341");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.f (of order $2$, degree $1$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.7278137344.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} + 6x^{5} - 20x^{4} + 18x^{3} + 9x^{2} - 54x + 81 $ x^8 - 2x^7 + x^6 + 6x^5 - 20x^4 + 18x^3 + 9x^2 - 54x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			341.7
Root			$-1.71731 + 0.225499i$ of defining polynomial
Character	$\chi$	$=$	570.341
Dual form			570.2.f.d.341.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.71731 - 0.225499i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(1.71731 - 0.225499i) q^{6} -0.631989 q^{7} +1.00000 q^{8} +(2.89830 - 0.774501i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.71731 - 0.225499i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(1.71731 - 0.225499i) q^{6} -0.631989 q^{7} +1.00000 q^{8} +(2.89830 - 0.774501i) q^{9} -1.00000i q^{10} -2.00000i q^{11} +(1.71731 - 0.225499i) q^{12} -2.45100i q^{13} -0.631989 q^{14} +(-0.225499 - 1.71731i) q^{15} +1.00000 q^{16} +3.25363i q^{17} +(2.89830 - 0.774501i) q^{18} +(-2.43462 + 3.61561i) q^{19} -1.00000i q^{20} +(-1.08532 + 0.142513i) q^{21} -2.00000i q^{22} -0.812981i q^{23} +(1.71731 - 0.225499i) q^{24} -1.00000 q^{25} -2.45100i q^{26} +(4.80263 - 1.98362i) q^{27} -0.631989 q^{28} +3.43462 q^{29} +(-0.225499 - 1.71731i) q^{30} +7.16461i q^{31} +1.00000 q^{32} +(-0.450997 - 3.43462i) q^{33} +3.25363i q^{34} +0.631989i q^{35} +(2.89830 - 0.774501i) q^{36} +5.60526i q^{37} +(-2.43462 + 3.61561i) q^{38} +(-0.552696 - 4.20912i) q^{39} -1.00000i q^{40} -0.802629 q^{41} +(-1.08532 + 0.142513i) q^{42} -11.9672 q^{43} -2.00000i q^{44} +(-0.774501 - 2.89830i) q^{45} -0.812981i q^{46} -7.96724i q^{47} +(1.71731 - 0.225499i) q^{48} -6.60059 q^{49} -1.00000 q^{50} +(0.733688 + 5.58748i) q^{51} -2.45100i q^{52} +6.53262 q^{53} +(4.80263 - 1.98362i) q^{54} -2.00000 q^{55} -0.631989 q^{56} +(-3.36568 + 6.75812i) q^{57} +3.43462 q^{58} -2.09198 q^{59} +(-0.225499 - 1.71731i) q^{60} -2.70326 q^{61} +7.16461i q^{62} +(-1.83169 + 0.489476i) q^{63} +1.00000 q^{64} -2.45100 q^{65} +(-0.450997 - 3.43462i) q^{66} +14.9462i q^{67} +3.25363i q^{68} +(-0.183326 - 1.39614i) q^{69} +0.631989i q^{70} +6.16597 q^{71} +(2.89830 - 0.774501i) q^{72} -4.89461 q^{73} +5.60526i q^{74} +(-1.71731 + 0.225499i) q^{75} +(-2.43462 + 3.61561i) q^{76} +1.26398i q^{77} +(-0.552696 - 4.20912i) q^{78} -4.42859i q^{79} -1.00000i q^{80} +(7.80030 - 4.48948i) q^{81} -0.802629 q^{82} -5.86788i q^{83} +(-1.08532 + 0.142513i) q^{84} +3.25363 q^{85} -11.9672 q^{86} +(5.89830 - 0.774501i) q^{87} -2.00000i q^{88} -5.93339 q^{89} +(-0.774501 - 2.89830i) q^{90} +1.54900i q^{91} -0.812981i q^{92} +(1.61561 + 12.3039i) q^{93} -7.96724i q^{94} +(3.61561 + 2.43462i) q^{95} +(1.71731 - 0.225499i) q^{96} +3.26398i q^{97} -6.60059 q^{98} +(-1.54900 - 5.79660i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{6} + 4 q^{7} + 8 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^6 + 4 * q^7 + 8 * q^8 + 2 * q^9	$ 8 q + 8 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{6} + 4 q^{7} + 8 q^{8} + 2 q^{9} - 2 q^{12} + 4 q^{14} + 8 q^{16} + 2 q^{18} + 12 q^{19} - 2 q^{21} - 2 q^{24} - 8 q^{25} + 16 q^{27} + 4 q^{28} - 4 q^{29} + 8 q^{32} + 2 q^{36} + 12 q^{38} - 22 q^{39} + 16 q^{41} - 2 q^{42} - 40 q^{43} - 8 q^{45} - 2 q^{48} + 4 q^{49} - 8 q^{50} + 18 q^{51} + 28 q^{53} + 16 q^{54} - 16 q^{55} + 4 q^{56} - 30 q^{57} - 4 q^{58} - 4 q^{59} + 16 q^{61} - 34 q^{63} + 8 q^{64} - 16 q^{65} - 2 q^{69} + 24 q^{71} + 2 q^{72} - 4 q^{73} + 2 q^{75} + 12 q^{76} - 22 q^{78} + 34 q^{81} + 16 q^{82} - 2 q^{84} - 40 q^{86} + 26 q^{87} - 88 q^{89} - 8 q^{90} - 24 q^{93} - 8 q^{95} - 2 q^{96} + 4 q^{98} - 16 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^6 + 4 * q^7 + 8 * q^8 + 2 * q^9 - 2 * q^12 + 4 * q^14 + 8 * q^16 + 2 * q^18 + 12 * q^19 - 2 * q^21 - 2 * q^24 - 8 * q^25 + 16 * q^27 + 4 * q^28 - 4 * q^29 + 8 * q^32 + 2 * q^36 + 12 * q^38 - 22 * q^39 + 16 * q^41 - 2 * q^42 - 40 * q^43 - 8 * q^45 - 2 * q^48 + 4 * q^49 - 8 * q^50 + 18 * q^51 + 28 * q^53 + 16 * q^54 - 16 * q^55 + 4 * q^56 - 30 * q^57 - 4 * q^58 - 4 * q^59 + 16 * q^61 - 34 * q^63 + 8 * q^64 - 16 * q^65 - 2 * q^69 + 24 * q^71 + 2 * q^72 - 4 * q^73 + 2 * q^75 + 12 * q^76 - 22 * q^78 + 34 * q^81 + 16 * q^82 - 2 * q^84 - 40 * q^86 + 26 * q^87 - 88 * q^89 - 8 * q^90 - 24 * q^93 - 8 * q^95 - 2 * q^96 + 4 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.71731	−	0.225499i	0.991489	−	0.130192i
$3$	1.71731	−	0.225499i	0.991489	−	0.130192i
$4$	1.00000			0.500000
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	1.71731	−	0.225499i	0.701088	−	0.0920594i
$7$	−0.631989			−0.238869			−0.119435	−	0.992842i	$-0.538108\pi$
$7$	−0.631989			−0.238869			−0.119435	+	0.992842i	$0.538108\pi$
$8$	1.00000			0.353553
$9$	2.89830	−	0.774501i	0.966100	−	0.258167i
$10$		−	1.00000i		−	0.316228i
$11$		−	2.00000i		−	0.603023i	−0.953463	−	0.301511i	$-0.902509\pi$
$11$		−	2.00000i		−	0.603023i	0.953463	−	0.301511i	$-0.0974911\pi$
$12$	1.71731	−	0.225499i	0.495744	−	0.0650958i
$13$		−	2.45100i		−	0.679784i	−0.940464	−	0.339892i	$-0.889609\pi$
$13$		−	2.45100i		−	0.679784i	0.940464	−	0.339892i	$-0.110391\pi$
$14$	−0.631989			−0.168906
$15$	−0.225499	−	1.71731i	−0.0582235	−	0.443407i
$16$	1.00000			0.250000
$17$			3.25363i			0.789120i	0.918870	+	0.394560i	$0.129103\pi$
$17$			3.25363i			0.789120i	−0.918870	+	0.394560i	$0.870897\pi$
$18$	2.89830	−	0.774501i	0.683136	−	0.182552i
$19$	−2.43462	+	3.61561i	−0.558540	+	0.829478i
$19$	−2.43462	+	3.61561i	−0.558540	+	0.829478i
$20$		−	1.00000i		−	0.223607i
$21$	−1.08532	+	0.142513i	−0.236836	+	0.0310988i
$22$		−	2.00000i		−	0.426401i
$23$		−	0.812981i		−	0.169518i	−0.996401	−	0.0847591i	$-0.972988\pi$
$23$		−	0.812981i		−	0.169518i	0.996401	−	0.0847591i	$-0.0270121\pi$
$24$	1.71731	−	0.225499i	0.350544	−	0.0460297i
$25$	−1.00000			−0.200000
$26$		−	2.45100i		−	0.480680i
$27$	4.80263	−	1.98362i	0.924266	−	0.381748i
$28$	−0.631989			−0.119435
$29$	3.43462			0.637793			0.318896	−	0.947790i	$-0.396688\pi$
$29$	3.43462			0.637793			0.318896	+	0.947790i	$0.396688\pi$
$30$	−0.225499	−	1.71731i	−0.0411702	−	0.313536i
$31$			7.16461i			1.28680i	0.765529	+	0.643401i	$0.222477\pi$
$31$			7.16461i			1.28680i	−0.765529	+	0.643401i	$0.777523\pi$
$32$	1.00000			0.176777
$33$	−0.450997	−	3.43462i	−0.0785085	−	0.597890i
$34$			3.25363i			0.557992i
$35$			0.631989i			0.106826i
$36$	2.89830	−	0.774501i	0.483050	−	0.129084i
$37$			5.60526i			0.921499i	0.887530	+	0.460749i	$0.152419\pi$
$37$			5.60526i			0.921499i	−0.887530	+	0.460749i	$0.847581\pi$
$38$	−2.43462	+	3.61561i	−0.394947	+	0.586529i
$39$	−0.552696	−	4.20912i	−0.0885022	−	0.673999i
$40$		−	1.00000i		−	0.158114i
$41$	−0.802629			−0.125350			−0.0626748	−	0.998034i	$-0.519963\pi$
$41$	−0.802629			−0.125350			−0.0626748	+	0.998034i	$0.519963\pi$
$42$	−1.08532	+	0.142513i	−0.167469	+	0.0219902i
$43$	−11.9672			−1.82499			−0.912494	−	0.409091i	$-0.865846\pi$
$43$	−11.9672			−1.82499			−0.912494	+	0.409091i	$0.865846\pi$
$44$		−	2.00000i		−	0.301511i
$45$	−0.774501	−	2.89830i	−0.115456	−	0.432053i
$46$		−	0.812981i		−	0.119867i
$47$		−	7.96724i		−	1.16214i	−0.813853	−	0.581071i	$-0.802634\pi$
$47$		−	7.96724i		−	1.16214i	0.813853	−	0.581071i	$-0.197366\pi$
$48$	1.71731	−	0.225499i	0.247872	−	0.0325479i
$49$	−6.60059			−0.942941
$50$	−1.00000			−0.141421
$51$	0.733688	+	5.58748i	0.102737	+	0.782404i
$52$		−	2.45100i		−	0.339892i
$53$	6.53262			0.897325			0.448662	−	0.893701i	$-0.351901\pi$
$53$	6.53262			0.897325			0.448662	+	0.893701i	$0.351901\pi$
$54$	4.80263	−	1.98362i	0.653555	−	0.269937i
$55$	−2.00000			−0.269680
$56$	−0.631989			−0.0844531
$57$	−3.36568	+	6.75812i	−0.445795	+	0.895135i
$58$	3.43462			0.450987
$59$	−2.09198			−0.272352			−0.136176	−	0.990685i	$-0.543481\pi$
$59$	−2.09198			−0.272352			−0.136176	+	0.990685i	$0.543481\pi$
$60$	−0.225499	−	1.71731i	−0.0291117	−	0.221704i
$61$	−2.70326			−0.346118			−0.173059	−	0.984912i	$-0.555365\pi$
$61$	−2.70326			−0.346118			−0.173059	+	0.984912i	$0.555365\pi$
$62$			7.16461i			0.909907i
$63$	−1.83169	+	0.489476i	−0.230772	+	0.0616682i
$64$	1.00000			0.125000
$65$	−2.45100			−0.304009
$66$	−0.450997	−	3.43462i	−0.0555139	−	0.422772i
$67$			14.9462i			1.82597i	0.407995	+	0.912984i	$0.366228\pi$
$67$			14.9462i			1.82597i	−0.407995	+	0.912984i	$0.633772\pi$
$68$			3.25363i			0.394560i
$69$	−0.183326	−	1.39614i	−0.0220699	−	0.168075i
$70$			0.631989i			0.0755371i
$71$	6.16597			0.731766			0.365883	−	0.930661i	$-0.380767\pi$
$71$	6.16597			0.731766			0.365883	+	0.930661i	$0.380767\pi$
$72$	2.89830	−	0.774501i	0.341568	−	0.0912759i
$73$	−4.89461			−0.572870			−0.286435	−	0.958100i	$-0.592470\pi$
$73$	−4.89461			−0.572870			−0.286435	+	0.958100i	$0.592470\pi$
$74$			5.60526i			0.651598i
$75$	−1.71731	+	0.225499i	−0.198298	+	0.0260383i
$76$	−2.43462	+	3.61561i	−0.279270	+	0.414739i
$77$			1.26398i			0.144044i
$78$	−0.552696	−	4.20912i	−0.0625805	−	0.476589i
$79$		−	4.42859i		−	0.498255i	−0.968471	−	0.249128i	$-0.919856\pi$
$79$		−	4.42859i		−	0.498255i	0.968471	−	0.249128i	$-0.0801439\pi$
$80$		−	1.00000i		−	0.111803i
$81$	7.80030	−	4.48948i	0.866699	−	0.498831i
$82$	−0.802629			−0.0886356
$83$		−	5.86788i		−	0.644083i	−0.946726	−	0.322042i	$-0.895631\pi$
$83$		−	5.86788i		−	0.644083i	0.946726	−	0.322042i	$-0.104369\pi$
$84$	−1.08532	+	0.142513i	−0.118418	+	0.0155494i
$85$	3.25363			0.352905
$86$	−11.9672			−1.29046
$87$	5.89830	−	0.774501i	0.632364	−	0.0830353i
$88$		−	2.00000i		−	0.213201i
$89$	−5.93339			−0.628938			−0.314469	−	0.949268i	$-0.601827\pi$
$89$	−5.93339			−0.628938			−0.314469	+	0.949268i	$0.601827\pi$
$90$	−0.774501	−	2.89830i	−0.0816396	−	0.305508i
$91$			1.54900i			0.162380i
$92$		−	0.812981i		−	0.0847591i
$93$	1.61561	+	12.3039i	0.167531	+	1.27585i
$94$		−	7.96724i		−	0.821758i
$95$	3.61561	+	2.43462i	0.370954	+	0.249787i
$96$	1.71731	−	0.225499i	0.175272	−	0.0230149i
$97$			3.26398i			0.331407i	0.986176	+	0.165703i	$0.0529894\pi$
$97$			3.26398i			0.331407i	−0.986176	+	0.165703i	$0.947011\pi$
$98$	−6.60059			−0.666760
$99$	−1.54900	−	5.79660i	−0.155681	−	0.582580i
$100$	−1.00000			−0.100000
$101$			7.45999i			0.742297i	0.928574	+	0.371148i	$0.121036\pi$
$101$			7.45999i			0.742297i	−0.928574	+	0.371148i	$0.878964\pi$
$102$	0.733688	+	5.58748i	0.0726459	+	0.553243i
$103$		−	17.9345i		−	1.76714i	−0.468302	−	0.883569i	$-0.655134\pi$
$103$		−	17.9345i		−	1.76714i	0.468302	−	0.883569i	$-0.344866\pi$
$104$		−	2.45100i		−	0.240340i
$105$	0.142513	+	1.08532i	0.0139078	+	0.105916i
$106$	6.53262			0.634505
$107$	−5.63063			−0.544334			−0.272167	−	0.962250i	$-0.587740\pi$
$107$	−5.63063			−0.544334			−0.272167	+	0.962250i	$0.587740\pi$
$108$	4.80263	−	1.98362i	0.462133	−	0.190874i
$109$		−	8.71362i		−	0.834613i	−0.908766	−	0.417307i	$-0.862974\pi$
$109$		−	8.71362i		−	0.834613i	0.908766	−	0.417307i	$-0.137026\pi$
$110$	−2.00000			−0.190693
$111$	1.26398	+	9.62596i	0.119971	+	0.913656i
$112$	−0.631989			−0.0597173
$113$	−0.705983			−0.0664133			−0.0332066	−	0.999449i	$-0.510572\pi$
$113$	−0.705983			−0.0664133			−0.0332066	+	0.999449i	$0.510572\pi$
$114$	−3.36568	+	6.75812i	−0.315225	+	0.632956i
$115$	−0.812981			−0.0758108
$116$	3.43462			0.318896
$117$	−1.89830	−	7.10373i	−0.175498	−	0.656740i
$118$	−2.09198			−0.192582
$119$		−	2.05626i		−	0.188497i
$120$	−0.225499	−	1.71731i	−0.0205851	−	0.156768i
$121$	7.00000			0.636364
$122$	−2.70326			−0.244742
$123$	−1.37836	+	0.180992i	−0.124283	+	0.0163195i
$124$			7.16461i			0.643401i
$125$			1.00000i			0.0894427i
$126$	−1.83169	+	0.489476i	−0.163180	+	0.0436060i
$127$			4.86924i			0.432075i	0.976385	+	0.216037i	$0.0693133\pi$
$127$			4.86924i			0.432075i	−0.976385	+	0.216037i	$0.930687\pi$
$128$	1.00000			0.0883883
$129$	−20.5515	+	2.69860i	−1.80945	+	0.237598i
$130$	−2.45100			−0.214967
$131$			20.1005i			1.75618i	0.478491	+	0.878092i	$0.341184\pi$
$131$			20.1005i			1.75618i	−0.478491	+	0.878092i	$0.658816\pi$
$132$	−0.450997	−	3.43462i	−0.0392543	−	0.298945i
$133$	1.53865	−	2.28503i	0.133418	−	0.198137i
$134$			14.9462i			1.29115i
$135$	−1.98362	−	4.80263i	−0.170723	−	0.413345i
$136$			3.25363i			0.278996i
$137$		−	8.28883i		−	0.708163i	−0.935215	−	0.354081i	$-0.884794\pi$
$137$		−	8.28883i		−	0.708163i	0.935215	−	0.354081i	$-0.115206\pi$
$138$	−0.183326	−	1.39614i	−0.0156057	−	0.118847i
$139$	−0.196012			−0.0166255			−0.00831274	−	0.999965i	$-0.502646\pi$
$139$	−0.196012			−0.0166255			−0.00831274	+	0.999965i	$0.502646\pi$
$140$			0.631989i			0.0534128i
$141$	−1.79660	−	13.6822i	−0.151301	−	1.15225i
$142$	6.16597			0.517437
$143$	−4.90199			−0.409925
$144$	2.89830	−	0.774501i	0.241525	−	0.0645418i
$145$		−	3.43462i		−	0.285230i
$146$	−4.89461			−0.405081
$147$	−11.3353	+	1.48842i	−0.934916	+	0.122763i
$148$			5.60526i			0.460749i
$149$		−	11.4092i		−	0.934682i	−0.884077	−	0.467341i	$-0.845212\pi$
$149$		−	11.4092i		−	0.934682i	0.884077	−	0.467341i	$-0.154788\pi$
$150$	−1.71731	+	0.225499i	−0.140218	+	0.0184119i
$151$			10.2119i			0.831031i	0.909586	+	0.415515i	$0.136399\pi$
$151$			10.2119i			0.831031i	−0.909586	+	0.415515i	$0.863601\pi$
$152$	−2.43462	+	3.61561i	−0.197474	+	0.293265i
$153$	2.51994	+	9.42999i	0.203725	+	0.762369i
$154$			1.26398i			0.101854i
$155$	7.16461			0.575476
$156$	−0.552696	−	4.20912i	−0.0442511	−	0.336999i
$157$	14.0338			1.12002			0.560012	−	0.828485i	$-0.310797\pi$
$157$	14.0338			1.12002			0.560012	+	0.828485i	$0.310797\pi$
$158$		−	4.42859i		−	0.352320i
$159$	11.2185	−	1.47310i	0.889688	−	0.116824i
$160$		−	1.00000i		−	0.0790569i
$161$			0.513795i			0.0404927i
$162$	7.80030	−	4.48948i	0.612849	−	0.352727i
$163$	−19.3765			−1.51768			−0.758842	−	0.651275i	$-0.774234\pi$
$163$	−19.3765			−1.51768			−0.758842	+	0.651275i	$0.774234\pi$
$164$	−0.802629			−0.0626748
$165$	−3.43462	+	0.450997i	−0.267385	+	0.0351101i
$166$		−	5.86788i		−	0.455436i
$167$	−9.23122			−0.714333			−0.357167	−	0.934041i	$-0.616257\pi$
$167$	−9.23122			−0.714333			−0.357167	+	0.934041i	$0.616257\pi$
$168$	−1.08532	+	0.142513i	−0.0837343	+	0.0109951i
$169$	6.99261			0.537893
$170$	3.25363			0.249542
$171$	−4.25596	+	12.3647i	−0.325461	+	0.945555i
$172$	−11.9672			−0.912494
$173$	1.98794			0.151141			0.0755703	−	0.997140i	$-0.475922\pi$
$173$	1.98794			0.151141			0.0755703	+	0.997140i	$0.475922\pi$
$174$	5.89830	−	0.774501i	0.447149	−	0.0587148i
$175$	0.631989			0.0477739
$176$		−	2.00000i		−	0.150756i
$177$	−3.59257	+	0.471738i	−0.270034	+	0.0354580i
$178$	−5.93339			−0.444727
$179$	11.4938			0.859090			0.429545	−	0.903046i	$-0.358674\pi$
$179$	11.4938			0.859090			0.429545	+	0.903046i	$0.358674\pi$
$180$	−0.774501	−	2.89830i	−0.0577279	−	0.216027i
$181$			18.1671i			1.35035i	0.737659	+	0.675174i	$0.235931\pi$
$181$			18.1671i			1.35035i	−0.737659	+	0.675174i	$0.764069\pi$
$182$			1.54900i			0.114820i
$183$	−4.64234	+	0.609582i	−0.343172	+	0.0450616i
$184$		−	0.812981i		−	0.0599337i
$185$	5.60526			0.412107
$186$	1.61561	+	12.3039i	0.118462	+	0.902162i
$187$	6.50725			0.475857
$188$		−	7.96724i		−	0.581071i
$189$	−3.03521	+	1.25363i	−0.220779	+	0.0911879i
$190$	3.61561	+	2.43462i	0.262304	+	0.176626i
$191$		−	2.80093i		−	0.202668i	−0.994852	−	0.101334i	$-0.967689\pi$
$191$		−	2.80093i		−	0.202668i	0.994852	−	0.101334i	$-0.0323110\pi$
$192$	1.71731	−	0.225499i	0.123936	−	0.0162740i
$193$		−	15.9552i		−	1.14848i	−0.818687	−	0.574240i	$-0.805298\pi$
$193$		−	15.9552i		−	1.14848i	0.818687	−	0.574240i	$-0.194702\pi$
$194$			3.26398i			0.234340i
$195$	−4.20912	+	0.552696i	−0.301421	+	0.0395794i
$196$	−6.60059			−0.471471
$197$		−	19.0352i		−	1.35620i	−0.734969	−	0.678101i	$-0.762803\pi$
$197$		−	19.0352i		−	1.35620i	0.734969	−	0.678101i	$-0.237197\pi$
$198$	−1.54900	−	5.79660i	−0.110083	−	0.411947i
$199$	−15.3691			−1.08949			−0.544743	−	0.838603i	$-0.683373\pi$
$199$	−15.3691			−1.08949			−0.544743	+	0.838603i	$0.683373\pi$
$200$	−1.00000			−0.0707107
$201$	3.37035	+	25.6672i	0.237726	+	1.81043i
$202$			7.45999i			0.524883i
$203$	−2.17064			−0.152349
$204$	0.733688	+	5.58748i	0.0513684	+	0.391202i
$205$			0.802629i			0.0560581i
$206$		−	17.9345i		−	1.24955i
$207$	−0.629655	−	2.35626i	−0.0437640	−	0.163772i
$208$		−	2.45100i		−	0.169946i
$209$	7.23122	+	4.86924i	0.500194	+	0.336812i
$210$	0.142513	+	1.08532i	0.00983430	+	0.0748942i
$211$			2.13976i			0.147307i	0.997284	+	0.0736534i	$0.0234659\pi$
$211$			2.13976i			0.147307i	−0.997284	+	0.0736534i	$0.976534\pi$
$212$	6.53262			0.448662
$213$	10.5889	−	1.39042i	0.725538	−	0.0952699i
$214$	−5.63063			−0.384902
$215$			11.9672i			0.816159i
$216$	4.80263	−	1.98362i	0.326778	−	0.134968i
$217$		−	4.52796i		−	0.307378i
$218$		−	8.71362i		−	0.590161i
$219$	−8.40555	+	1.10373i	−0.567995	+	0.0745830i
$220$	−2.00000			−0.134840
$221$	7.97463			0.536432
$222$	1.26398	+	9.62596i	0.0848326	+	0.646052i
$223$		−	17.9044i		−	1.19897i	−0.800386	−	0.599485i	$-0.795372\pi$
$223$		−	17.9044i		−	1.19897i	0.800386	−	0.599485i	$-0.204628\pi$
$224$	−0.631989			−0.0422265
$225$	−2.89830	+	0.774501i	−0.193220	+	0.0516334i
$226$	−0.705983			−0.0469613
$227$	−3.97463			−0.263805			−0.131903	−	0.991263i	$-0.542109\pi$
$227$	−3.97463			−0.263805			−0.131903	+	0.991263i	$0.542109\pi$
$228$	−3.36568	+	6.75812i	−0.222897	+	0.447568i
$229$	13.5932			0.898264			0.449132	−	0.893465i	$-0.351733\pi$
$229$	13.5932			0.898264			0.449132	+	0.893465i	$0.351733\pi$
$230$	−0.812981			−0.0536064
$231$	0.285025	+	2.17064i	0.0187533	+	0.142818i
$232$	3.43462			0.225494
$233$		−	21.2323i		−	1.39097i	−0.718538	−	0.695487i	$-0.755188\pi$
$233$		−	21.2323i		−	1.39097i	0.718538	−	0.695487i	$-0.244812\pi$
$234$	−1.89830	−	7.10373i	−0.124096	−	0.464385i
$235$	−7.96724			−0.519726
$236$	−2.09198			−0.136176
$237$	−0.998641	−	7.60526i	−0.0648687	−	0.494015i
$238$		−	2.05626i		−	0.133287i
$239$			22.2899i			1.44182i	0.693031	+	0.720908i	$0.256275\pi$
$239$			22.2899i			1.44182i	−0.693031	+	0.720908i	$0.743725\pi$
$240$	−0.225499	−	1.71731i	−0.0145559	−	0.110852i
$241$		−	4.19873i		−	0.270464i	−0.990814	−	0.135232i	$-0.956822\pi$
$241$		−	4.19873i		−	0.270464i	0.990814	−	0.135232i	$-0.0431780\pi$
$242$	7.00000			0.449977
$243$	12.3831	−	9.46877i	0.794379	−	0.607422i
$244$	−2.70326			−0.173059
$245$			6.60059i			0.421696i
$246$	−1.37836	+	0.180992i	−0.0878812	+	0.0115396i
$247$	8.86185	+	5.96724i	0.563866	+	0.379687i
$248$			7.16461i			0.454953i
$249$	−1.32320	−	10.0770i	−0.0838543	−	0.638601i
$250$			1.00000i			0.0632456i
$251$		−	18.6377i		−	1.17640i	−0.808714	−	0.588202i	$-0.799836\pi$
$251$		−	18.6377i		−	1.17640i	0.808714	−	0.588202i	$-0.200164\pi$
$252$	−1.83169	+	0.489476i	−0.115386	+	0.0308341i
$253$	−1.62596			−0.102223
$254$			4.86924i			0.305523i
$255$	5.58748	−	0.733688i	0.349902	−	0.0459453i
$256$	1.00000			0.0625000
$257$	−5.63802			−0.351690			−0.175845	−	0.984418i	$-0.556266\pi$
$257$	−5.63802			−0.351690			−0.175845	+	0.984418i	$0.556266\pi$
$258$	−20.5515	+	2.69860i	−1.27948	+	0.168007i
$259$		−	3.54246i		−	0.220118i
$260$	−2.45100			−0.152004
$261$	9.95456	−	2.66012i	0.616172	−	0.164657i
$262$			20.1005i			1.24181i
$263$		−	25.9044i		−	1.59734i	−0.601772	−	0.798668i	$-0.705538\pi$
$263$		−	25.9044i		−	1.59734i	0.601772	−	0.798668i	$-0.294462\pi$
$264$	−0.450997	−	3.43462i	−0.0277570	−	0.211386i
$265$		−	6.53262i		−	0.401296i
$266$	1.53865	−	2.28503i	0.0943408	−	0.140104i
$267$	−10.1895	+	1.33797i	−0.623585	+	0.0818825i
$268$			14.9462i			0.912984i
$269$	25.3317			1.54450			0.772250	−	0.635319i	$-0.219131\pi$
$269$	25.3317			1.54450			0.772250	+	0.635319i	$0.219131\pi$
$270$	−1.98362	−	4.80263i	−0.120719	−	0.292279i
$271$	17.5799			1.06790			0.533951	−	0.845515i	$-0.320707\pi$
$271$	17.5799			1.06790			0.533951	+	0.845515i	$0.320707\pi$
$272$			3.25363i			0.197280i
$273$	0.349298	+	2.66012i	0.0211405	+	0.160998i
$274$		−	8.28883i		−	0.500747i
$275$			2.00000i			0.120605i
$276$	−0.183326	−	1.39614i	−0.0110349	−	0.0840377i
$277$	21.6271			1.29944			0.649722	−	0.760172i	$-0.274885\pi$
$277$	21.6271			1.29944			0.649722	+	0.760172i	$0.274885\pi$
$278$	−0.196012			−0.0117560
$279$	5.54900	+	20.7652i	0.332210	+	1.24318i
$280$			0.631989i			0.0377686i
$281$	21.6598			1.29212			0.646058	−	0.763288i	$-0.276416\pi$
$281$	21.6598			1.29212			0.646058	+	0.763288i	$0.276416\pi$
$282$	−1.79660	−	13.6822i	−0.106986	−	0.814764i
$283$	−15.2132			−0.904333			−0.452166	−	0.891934i	$-0.649349\pi$
$283$	−15.2132			−0.904333			−0.452166	+	0.891934i	$0.649349\pi$
$284$	6.16597			0.365883
$285$	6.75812	+	3.36568i	0.400317	+	0.199365i
$286$	−4.90199			−0.289861
$287$	0.507253			0.0299422
$288$	2.89830	−	0.774501i	0.170784	−	0.0456379i
$289$	6.41392			0.377289
$290$		−	3.43462i		−	0.201688i
$291$	0.736022	+	5.60526i	0.0431464	+	0.328586i
$292$	−4.89461			−0.286435
$293$	−5.38980			−0.314876			−0.157438	−	0.987529i	$-0.550323\pi$
$293$	−5.38980			−0.314876			−0.157438	+	0.987529i	$0.550323\pi$
$294$	−11.3353	+	1.48842i	−0.661085	+	0.0868066i
$295$			2.09198i			0.121800i
$296$			5.60526i			0.325799i
$297$	−3.96724	−	9.60526i	−0.230203	−	0.557354i
$298$		−	11.4092i		−	0.660920i
$299$	−1.99261			−0.115236
$300$	−1.71731	+	0.225499i	−0.0991489	+	0.0130192i
$301$	7.56316			0.435934
$302$			10.2119i			0.587627i
$303$	1.68222	+	12.8111i	0.0966408	+	0.735979i
$304$	−2.43462	+	3.61561i	−0.139635	+	0.207369i
$305$			2.70326i			0.154788i
$306$	2.51994	+	9.42999i	0.144055	+	0.539077i
$307$		−	0.570050i		−	0.0325345i	−0.999868	−	0.0162672i	$-0.994822\pi$
$307$		−	0.570050i		−	0.0325345i	0.999868	−	0.0162672i	$-0.00517825\pi$
$308$			1.26398i			0.0720218i
$309$	−4.04420	−	30.7991i	−0.230067	−	1.75210i
$310$	7.16461			0.406923
$311$			8.38548i			0.475497i	0.971327	+	0.237749i	$0.0764094\pi$
$311$			8.38548i			0.475497i	−0.971327	+	0.237749i	$0.923591\pi$
$312$	−0.552696	−	4.20912i	−0.0312903	−	0.238294i
$313$	24.6358			1.39250			0.696249	−	0.717801i	$-0.254851\pi$
$313$	24.6358			1.39250			0.696249	+	0.717801i	$0.254851\pi$
$314$	14.0338			0.791976
$315$	0.489476	+	1.83169i	0.0275789	+	0.103204i
$316$		−	4.42859i		−	0.249128i
$317$	17.0071			0.955215			0.477607	−	0.878573i	$-0.341504\pi$
$317$	17.0071			0.955215			0.477607	+	0.878573i	$0.341504\pi$
$318$	11.2185	−	1.47310i	0.629104	−	0.0826072i
$319$		−	6.86924i		−	0.384603i
$320$		−	1.00000i		−	0.0559017i
$321$	−9.66953	+	1.26970i	−0.539701	+	0.0708677i
$322$			0.513795i			0.0286327i
$323$	−11.7638	−	7.92134i	−0.654558	−	0.440755i
$324$	7.80030	−	4.48948i	0.433350	−	0.249415i
$325$			2.45100i			0.135957i
$326$	−19.3765			−1.07316
$327$	−1.96491	−	14.9640i	−0.108660	−	0.827509i
$328$	−0.802629			−0.0443178
$329$			5.03521i			0.277600i
$330$	−3.43462	+	0.450997i	−0.189070	+	0.0248266i
$331$			9.74773i			0.535784i	0.963449	+	0.267892i	$0.0863270\pi$
$331$			9.74773i			0.535784i	−0.963449	+	0.267892i	$0.913673\pi$
$332$		−	5.86788i		−	0.322042i
$333$	4.34128	+	16.2457i	0.237901	+	0.890260i
$334$	−9.23122			−0.505110
$335$	14.9462			0.816598
$336$	−1.08532	+	0.142513i	−0.0592091	+	0.00777470i
$337$		−	23.7505i		−	1.29377i	−0.762586	−	0.646887i	$-0.776071\pi$
$337$		−	23.7505i		−	1.29377i	0.762586	−	0.646887i	$-0.223929\pi$
$338$	6.99261			0.380348
$339$	−1.21239	+	0.159198i	−0.0658480	+	0.00864645i
$340$	3.25363			0.176453
$341$	14.3292			0.775971
$342$	−4.25596	+	12.3647i	−0.230136	+	0.668609i
$343$	8.59542			0.464109
$344$	−11.9672			−0.645230
$345$	−1.39614	+	0.183326i	−0.0751656	+	0.00986994i
$346$	1.98794			0.106873
$347$		−	22.9031i		−	1.22950i	−0.788721	−	0.614751i	$-0.789256\pi$
$347$		−	22.9031i		−	1.22950i	0.788721	−	0.614751i	$-0.210744\pi$
$348$	5.89830	−	0.774501i	0.316182	−	0.0415176i
$349$	11.1985			0.599440			0.299720	−	0.954027i	$-0.403107\pi$
$349$	11.1985			0.599440			0.299720	+	0.954027i	$0.403107\pi$
$350$	0.631989			0.0337812
$351$	−4.86185	−	11.7712i	−0.259506	−	0.628302i
$352$		−	2.00000i		−	0.106600i
$353$		−	1.64837i		−	0.0877338i	−0.999037	−	0.0438669i	$-0.986032\pi$
$353$		−	1.64837i		−	0.0877338i	0.999037	−	0.0438669i	$-0.0139677\pi$
$354$	−3.59257	+	0.471738i	−0.190943	+	0.0250726i
$355$		−	6.16597i		−	0.327256i
$356$	−5.93339			−0.314469
$357$	−0.463683	−	3.53123i	−0.0245407	−	0.186892i
$358$	11.4938			0.607468
$359$			32.3079i			1.70515i	0.522608	+	0.852573i	$0.324959\pi$
$359$			32.3079i			1.70515i	−0.522608	+	0.852573i	$0.675041\pi$
$360$	−0.774501	−	2.89830i	−0.0408198	−	0.152754i
$361$	−7.14527	−	17.6053i	−0.376067	−	0.926593i
$362$			18.1671i			0.954840i
$363$	12.0212	−	1.57849i	0.630947	−	0.0828492i
$364$			1.54900i			0.0811898i
$365$			4.89461i			0.256195i
$366$	−4.64234	+	0.609582i	−0.242659	+	0.0318634i
$367$	−4.78465			−0.249756			−0.124878	−	0.992172i	$-0.539854\pi$
$367$	−4.78465			−0.249756			−0.124878	+	0.992172i	$0.539854\pi$
$368$		−	0.812981i		−	0.0423795i
$369$	−2.32626	+	0.621638i	−0.121100	+	0.0323612i
$370$	5.60526			0.291404
$371$	−4.12855			−0.214343
$372$	1.61561	+	12.3039i	0.0837655	+	0.637925i
$373$			3.21978i			0.166714i	0.996520	+	0.0833569i	$0.0265641\pi$
$373$			3.21978i			0.166714i	−0.996520	+	0.0833569i	$0.973436\pi$
$374$	6.50725			0.336482
$375$	0.225499	+	1.71731i	0.0116447	+	0.0886815i
$376$		−	7.96724i		−	0.410879i
$377$		−	8.41824i		−	0.433561i
$378$	−3.03521	+	1.25363i	−0.156114	+	0.0644796i
$379$			23.0887i			1.18599i	0.805206	+	0.592995i	$0.202054\pi$
$379$			23.0887i			1.18599i	−0.805206	+	0.592995i	$0.797946\pi$
$380$	3.61561	+	2.43462i	0.185477	+	0.124893i
$381$	1.09801	+	8.36198i	0.0562525	+	0.428397i
$382$		−	2.80093i		−	0.143308i
$383$	−28.8124			−1.47224			−0.736122	−	0.676849i	$-0.763345\pi$
$383$	−28.8124			−1.47224			−0.736122	+	0.676849i	$0.763345\pi$
$384$	1.71731	−	0.225499i	0.0876361	−	0.0115074i
$385$	1.26398			0.0644183
$386$		−	15.9552i		−	0.812098i
$387$	−34.6847	+	9.26865i	−1.76312	+	0.471152i
$388$			3.26398i			0.165703i
$389$		−	13.5545i		−	0.687241i	−0.939109	−	0.343621i	$-0.888347\pi$
$389$		−	13.5545i		−	0.687241i	0.939109	−	0.343621i	$-0.111653\pi$
$390$	−4.20912	+	0.552696i	−0.213137	+	0.0279869i
$391$	2.64514			0.133770
$392$	−6.60059			−0.333380
$393$	4.53262	+	34.5187i	0.228641	+	1.74124i
$394$		−	19.0352i		−	0.958980i
$395$	−4.42859			−0.222827
$396$	−1.54900	−	5.79660i	−0.0778403	−	0.291290i
$397$	1.51795			0.0761837			0.0380918	−	0.999274i	$-0.487872\pi$
$397$	1.51795			0.0761837			0.0380918	+	0.999274i	$0.487872\pi$
$398$	−15.3691			−0.770383
$399$	2.12707	−	4.27106i	0.106487	−	0.213820i
$400$	−1.00000			−0.0500000
$401$	−9.81713			−0.490244			−0.245122	−	0.969492i	$-0.578828\pi$
$401$	−9.81713			−0.490244			−0.245122	+	0.969492i	$0.578828\pi$
$402$	3.37035	+	25.6672i	0.168098	+	1.28017i
$403$	17.5604			0.874748
$404$			7.45999i			0.371148i
$405$	−4.48948	−	7.80030i	−0.223084	−	0.387600i
$406$	−2.17064			−0.107727
$407$	11.2105			0.555685
$408$	0.733688	+	5.58748i	0.0363230	+	0.276622i
$409$			18.1453i			0.897226i	0.893726	+	0.448613i	$0.148082\pi$
$409$			18.1453i			0.897226i	−0.893726	+	0.448613i	$0.851918\pi$
$410$			0.802629i			0.0396390i
$411$	−1.86912	−	14.2345i	−0.0921969	−	0.702136i
$412$		−	17.9345i		−	0.883569i
$413$	1.32211			0.0650566
$414$	−0.629655	−	2.35626i	−0.0309458	−	0.115804i
$415$	−5.86788			−0.288043
$416$		−	2.45100i		−	0.120170i
$417$	−0.336612	+	0.0442003i	−0.0164840	+	0.00216450i
$418$	7.23122	+	4.86924i	0.353691	+	0.238162i
$419$			15.0145i			0.733507i	0.930318	+	0.366753i	$0.119531\pi$
$419$			15.0145i			0.733507i	−0.930318	+	0.366753i	$0.880469\pi$
$420$	0.142513	+	1.08532i	0.00695390	+	0.0529582i
$421$		−	24.4341i		−	1.19085i	−0.803413	−	0.595423i	$-0.796985\pi$
$421$		−	24.4341i		−	1.19085i	0.803413	−	0.595423i	$-0.203015\pi$
$422$			2.13976i			0.104162i
$423$	−6.17064	−	23.0915i	−0.300027	−	1.12275i
$424$	6.53262			0.317252
$425$		−	3.25363i		−	0.157824i
$426$	10.5889	−	1.39042i	0.513033	−	0.0673660i
$427$	1.70843			0.0826769
$428$	−5.63063			−0.272167
$429$	−8.41824	+	1.10539i	−0.406436	+	0.0533689i
$430$			11.9672i			0.577112i
$431$	−41.0522			−1.97741			−0.988707	−	0.149864i	$-0.952116\pi$
$431$	−41.0522			−1.97741			−0.988707	+	0.149864i	$0.952116\pi$
$432$	4.80263	−	1.98362i	0.231067	−	0.0954370i
$433$			18.0121i			0.865604i	0.901489	+	0.432802i	$0.142475\pi$
$433$			18.0121i			0.865604i	−0.901489	+	0.432802i	$0.857525\pi$
$434$		−	4.52796i		−	0.217349i
$435$	−0.774501	−	5.89830i	−0.0371345	−	0.282802i
$436$		−	8.71362i		−	0.417307i
$437$	2.93942	+	1.97930i	0.140612	+	0.0946826i
$438$	−8.40555	+	1.10373i	−0.401633	+	0.0527381i
$439$		−	27.8024i		−	1.32693i	−0.748205	−	0.663467i	$-0.769084\pi$
$439$		−	27.8024i		−	1.32693i	0.748205	−	0.663467i	$-0.230916\pi$
$440$	−2.00000			−0.0953463
$441$	−19.1305	+	5.11217i	−0.910976	+	0.243437i
$442$	7.97463			0.379314
$443$			10.0366i			0.476852i	0.971161	+	0.238426i	$0.0766314\pi$
$443$			10.0366i			0.476852i	−0.971161	+	0.238426i	$0.923369\pi$
$444$	1.26398	+	9.62596i	0.0599857	+	0.456828i
$445$			5.93339i			0.281270i
$446$		−	17.9044i		−	0.847800i
$447$	−2.57277	−	19.5932i	−0.121688	−	0.926727i
$448$	−0.631989			−0.0298587
$449$	33.9055			1.60010			0.800051	−	0.599933i	$-0.204806\pi$
$449$	33.9055			1.60010			0.800051	+	0.599933i	$0.204806\pi$
$450$	−2.89830	+	0.774501i	−0.136627	+	0.0365103i
$451$			1.60526i			0.0755887i
$452$	−0.705983			−0.0332066
$453$	2.30276	+	17.5369i	0.108193	+	0.823958i
$454$	−3.97463			−0.186539
$455$	1.54900			0.0726184
$456$	−3.36568	+	6.75812i	−0.157612	+	0.316478i
$457$	−31.7131			−1.48348			−0.741738	−	0.670690i	$-0.765998\pi$
$457$	−31.7131			−1.48348			−0.741738	+	0.670690i	$0.765998\pi$
$458$	13.5932			0.635169
$459$	6.45396	+	15.6260i	0.301245	+	0.729357i
$460$	−0.812981			−0.0379054
$461$		−	23.1029i		−	1.07601i	−0.842942	−	0.538005i	$-0.819178\pi$
$461$		−	23.1029i		−	1.07601i	0.842942	−	0.538005i	$-0.180822\pi$
$462$	0.285025	+	2.17064i	0.0132606	+	0.100987i
$463$	32.6950			1.51947			0.759733	−	0.650235i	$-0.225330\pi$
$463$	32.6950			1.51947			0.759733	+	0.650235i	$0.225330\pi$
$464$	3.43462			0.159448
$465$	12.3039	−	1.61561i	0.570578	−	0.0749221i
$466$		−	21.2323i		−	0.983568i
$467$			29.2023i			1.35132i	0.737213	+	0.675660i	$0.236141\pi$
$467$			29.2023i			1.35132i	−0.737213	+	0.675660i	$0.763859\pi$
$468$	−1.89830	−	7.10373i	−0.0877490	−	0.328370i
$469$		−	9.44583i		−	0.436168i
$470$	−7.96724			−0.367501
$471$	24.1005	−	3.16461i	1.11049	−	0.145818i
$472$	−2.09198			−0.0962911
$473$			23.9345i			1.10051i
$474$	−0.998641	−	7.60526i	−0.0458691	−	0.349321i
$475$	2.43462	−	3.61561i	0.111708	−	0.165896i
$476$		−	2.05626i		−	0.0942483i
$477$	18.9335	−	5.05953i	0.866906	−	0.231660i
$478$			22.2899i			1.01952i
$479$			17.7712i			0.811988i	0.913876	+	0.405994i	$0.133075\pi$
$479$			17.7712i			0.811988i	−0.913876	+	0.405994i	$0.866925\pi$
$480$	−0.225499	−	1.71731i	−0.0102926	−	0.0783841i
$481$	13.7385			0.626420
$482$		−	4.19873i		−	0.191247i
$483$	0.115860	+	0.882344i	0.00527181	+	0.0401481i
$484$	7.00000			0.318182
$485$	3.26398			0.148210
$486$	12.3831	−	9.46877i	0.561711	−	0.429512i
$487$		−	10.3620i		−	0.469546i	−0.972050	−	0.234773i	$-0.924565\pi$
$487$		−	10.3620i		−	0.469546i	0.972050	−	0.234773i	$-0.0754347\pi$
$488$	−2.70326			−0.122371
$489$	−33.2754	+	4.36937i	−1.50477	+	0.197590i
$490$			6.60059i			0.298184i
$491$		−	16.8993i		−	0.762654i	−0.924440	−	0.381327i	$-0.875467\pi$
$491$		−	16.8993i		−	0.762654i	0.924440	−	0.381327i	$-0.124533\pi$
$492$	−1.37836	+	0.180992i	−0.0621414	+	0.00815974i
$493$			11.1750i			0.503295i
$494$	8.86185	+	5.96724i	0.398713	+	0.268479i
$495$	−5.79660	+	1.54900i	−0.260538	+	0.0696225i
$496$			7.16461i			0.321701i
$497$	−3.89683			−0.174797
$498$	−1.32320	−	10.0770i	−0.0592939	−	0.451559i
$499$	0.364702			0.0163263			0.00816315	−	0.999967i	$-0.497402\pi$
$499$	0.364702			0.0163263			0.00816315	+	0.999967i	$0.497402\pi$
$500$			1.00000i			0.0447214i
$501$	−15.8529	+	2.08163i	−0.708253	+	0.0930002i
$502$		−	18.6377i		−	0.831843i
$503$		−	30.0939i		−	1.34182i	−0.741538	−	0.670911i	$-0.765903\pi$
$503$		−	30.0939i		−	1.34182i	0.741538	−	0.670911i	$-0.234097\pi$
$504$	−1.83169	+	0.489476i	−0.0815901	+	0.0218030i
$505$	7.45999			0.331965
$506$	−1.62596			−0.0722828
$507$	12.0085	−	1.57682i	0.533315	−	0.0700292i
$508$			4.86924i			0.216037i
$509$	−44.3849			−1.96732			−0.983662	−	0.180023i	$-0.942383\pi$
$509$	−44.3849			−1.96732			−0.983662	+	0.180023i	$0.942383\pi$
$510$	5.58748	−	0.733688i	0.247418	−	0.0324883i
$511$	3.09334			0.136841
$512$	1.00000			0.0441942
$513$	−4.52057	+	22.1938i	−0.199588	+	0.979880i
$514$	−5.63802			−0.248682
$515$	−17.9345			−0.790288
$516$	−20.5515	+	2.69860i	−0.904727	+	0.118799i
$517$	−15.9345			−0.700798
$518$		−	3.54246i		−	0.155647i
$519$	3.41392	−	0.448279i	0.149854	−	0.0196772i
$520$	−2.45100			−0.107483
$521$	−17.8472			−0.781899			−0.390949	−	0.920412i	$-0.627853\pi$
$521$	−17.8472			−0.781899			−0.390949	+	0.920412i	$0.627853\pi$
$522$	9.95456	−	2.66012i	0.435699	−	0.116430i
$523$			14.2222i			0.621895i	0.950427	+	0.310947i	$0.100646\pi$
$523$			14.2222i			0.621895i	−0.950427	+	0.310947i	$0.899354\pi$
$524$			20.1005i			0.878092i
$525$	1.08532	−	0.142513i	0.0473673	−	0.00621976i
$526$		−	25.9044i		−	1.12949i
$527$	−23.3110			−1.01544
$528$	−0.450997	−	3.43462i	−0.0196271	−	0.149473i
$529$	22.3391			0.971264
$530$		−	6.53262i		−	0.283759i
$531$	−6.06318	+	1.62024i	−0.263120	+	0.0703124i
$532$	1.53865	−	2.28503i	0.0667090	−	0.0990684i
$533$			1.96724i			0.0852107i
$534$	−10.1895	+	1.33797i	−0.440941	+	0.0578997i
$535$			5.63063i			0.243433i
$536$			14.9462i			0.645577i
$537$	19.7385	−	2.59184i	0.851778	−	0.111846i
$538$	25.3317			1.09213
$539$			13.2012i			0.568615i
$540$	−1.98362	−	4.80263i	−0.0853615	−	0.206672i
$541$	−37.2164			−1.60006			−0.800030	−	0.599960i	$-0.795183\pi$
$541$	−37.2164			−1.60006			−0.800030	+	0.599960i	$0.795183\pi$
$542$	17.5799			0.755121
$543$	4.09665	+	31.1985i	0.175804	+	1.33885i
$544$			3.25363i			0.139498i
$545$	−8.71362			−0.373250
$546$	0.349298	+	2.66012i	0.0149486	+	0.113842i
$547$		−	16.3789i		−	0.700313i	−0.936691	−	0.350156i	$-0.886128\pi$
$547$		−	16.3789i		−	0.700313i	0.936691	−	0.350156i	$-0.113872\pi$
$548$		−	8.28883i		−	0.354081i
$549$	−7.83487	+	2.09368i	−0.334384	+	0.0893562i
$550$			2.00000i			0.0852803i
$551$	−8.36198	+	12.4182i	−0.356232	+	0.529035i
$552$	−0.183326	−	1.39614i	−0.00780287	−	0.0594236i
$553$			2.79882i			0.119018i
$554$	21.6271			0.918845
$555$	9.62596	−	1.26398i	0.408599	−	0.0536529i
$556$	−0.196012			−0.00831274
$557$			36.8244i			1.56030i	0.625592	+	0.780150i	$0.284858\pi$
$557$			36.8244i			1.56030i	−0.625592	+	0.780150i	$0.715142\pi$
$558$	5.54900	+	20.7652i	0.234908	+	0.879061i
$559$			29.3317i			1.24060i
$560$			0.631989i			0.0267064i
$561$	11.1750	−	1.46738i	0.471807	−	0.0619527i
$562$	21.6598			0.913664
$563$	−40.0022			−1.68589			−0.842945	−	0.537999i	$-0.819180\pi$
$563$	−40.0022			−1.68589			−0.842945	+	0.537999i	$0.819180\pi$
$564$	−1.79660	−	13.6822i	−0.0756506	−	0.576125i
$565$			0.705983i			0.0297009i
$566$	−15.2132			−0.639460
$567$	−4.92970	+	2.83730i	−0.207028	+	0.119155i
$568$	6.16597			0.258718
$569$	−21.6953			−0.909514			−0.454757	−	0.890616i	$-0.650274\pi$
$569$	−21.6953			−0.909514			−0.454757	+	0.890616i	$0.650274\pi$
$570$	6.75812	+	3.36568i	0.283067	+	0.140973i
$571$	3.37377			0.141188			0.0705940	−	0.997505i	$-0.477511\pi$
$571$	3.37377			0.141188			0.0705940	+	0.997505i	$0.477511\pi$
$572$	−4.90199			−0.204963
$573$	−0.631605	−	4.81005i	−0.0263857	−	0.200943i
$574$	0.507253			0.0211723
$575$			0.812981i			0.0339036i
$576$	2.89830	−	0.774501i	0.120763	−	0.0322709i
$577$	−31.3740			−1.30612			−0.653058	−	0.757308i	$-0.726514\pi$
$577$	−31.3740			−1.30612			−0.653058	+	0.757308i	$0.726514\pi$
$578$	6.41392			0.266784
$579$	−3.59787	−	27.4000i	−0.149522	−	1.13870i
$580$		−	3.43462i		−	0.142615i
$581$			3.70843i			0.153852i
$582$	0.736022	+	5.60526i	0.0305091	+	0.232345i
$583$		−	13.0652i		−	0.541107i
$584$	−4.89461			−0.202540
$585$	−7.10373	+	1.89830i	−0.293703	+	0.0784851i
$586$	−5.38980			−0.222651
$587$			39.0718i			1.61266i	0.591463	+	0.806332i	$0.298551\pi$
$587$			39.0718i			1.61266i	−0.591463	+	0.806332i	$0.701449\pi$
$588$	−11.3353	+	1.48842i	−0.467458	+	0.0613816i
$589$	−25.9044	−	17.4431i	−1.06737	−	0.718730i
$590$			2.09198i			0.0861254i
$591$	−4.29241	−	32.6893i	−0.176566	−	1.34466i
$592$			5.60526i			0.230375i
$593$			26.6367i			1.09384i	0.837186	+	0.546918i	$0.184199\pi$
$593$			26.6367i			1.09384i	−0.837186	+	0.546918i	$0.815801\pi$
$594$	−3.96724	−	9.60526i	−0.162778	−	0.394109i
$595$	−2.05626			−0.0842983
$596$		−	11.4092i		−	0.467341i
$597$	−26.3935	+	3.46571i	−1.08021	+	0.141842i
$598$	−1.99261			−0.0814840
$599$	0.952736			0.0389278			0.0194639	−	0.999811i	$-0.493804\pi$
$599$	0.952736			0.0389278			0.0194639	+	0.999811i	$0.493804\pi$
$600$	−1.71731	+	0.225499i	−0.0701088	+	0.00920594i
$601$		−	14.6050i		−	0.595750i	−0.954605	−	0.297875i	$-0.903722\pi$
$601$		−	14.6050i		−	0.595750i	0.954605	−	0.297875i	$-0.0962779\pi$
$602$	7.56316			0.308252
$603$	11.5758	+	43.3186i	0.471405	+	1.76407i
$604$			10.2119i			0.415515i
$605$		−	7.00000i		−	0.284590i
$606$	1.68222	+	12.8111i	0.0683354	+	0.520416i
$607$			11.5304i			0.468005i	0.972236	+	0.234002i	$0.0751823\pi$
$607$			11.5304i			0.468005i	−0.972236	+	0.234002i	$0.924818\pi$
$608$	−2.43462	+	3.61561i	−0.0987368	+	0.146632i
$609$	−3.72766	+	0.489476i	−0.151052	+	0.0198346i
$610$			2.70326i			0.109452i
$611$	−19.5277			−0.790006
$612$	2.51994	+	9.42999i	0.101862	+	0.381185i
$613$	−25.1996			−1.01780			−0.508900	−	0.860826i	$-0.669948\pi$
$613$	−25.1996			−1.01780			−0.508900	+	0.860826i	$0.669948\pi$
$614$		−	0.570050i		−	0.0230054i
$615$	0.180992	+	1.37836i	0.00729829	+	0.0555809i
$616$			1.26398i			0.0509271i
$617$		−	18.3724i		−	0.739645i	−0.929102	−	0.369823i	$-0.879418\pi$
$617$		−	18.3724i		−	0.739645i	0.929102	−	0.369823i	$-0.120582\pi$
$618$	−4.04420	−	30.7991i	−0.162682	−	1.23892i
$619$	−16.4952			−0.662998			−0.331499	−	0.943456i	$-0.607554\pi$
$619$	−16.4952			−0.662998			−0.331499	+	0.943456i	$0.607554\pi$
$620$	7.16461			0.287738
$621$	−1.61265	−	3.90444i	−0.0647132	−	0.156680i
$622$			8.38548i			0.336227i
$623$	3.74984			0.150234
$624$	−0.552696	−	4.20912i	−0.0221256	−	0.168500i
$625$	1.00000			0.0400000
$626$	24.6358			0.984645
$627$	13.5162	+	6.73135i	0.539787	+	0.268824i
$628$	14.0338			0.560012
$629$	−18.2374			−0.727173
$630$	0.489476	+	1.83169i	0.0195012	+	0.0729764i
$631$	−11.0532			−0.440021			−0.220010	−	0.975498i	$-0.570609\pi$
$631$	−11.0532			−0.440021			−0.220010	+	0.975498i	$0.570609\pi$
$632$		−	4.42859i		−	0.176160i
$633$	0.482512	+	3.67462i	0.0191781	+	0.146053i
$634$	17.0071			0.675439
$635$	4.86924			0.193230
$636$	11.2185	−	1.47310i	0.444844	−	0.0584121i
$637$			16.1780i			0.640997i
$638$		−	6.86924i		−	0.271956i
$639$	17.8708	−	4.77555i	0.706960	−	0.188918i
$640$		−	1.00000i		−	0.0395285i
$641$	33.7368			1.33253			0.666263	−	0.745717i	$-0.267893\pi$
$641$	33.7368			1.33253			0.666263	+	0.745717i	$0.267893\pi$
$642$	−9.66953	+	1.26970i	−0.381626	+	0.0501110i
$643$	−28.9369			−1.14116			−0.570581	−	0.821242i	$-0.693282\pi$
$643$	−28.9369			−1.14116			−0.570581	+	0.821242i	$0.693282\pi$
$644$			0.513795i			0.0202463i
$645$	2.69860	+	20.5515i	0.106257	+	0.809213i
$646$	−11.7638	−	7.92134i	−0.462842	−	0.311661i
$647$		−	35.3409i		−	1.38940i	−0.719302	−	0.694698i	$-0.755538\pi$
$647$		−	35.3409i		−	1.38940i	0.719302	−	0.694698i	$-0.244462\pi$
$648$	7.80030	−	4.48948i	0.306425	−	0.176363i
$649$			4.18396i			0.164235i
$650$			2.45100i			0.0961360i
$651$	−1.02105	−	7.77590i	−0.0400180	−	0.304762i
$652$	−19.3765			−0.758842
$653$		−	5.41518i		−	0.211912i	−0.994371	−	0.105956i	$-0.966210\pi$
$653$		−	5.41518i		−	0.211912i	0.994371	−	0.105956i	$-0.0337903\pi$
$654$	−1.96491	−	14.9640i	−0.0768340	−	0.585138i
$655$	20.1005			0.785390
$656$	−0.802629			−0.0313374
$657$	−14.1860	+	3.79088i	−0.553450	+	0.147896i
$658$			5.03521i			0.196293i
$659$	23.8546			0.929242			0.464621	−	0.885510i	$-0.346191\pi$
$659$	23.8546			0.929242			0.464621	+	0.885510i	$0.346191\pi$
$660$	−3.43462	+	0.450997i	−0.133692	+	0.0175550i
$661$			14.3396i			0.557745i	0.960328	+	0.278872i	$0.0899607\pi$
$661$			14.3396i			0.557745i	−0.960328	+	0.278872i	$0.910039\pi$
$662$			9.74773i			0.378856i
$663$	13.6949	−	1.79827i	0.531866	−	0.0698389i
$664$		−	5.86788i		−	0.227718i
$665$	−2.28503	−	1.53865i	−0.0886095	−	0.0596663i
$666$	4.34128	+	16.2457i	0.168221	+	0.629509i
$667$		−	2.79228i		−	0.108117i
$668$	−9.23122			−0.357167
$669$	−4.03743	−	30.7475i	−0.156096	−	1.18877i
$670$	14.9462			0.577422
$671$			5.40653i			0.208717i
$672$	−1.08532	+	0.142513i	−0.0418671	+	0.00549754i
$673$			49.3290i			1.90149i	0.309972	+	0.950746i	$0.399680\pi$
$673$			49.3290i			1.90149i	−0.309972	+	0.950746i	$0.600320\pi$
$674$		−	23.7505i		−	0.914836i
$675$	−4.80263	+	1.98362i	−0.184853	+	0.0763496i
$676$	6.99261			0.268947
$677$	−23.1431			−0.889460			−0.444730	−	0.895665i	$-0.646700\pi$
$677$	−23.1431			−0.889460			−0.444730	+	0.895665i	$0.646700\pi$
$678$	−1.21239	+	0.159198i	−0.0465616	+	0.00611397i
$679$		−	2.06280i		−	0.0791629i
$680$	3.25363			0.124771
$681$	−6.82567	+	0.896273i	−0.261560	+	0.0343453i
$682$	14.3292			0.548694
$683$	20.2905			0.776396			0.388198	−	0.921576i	$-0.373098\pi$
$683$	20.2905			0.776396			0.388198	+	0.921576i	$0.373098\pi$
$684$	−4.25596	+	12.3647i	−0.162731	+	0.472778i
$685$	−8.28883			−0.316700
$686$	8.59542			0.328175
$687$	23.3437	−	3.06525i	0.890619	−	0.116946i
$688$	−11.9672			−0.456247
$689$		−	16.0114i		−	0.609987i
$690$	−1.39614	+	0.183326i	−0.0531501	+	0.00697910i
$691$	−18.5280			−0.704837			−0.352418	−	0.935843i	$-0.614641\pi$
$691$	−18.5280			−0.704837			−0.352418	+	0.935843i	$0.614641\pi$
$692$	1.98794			0.0755703
$693$	0.978953	+	3.66339i	0.0371873	+	0.139161i
$694$		−	22.9031i		−	0.869389i
$695$			0.196012i			0.00743514i
$696$	5.89830	−	0.774501i	0.223575	−	0.0293574i
$697$		−	2.61146i		−	0.0989159i
$698$	11.1985			0.423868
$699$	−4.78786	−	36.4624i	−0.181093	−	1.37914i
$700$	0.631989			0.0238869
$701$			3.42130i			0.129221i	0.997911	+	0.0646104i	$0.0205805\pi$
$701$			3.42130i			0.129221i	−0.997911	+	0.0646104i	$0.979420\pi$
$702$	−4.86185	−	11.7712i	−0.183499	−	0.444276i
$703$	−20.2664	−	13.6467i	−0.764363	−	0.514694i
$704$		−	2.00000i		−	0.0753778i
$705$	−13.6822	+	1.79660i	−0.515302	+	0.0676639i
$706$		−	1.64837i		−	0.0620371i
$707$		−	4.71463i		−	0.177312i
$708$	−3.59257	+	0.471738i	−0.135017	+	0.0177290i
$709$	15.1329			0.568330			0.284165	−	0.958775i	$-0.408284\pi$
$709$	15.1329			0.568330			0.284165	+	0.958775i	$0.408284\pi$
$710$		−	6.16597i		−	0.231405i
$711$	−3.42995	−	12.8354i	−0.128633	−	0.481365i
$712$	−5.93339			−0.222363
$713$	5.82469			0.218136
$714$	−0.463683	−	3.53123i	−0.0173529	−	0.132153i
$715$			4.90199i			0.183324i
$716$	11.4938			0.429545
$717$	5.02635	+	38.2787i	0.187712	+	1.42954i
$718$			32.3079i			1.20572i
$719$			4.37343i			0.163101i	0.996669	+	0.0815506i	$0.0259872\pi$
$719$			4.37343i			0.163101i	−0.996669	+	0.0815506i	$0.974013\pi$
$720$	−0.774501	−	2.89830i	−0.0288640	−	0.108013i
$721$			11.3344i			0.422115i
$722$	−7.14527	−	17.6053i	−0.265919	−	0.655200i
$723$	−0.946808	−	7.21052i	−0.0352122	−	0.268162i
$724$			18.1671i			0.675174i
$725$	−3.43462			−0.127559
$726$	12.0212	−	1.57849i	0.446147	−	0.0585833i
$727$	26.6517			0.988455			0.494228	−	0.869332i	$-0.335451\pi$
$727$	26.6517			0.988455			0.494228	+	0.869332i	$0.335451\pi$
$728$			1.54900i			0.0574099i
$729$	19.1305	−	19.0532i	0.708537	−	0.705674i
$730$			4.89461i			0.181158i
$731$		−	38.9369i		−	1.44013i
$732$	−4.64234	+	0.609582i	−0.171586	+	0.0225308i
$733$	14.1501			0.522646			0.261323	−	0.965251i	$-0.415841\pi$
$733$	14.1501			0.522646			0.261323	+	0.965251i	$0.415841\pi$
$734$	−4.78465			−0.176604
$735$	1.48842	+	11.3353i	0.0549013	+	0.418107i
$736$		−	0.812981i		−	0.0299669i
$737$	29.8924			1.10110
$738$	−2.32626	+	0.621638i	−0.0856309	+	0.0228828i
$739$	−47.9721			−1.76468			−0.882342	−	0.470609i	$-0.844034\pi$
$739$	−47.9721			−1.76468			−0.882342	+	0.470609i	$0.844034\pi$
$740$	5.60526			0.206053
$741$	16.5641	+	8.24926i	0.608499	+	0.303044i
$742$	−4.12855			−0.151564
$743$	43.3765			1.59133			0.795665	−	0.605738i	$-0.207122\pi$
$743$	43.3765			1.59133			0.795665	+	0.605738i	$0.207122\pi$
$744$	1.61561	+	12.3039i	0.0592311	+	0.451081i
$745$	−11.4092			−0.418002
$746$			3.21978i			0.117884i
$747$	−4.54468	−	17.0069i	−0.166281	−	0.622249i
$748$	6.50725			0.237929
$749$	3.55850			0.130025
$750$	0.225499	+	1.71731i	0.00823404	+	0.0627073i
$751$		−	3.58278i		−	0.130737i	−0.997861	−	0.0653687i	$-0.979178\pi$
$751$		−	3.58278i		−	0.130737i	0.997861	−	0.0653687i	$-0.0208223\pi$
$752$		−	7.96724i		−	0.290535i
$753$	−4.20279	−	32.0068i	−0.153158	−	1.16639i
$754$		−	8.41824i		−	0.306574i
$755$	10.2119			0.371648
$756$	−3.03521	+	1.25363i	−0.110389	+	0.0455940i
$757$	−16.5618			−0.601949			−0.300975	−	0.953632i	$-0.597312\pi$
$757$	−16.5618			−0.601949			−0.300975	+	0.953632i	$0.597312\pi$
$758$			23.0887i			0.838621i
$759$	−2.79228	+	0.366652i	−0.101353	+	0.0133086i
$760$	3.61561	+	2.43462i	0.131152	+	0.0883129i
$761$			34.6726i			1.25688i	0.777858	+	0.628441i	$0.216306\pi$
$761$			34.6726i			1.25688i	−0.777858	+	0.628441i	$0.783694\pi$
$762$	1.09801	+	8.36198i	0.0397766	+	0.302923i
$763$			5.50691i			0.199363i
$764$		−	2.80093i		−	0.101334i
$765$	9.42999	−	2.51994i	0.340942	−	0.0911086i
$766$	−28.8124			−1.04103
$767$			5.12743i			0.185141i
$768$	1.71731	−	0.225499i	0.0619681	−	0.00813698i
$769$	−20.4698			−0.738161			−0.369080	−	0.929397i	$-0.620327\pi$
$769$	−20.4698			−0.738161			−0.369080	+	0.929397i	$0.620327\pi$
$770$	1.26398			0.0455506
$771$	−9.68222	+	1.27136i	−0.348697	+	0.0457871i
$772$		−	15.9552i		−	0.574240i
$773$	27.5738			0.991759			0.495880	−	0.868391i	$-0.334846\pi$
$773$	27.5738			0.991759			0.495880	+	0.868391i	$0.334846\pi$
$774$	−34.6847	+	9.26865i	−1.24671	+	0.333155i
$775$		−	7.16461i		−	0.257360i
$776$			3.26398i			0.117170i
$777$	−0.798820	−	6.08350i	−0.0286575	−	0.218244i
$778$		−	13.5545i		−	0.485953i
$779$	1.95410	−	2.90199i	0.0700127	−	0.103975i
$780$	−4.20912	+	0.552696i	−0.150711	+	0.0197897i
$781$		−	12.3319i		−	0.441272i
$782$	2.64514			0.0945898
$783$	16.4952	−	6.81298i	0.589490	−	0.243476i
$784$	−6.60059			−0.235735
$785$		−	14.0338i		−	0.500890i
$786$	4.53262	+	34.5187i	0.161673	+	1.23124i
$787$			54.0584i			1.92698i	0.267753	+	0.963488i	$0.413719\pi$
$787$			54.0584i			1.92698i	−0.267753	+	0.963488i	$0.586281\pi$
$788$		−	19.0352i		−	0.678101i
$789$	−5.84141	−	44.4859i	−0.207960	−	1.58374i
$790$	−4.42859			−0.157562
$791$	0.446173			0.0158641
$792$	−1.54900	−	5.79660i	−0.0550414	−	0.205973i
$793$			6.62569i			0.235285i
$794$	1.51795			0.0538700
$795$	−1.47310	−	11.2185i	−0.0522454	−	0.397880i
$796$	−15.3691			−0.544743
$797$	−41.6148			−1.47407			−0.737036	−	0.675853i	$-0.763775\pi$
$797$	−41.6148			−1.47407			−0.737036	+	0.675853i	$0.763775\pi$
$798$	2.12707	−	4.27106i	0.0752975	−	0.151194i
$799$	25.9224			0.917070
$800$	−1.00000			−0.0353553
$801$	−17.1968	+	4.59542i	−0.607618	+	0.162371i
$802$	−9.81713			−0.346655
$803$			9.78921i			0.345454i
$804$	3.37035	+	25.6672i	0.118863	+	0.905214i
$805$	0.513795			0.0181089
$806$	17.5604			0.618540
$807$	43.5023	−	5.71226i	1.53135	−	0.201081i
$808$			7.45999i			0.262442i
$809$		−	50.5187i		−	1.77614i	−0.459706	−	0.888071i	$-0.652045\pi$
$809$		−	50.5187i		−	1.77614i	0.459706	−	0.888071i	$-0.347955\pi$
$810$	−4.48948	−	7.80030i	−0.157744	−	0.274074i
$811$			16.1447i			0.566916i	0.958985	+	0.283458i	$0.0914816\pi$
$811$			16.1447i			0.566916i	−0.958985	+	0.283458i	$0.908518\pi$
$812$	−2.17064			−0.0761745
$813$	30.1901	−	3.96424i	1.05881	−	0.139032i
$814$	11.2105			0.392928
$815$			19.3765i			0.678729i
$816$	0.733688	+	5.58748i	0.0256842	+	0.195601i
$817$	29.1357	−	43.2689i	1.01933	−	1.51379i
$818$			18.1453i			0.634434i
$819$	1.19970	+	4.48948i	0.0419211	+	0.156875i
$820$			0.802629i			0.0280290i
$821$			11.9793i			0.418080i	0.977907	+	0.209040i	$0.0670339\pi$
$821$			11.9793i			0.418080i	−0.977907	+	0.209040i	$0.932966\pi$
$822$	−1.86912	−	14.2345i	−0.0651931	−	0.496485i
$823$	8.11609			0.282909			0.141455	−	0.989945i	$-0.454822\pi$
$823$	8.11609			0.282909			0.141455	+	0.989945i	$0.454822\pi$
$824$		−	17.9345i		−	0.624777i
$825$	0.450997	+	3.43462i	0.0157017	+	0.119578i
$826$	1.32211			0.0460020
$827$	5.83870			0.203031			0.101516	−	0.994834i	$-0.467631\pi$
$827$	5.83870			0.203031			0.101516	+	0.994834i	$0.467631\pi$
$828$	−0.629655	−	2.35626i	−0.0218820	−	0.0818858i
$829$			15.7254i			0.546166i	0.961991	+	0.273083i	$0.0880433\pi$
$829$			15.7254i			0.546166i	−0.961991	+	0.273083i	$0.911957\pi$
$830$	−5.86788			−0.203677
$831$	37.1403	−	4.87687i	1.28838	−	0.169177i
$832$		−	2.45100i		−	0.0849730i
$833$		−	21.4759i		−	0.744094i
$834$	−0.336612	+	0.0442003i	−0.0116559	+	0.00153053i
$835$			9.23122i			0.319460i
$836$	7.23122	+	4.86924i	0.250097	+	0.168406i
$837$	14.2119	+	34.4090i	0.491234	+	1.18935i
$838$			15.0145i			0.518667i
$839$	34.7796			1.20073			0.600363	−	0.799728i	$-0.295023\pi$
$839$	34.7796			1.20073			0.600363	+	0.799728i	$0.295023\pi$
$840$	0.142513	+	1.08532i	0.00491715	+	0.0374471i
$841$	−17.2034			−0.593221
$842$		−	24.4341i		−	0.842055i
$843$	37.1966	−	4.88426i	1.28112	−	0.168223i
$844$			2.13976i			0.0736534i
$845$		−	6.99261i		−	0.240553i
$846$	−6.17064	−	23.0915i	−0.212151	−	0.793901i
$847$	−4.42392			−0.152008
$848$	6.53262			0.224331
$849$	−26.1258	+	3.43056i	−0.896636	+	0.117737i
$850$		−	3.25363i		−	0.111598i
$851$	4.55697			0.156211
$852$	10.5889	−	1.39042i	0.362769	−	0.0476349i
$853$	1.55935			0.0533913			0.0266956	−	0.999644i	$-0.491502\pi$
$853$	1.55935			0.0533913			0.0266956	+	0.999644i	$0.491502\pi$
$854$	1.70843			0.0584614
$855$	12.3647	+	4.25596i	0.422865	+	0.145551i
$856$	−5.63063			−0.192451
$857$	31.4649			1.07482			0.537410	−	0.843321i	$-0.319403\pi$
$857$	31.4649			1.07482			0.537410	+	0.843321i	$0.319403\pi$
$858$	−8.41824	+	1.10539i	−0.287394	+	0.0377375i
$859$	36.4445			1.24347			0.621734	−	0.783228i	$-0.286428\pi$
$859$	36.4445			1.24347			0.621734	+	0.783228i	$0.286428\pi$
$860$			11.9672i			0.408080i
$861$	0.871110	−	0.114385i	0.0296873	−	0.00389822i
$862$	−41.0522			−1.39824
$863$	−52.3041			−1.78045			−0.890226	−	0.455519i	$-0.849454\pi$
$863$	−52.3041			−1.78045			−0.890226	+	0.455519i	$0.849454\pi$
$864$	4.80263	−	1.98362i	0.163389	−	0.0674842i
$865$		−	1.98794i		−	0.0675921i
$866$			18.0121i			0.612075i
$867$	11.0147	−	1.44633i	0.374078	−	0.0491199i
$868$		−	4.52796i		−	0.153689i
$869$	−8.85718			−0.300459
$870$	−0.774501	−	5.89830i	−0.0262581	−	0.199971i
$871$	36.6331			1.24126
$872$		−	8.71362i		−	0.295080i
$873$	2.52796	+	9.45999i	0.0855583	+	0.320172i
$874$	2.93942	+	1.97930i	0.0994274	+	0.0669507i
$875$		−	0.631989i		−	0.0213651i
$876$	−8.40555	+	1.10373i	−0.283997	+	0.0372915i
$877$		−	25.0259i		−	0.845066i	−0.906347	−	0.422533i	$-0.861141\pi$
$877$		−	25.0259i		−	0.845066i	0.906347	−	0.422533i	$-0.138859\pi$
$878$		−	27.8024i		−	0.938284i
$879$	−9.25596	+	1.21539i	−0.312196	+	0.0409942i
$880$	−2.00000			−0.0674200
$881$		−	12.4597i		−	0.419779i	−0.977725	−	0.209889i	$-0.932690\pi$
$881$		−	12.4597i		−	0.419779i	0.977725	−	0.209889i	$-0.0673104\pi$
$882$	−19.1305	+	5.11217i	−0.644157	+	0.172136i
$883$	3.72152			0.125239			0.0626195	−	0.998037i	$-0.480055\pi$
$883$	3.72152			0.125239			0.0626195	+	0.998037i	$0.480055\pi$
$884$	7.97463			0.268216
$885$	0.471738	+	3.59257i	0.0158573	+	0.120763i
$886$			10.0366i			0.337185i
$887$	8.17531			0.274500			0.137250	−	0.990536i	$-0.456174\pi$
$887$	8.17531			0.274500			0.137250	+	0.990536i	$0.456174\pi$
$888$	1.26398	+	9.62596i	0.0424163	+	0.323026i
$889$		−	3.07730i		−	0.103209i
$890$			5.93339i			0.198888i
$891$	−8.97895	−	15.6006i	−0.300806	−	0.522639i
$892$		−	17.9044i		−	0.599485i
$893$	28.8064	+	19.3972i	0.963971	+	0.649102i
$894$	−2.57277	−	19.5932i	−0.0860463	−	0.655295i
$895$		−	11.4938i		−	0.384197i
$896$	−0.631989			−0.0211133
$897$	−3.42193	+	0.449331i	−0.114255	+	0.0150027i
$898$	33.9055			1.13144
$899$			24.6077i			0.820713i
$900$	−2.89830	+	0.774501i	−0.0966100	+	0.0258167i
$901$			21.2547i			0.708097i
$902$			1.60526i			0.0534493i
$903$	12.9883	−	1.70548i	0.432223	−	0.0567549i
$904$	−0.705983			−0.0234806
$905$	18.1671			0.603894
$906$	2.30276	+	17.5369i	0.0765042	+	0.582626i
$907$		−	13.5724i		−	0.450665i	−0.974282	−	0.225332i	$-0.927653\pi$
$907$		−	13.5724i		−	0.450665i	0.974282	−	0.225332i	$-0.0723468\pi$
$908$	−3.97463			−0.131903
$909$	5.77777	+	21.6213i	0.191637	+	0.717133i
$910$	1.54900			0.0513489
$911$	41.6636			1.38038			0.690189	−	0.723629i	$-0.257528\pi$
$911$	41.6636			1.38038			0.690189	+	0.723629i	$0.257528\pi$
$912$	−3.36568	+	6.75812i	−0.111449	+	0.223784i
$913$	−11.7358			−0.388397
$914$	−31.7131			−1.04898
$915$	0.609582	+	4.64234i	0.0201522	+	0.153471i
$916$	13.5932			0.449132
$917$		−	12.7033i		−	0.419499i
$918$	6.45396	+	15.6260i	0.213012	+	0.515734i
$919$	27.9916			0.923357			0.461679	−	0.887047i	$-0.347247\pi$
$919$	27.9916			0.923357			0.461679	+	0.887047i	$0.347247\pi$
$920$	−0.812981			−0.0268032
$921$	−0.128546	−	0.978953i	−0.00423572	−	0.0322576i
$922$		−	23.1029i		−	0.760854i
$923$		−	15.1128i		−	0.497443i
$924$	0.285025	+	2.17064i	0.00937664	+	0.0714088i
$925$		−	5.60526i		−	0.184300i
$926$	32.6950			1.07442
$927$	−13.8903	−	51.9795i	−0.456217	−	1.70723i
$928$	3.43462			0.112747
$929$		−	15.0942i		−	0.495224i	−0.968859	−	0.247612i	$-0.920354\pi$
$929$		−	15.0942i		−	0.495224i	0.968859	−	0.247612i	$-0.0796458\pi$
$930$	12.3039	−	1.61561i	0.403459	−	0.0529779i
$931$	16.0699	−	23.8652i	0.526670	−	0.782149i
$932$		−	21.2323i		−	0.695487i
$933$	1.89091	+	14.4005i	0.0619057	+	0.471450i
$934$			29.2023i			0.955527i
$935$		−	6.50725i		−	0.212810i
$936$	−1.89830	−	7.10373i	−0.0620479	−	0.232193i
$937$	−53.5045			−1.74792			−0.873958	−	0.486002i	$-0.838455\pi$
$937$	−53.5045			−1.74792			−0.873958	+	0.486002i	$0.838455\pi$
$938$		−	9.44583i		−	0.308417i
$939$	42.3073	−	5.55534i	1.38065	−	0.181292i
$940$	−7.96724			−0.259863
$941$	−2.22682			−0.0725922			−0.0362961	−	0.999341i	$-0.511556\pi$
$941$	−2.22682			−0.0725922			−0.0362961	+	0.999341i	$0.511556\pi$
$942$	24.1005	−	3.16461i	0.785235	−	0.103109i
$943$			0.652522i			0.0212490i
$944$	−2.09198			−0.0680881
$945$	1.25363	+	3.03521i	0.0407805	+	0.0987353i
$946$			23.9345i			0.778177i
$947$		−	41.4103i		−	1.34566i	−0.739799	−	0.672828i	$-0.765080\pi$
$947$		−	41.4103i		−	1.34566i	0.739799	−	0.672828i	$-0.234920\pi$
$948$	−0.998641	−	7.60526i	−0.0324343	−	0.247007i
$949$			11.9967i			0.389428i
$950$	2.43462	−	3.61561i	0.0789894	−	0.117306i
$951$	29.2065	−	3.83508i	0.947085	−	0.124361i
$952$		−	2.05626i		−	0.0666436i
$953$	−23.7444			−0.769157			−0.384578	−	0.923092i	$-0.625653\pi$
$953$	−23.7444			−0.769157			−0.384578	+	0.923092i	$0.625653\pi$
$954$	18.9335	−	5.05953i	0.612995	−	0.163808i
$955$	−2.80093			−0.0906358
$956$			22.2899i			0.720908i
$957$	−1.54900	−	11.7966i	−0.0500722	−	0.381330i
$958$			17.7712i			0.574162i
$959$			5.23845i			0.169158i
$960$	−0.225499	−	1.71731i	−0.00727793	−	0.0554259i
$961$	−20.3317			−0.655861
$962$	13.7385			0.442946
$963$	−16.3193	+	4.36093i	−0.525881	+	0.140529i
$964$		−	4.19873i		−	0.135232i
$965$	−15.9552			−0.513616
$966$	0.115860	+	0.882344i	0.00372773	+	0.0283890i
$967$	39.8400			1.28117			0.640584	−	0.767888i	$-0.278692\pi$
$967$	39.8400			1.28117			0.640584	+	0.767888i	$0.278692\pi$
$968$	7.00000			0.224989
$969$	−21.9884	−	10.9507i	−0.706369	−	0.351786i
$970$	3.26398			0.104800
$971$	4.70489			0.150987			0.0754936	−	0.997146i	$-0.475947\pi$
$971$	4.70489			0.150987			0.0754936	+	0.997146i	$0.475947\pi$
$972$	12.3831	−	9.46877i	0.397190	−	0.303711i
$973$	0.123877			0.00397132
$974$		−	10.3620i		−	0.332019i
$975$	0.552696	+	4.20912i	0.0177004	+	0.134800i
$976$	−2.70326			−0.0865294
$977$	38.3620			1.22731			0.613654	−	0.789575i	$-0.289699\pi$
$977$	38.3620			1.22731			0.613654	+	0.789575i	$0.289699\pi$
$978$	−33.2754	+	4.36937i	−1.06403	+	0.139717i
$979$			11.8668i			0.379264i
$980$			6.60059i			0.210848i
$981$	−6.74871	−	25.2547i	−0.215470	−	0.806320i
$982$		−	16.8993i		−	0.539278i
$983$	−26.8720			−0.857082			−0.428541	−	0.903522i	$-0.640972\pi$
$983$	−26.8720			−0.857082			−0.428541	+	0.903522i	$0.640972\pi$
$984$	−1.37836	+	0.180992i	−0.0439406	+	0.00576981i
$985$	−19.0352			−0.606512
$986$			11.1750i			0.355883i
$987$	1.13543	+	8.64701i	0.0361412	+	0.275237i
$988$	8.86185	+	5.96724i	0.281933	+	0.189843i
$989$			9.72914i			0.309369i
$990$	−5.79660	+	1.54900i	−0.184228	+	0.0492305i
$991$		−	19.9782i		−	0.634629i	−0.948320	−	0.317314i	$-0.897219\pi$
$991$		−	19.9782i		−	0.634629i	0.948320	−	0.317314i	$-0.102781\pi$
$992$			7.16461i			0.227477i
$993$	2.19810	+	16.7399i	0.0697546	+	0.531224i
$994$	−3.89683			−0.123600
$995$			15.3691i			0.487233i
$996$	−1.32320	−	10.0770i	−0.0419271	−	0.319301i
$997$	36.8316			1.16647			0.583235	−	0.812304i	$-0.301787\pi$
$997$	36.8316			1.16647			0.583235	+	0.812304i	$0.301787\pi$
$998$	0.364702			0.0115444
$999$	11.1187	+	26.9200i	0.351780	+	0.851710i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.f.d.341.7	yes	8
3.2	odd	2		570.2.f.c.341.1	✓	8
19.18	odd	2		570.2.f.c.341.2	yes	8
57.56	even	2	inner	570.2.f.d.341.8	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.f.c.341.1	✓	8	3.2	odd	2
570.2.f.c.341.2	yes	8	19.18	odd	2
570.2.f.d.341.7	yes	8	1.1	even	1	trivial
570.2.f.d.341.8	yes	8	57.56	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.71731 - 0.225499i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(1.71731 - 0.225499i) q^{6} -0.631989 q^{7} +1.00000 q^{8} +(2.89830 - 0.774501i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.71731 - 0.225499i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(1.71731 - 0.225499i) q^{6} -0.631989 q^{7} +1.00000 q^{8} +(2.89830 - 0.774501i) q^{9} -1.00000i q^{10} -2.00000i q^{11} +(1.71731 - 0.225499i) q^{12} -2.45100i q^{13} -0.631989 q^{14} +(-0.225499 - 1.71731i) q^{15} +1.00000 q^{16} +3.25363i q^{17} +(2.89830 - 0.774501i) q^{18} +(-2.43462 + 3.61561i) q^{19} -1.00000i q^{20} +(-1.08532 + 0.142513i) q^{21} -2.00000i q^{22} -0.812981i q^{23} +(1.71731 - 0.225499i) q^{24} -1.00000 q^{25} -2.45100i q^{26} +(4.80263 - 1.98362i) q^{27} -0.631989 q^{28} +3.43462 q^{29} +(-0.225499 - 1.71731i) q^{30} +7.16461i q^{31} +1.00000 q^{32} +(-0.450997 - 3.43462i) q^{33} +3.25363i q^{34} +0.631989i q^{35} +(2.89830 - 0.774501i) q^{36} +5.60526i q^{37} +(-2.43462 + 3.61561i) q^{38} +(-0.552696 - 4.20912i) q^{39} -1.00000i q^{40} -0.802629 q^{41} +(-1.08532 + 0.142513i) q^{42} -11.9672 q^{43} -2.00000i q^{44} +(-0.774501 - 2.89830i) q^{45} -0.812981i q^{46} -7.96724i q^{47} +(1.71731 - 0.225499i) q^{48} -6.60059 q^{49} -1.00000 q^{50} +(0.733688 + 5.58748i) q^{51} -2.45100i q^{52} +6.53262 q^{53} +(4.80263 - 1.98362i) q^{54} -2.00000 q^{55} -0.631989 q^{56} +(-3.36568 + 6.75812i) q^{57} +3.43462 q^{58} -2.09198 q^{59} +(-0.225499 - 1.71731i) q^{60} -2.70326 q^{61} +7.16461i q^{62} +(-1.83169 + 0.489476i) q^{63} +1.00000 q^{64} -2.45100 q^{65} +(-0.450997 - 3.43462i) q^{66} +14.9462i q^{67} +3.25363i q^{68} +(-0.183326 - 1.39614i) q^{69} +0.631989i q^{70} +6.16597 q^{71} +(2.89830 - 0.774501i) q^{72} -4.89461 q^{73} +5.60526i q^{74} +(-1.71731 + 0.225499i) q^{75} +(-2.43462 + 3.61561i) q^{76} +1.26398i q^{77} +(-0.552696 - 4.20912i) q^{78} -4.42859i q^{79} -1.00000i q^{80} +(7.80030 - 4.48948i) q^{81} -0.802629 q^{82} -5.86788i q^{83} +(-1.08532 + 0.142513i) q^{84} +3.25363 q^{85} -11.9672 q^{86} +(5.89830 - 0.774501i) q^{87} -2.00000i q^{88} -5.93339 q^{89} +(-0.774501 - 2.89830i) q^{90} +1.54900i q^{91} -0.812981i q^{92} +(1.61561 + 12.3039i) q^{93} -7.96724i q^{94} +(3.61561 + 2.43462i) q^{95} +(1.71731 - 0.225499i) q^{96} +3.26398i q^{97} -6.60059 q^{98} +(-1.54900 - 5.79660i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{6} + 4 q^{7} + 8 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^6 + 4 * q^7 + 8 * q^8 + 2 * q^9	\( 8 q + 8 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{6} + 4 q^{7} + 8 q^{8} + 2 q^{9} - 2 q^{12} + 4 q^{14} + 8 q^{16} + 2 q^{18} + 12 q^{19} - 2 q^{21} - 2 q^{24} - 8 q^{25} + 16 q^{27} + 4 q^{28} - 4 q^{29} + 8 q^{32} + 2 q^{36} + 12 q^{38} - 22 q^{39} + 16 q^{41} - 2 q^{42} - 40 q^{43} - 8 q^{45} - 2 q^{48} + 4 q^{49} - 8 q^{50} + 18 q^{51} + 28 q^{53} + 16 q^{54} - 16 q^{55} + 4 q^{56} - 30 q^{57} - 4 q^{58} - 4 q^{59} + 16 q^{61} - 34 q^{63} + 8 q^{64} - 16 q^{65} - 2 q^{69} + 24 q^{71} + 2 q^{72} - 4 q^{73} + 2 q^{75} + 12 q^{76} - 22 q^{78} + 34 q^{81} + 16 q^{82} - 2 q^{84} - 40 q^{86} + 26 q^{87} - 88 q^{89} - 8 q^{90} - 24 q^{93} - 8 q^{95} - 2 q^{96} + 4 q^{98} - 16 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^6 + 4 * q^7 + 8 * q^8 + 2 * q^9 - 2 * q^12 + 4 * q^14 + 8 * q^16 + 2 * q^18 + 12 * q^19 - 2 * q^21 - 2 * q^24 - 8 * q^25 + 16 * q^27 + 4 * q^28 - 4 * q^29 + 8 * q^32 + 2 * q^36 + 12 * q^38 - 22 * q^39 + 16 * q^41 - 2 * q^42 - 40 * q^43 - 8 * q^45 - 2 * q^48 + 4 * q^49 - 8 * q^50 + 18 * q^51 + 28 * q^53 + 16 * q^54 - 16 * q^55 + 4 * q^56 - 30 * q^57 - 4 * q^58 - 4 * q^59 + 16 * q^61 - 34 * q^63 + 8 * q^64 - 16 * q^65 - 2 * q^69 + 24 * q^71 + 2 * q^72 - 4 * q^73 + 2 * q^75 + 12 * q^76 - 22 * q^78 + 34 * q^81 + 16 * q^82 - 2 * q^84 - 40 * q^86 + 26 * q^87 - 88 * q^89 - 8 * q^90 - 24 * q^93 - 8 * q^95 - 2 * q^96 + 4 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more