LMFDB - Embedded newform 430.2.k.c.21.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(11,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("430.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.k (of order $7$, degree $6$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} + 20 x^{16} - 61 x^{15} + 142 x^{14} - 195 x^{13} + 244 x^{12} + 320 x^{11} + \cdots + 49 $ x^18 - 5x^17 + 20x^16 - 61x^15 + 142x^14 - 195x^13 + 244x^12 + 320x^11 + 64x^10 - 562x^9 + 4114x^8 - 1933x^7 + 2941x^6 - 2555x^5 + 2807x^4 - 2366x^3 + 1225x^2 - 343*x + 49
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			21.1
Root			$-1.43931 + 0.693135i$ of defining polynomial
Character	$\chi$	$=$	430.21
Dual form			430.2.k.c.41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.900969 + 0.433884i) q^{2} +(-1.43931 + 0.693135i) q^{3} +(0.623490 + 0.781831i) q^{4} +(-0.222521 - 0.974928i) q^{5} -1.59751 q^{6} -1.15014 q^{7} +(0.222521 + 0.974928i) q^{8} +(-0.279294 + 0.350223i) q^{9} +O(q^{10})$	\(q+(0.900969 + 0.433884i) q^{2} +(-1.43931 + 0.693135i) q^{3} +(0.623490 + 0.781831i) q^{4} +(-0.222521 - 0.974928i) q^{5} -1.59751 q^{6} -1.15014 q^{7} +(0.222521 + 0.974928i) q^{8} +(-0.279294 + 0.350223i) q^{9} +(0.222521 - 0.974928i) q^{10} +(-1.95796 + 2.45521i) q^{11} +(-1.43931 - 0.693135i) q^{12} +(1.16406 + 5.10009i) q^{13} +(-1.03624 - 0.499026i) q^{14} +(0.996033 + 1.24899i) q^{15} +(-0.222521 + 0.974928i) q^{16} +(-1.36118 + 5.96372i) q^{17} +(-0.403591 + 0.194359i) q^{18} +(-2.57957 - 3.23468i) q^{19} +(0.623490 - 0.781831i) q^{20} +(1.65540 - 0.797200i) q^{21} +(-2.82934 + 1.36254i) q^{22} +(0.598721 - 0.750772i) q^{23} +(-0.996033 - 1.24899i) q^{24} +(-0.900969 + 0.433884i) q^{25} +(-1.16406 + 5.10009i) q^{26} +(1.22568 - 5.37005i) q^{27} +(-0.717099 - 0.899214i) q^{28} +(-3.60662 - 1.73686i) q^{29} +(0.355480 + 1.55746i) q^{30} +(-2.71659 - 1.30824i) q^{31} +(-0.623490 + 0.781831i) q^{32} +(1.11633 - 4.89094i) q^{33} +(-3.81394 + 4.78253i) q^{34} +(0.255930 + 1.12130i) q^{35} -0.447952 q^{36} +1.44368 q^{37} +(-0.920639 - 4.03358i) q^{38} +(-5.21050 - 6.53376i) q^{39} +(0.900969 - 0.433884i) q^{40} +(10.3953 + 5.00613i) q^{41} +1.83736 q^{42} +(6.55623 + 0.126009i) q^{43} -3.14033 q^{44} +(0.403591 + 0.194359i) q^{45} +(0.865177 - 0.416647i) q^{46} +(2.08921 + 2.61978i) q^{47} +(-0.355480 - 1.55746i) q^{48} -5.67718 q^{49} -1.00000 q^{50} +(-2.17450 - 9.52712i) q^{51} +(-3.26163 + 4.08995i) q^{52} +(-2.89908 + 12.7017i) q^{53} +(3.43427 - 4.30644i) q^{54} +(2.82934 + 1.36254i) q^{55} +(-0.255930 - 1.12130i) q^{56} +(5.95488 + 2.86772i) q^{57} +(-2.49586 - 3.12971i) q^{58} +(3.21743 - 14.0965i) q^{59} +(-0.355480 + 1.55746i) q^{60} +(6.85497 - 3.30118i) q^{61} +(-1.87994 - 2.35737i) q^{62} +(0.321226 - 0.402805i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(4.71319 - 2.26975i) q^{65} +(3.12787 - 3.92223i) q^{66} +(6.04127 + 7.57551i) q^{67} +(-5.51131 + 2.65411i) q^{68} +(-0.341358 + 1.49559i) q^{69} +(-0.255930 + 1.12130i) q^{70} +(3.84671 + 4.82362i) q^{71} +(-0.403591 - 0.194359i) q^{72} +(-1.03329 - 4.52714i) q^{73} +(1.30071 + 0.626389i) q^{74} +(0.996033 - 1.24899i) q^{75} +(0.920639 - 4.03358i) q^{76} +(2.25193 - 2.82383i) q^{77} +(-1.85960 - 8.14746i) q^{78} -9.69659 q^{79} +1.00000 q^{80} +(1.65900 + 7.26856i) q^{81} +(7.19379 + 9.02073i) q^{82} +(1.19476 - 0.575364i) q^{83} +(1.65540 + 0.797200i) q^{84} +6.11709 q^{85} +(5.85228 + 2.95817i) q^{86} +6.39492 q^{87} +(-2.82934 - 1.36254i) q^{88} +(3.63077 - 1.74849i) q^{89} +(0.279294 + 0.350223i) q^{90} +(-1.33883 - 5.86580i) q^{91} +0.960274 q^{92} +4.81680 q^{93} +(0.745630 + 3.26682i) q^{94} +(-2.57957 + 3.23468i) q^{95} +(0.355480 - 1.55746i) q^{96} +(7.10389 - 8.90799i) q^{97} +(-5.11497 - 2.46324i) q^{98} +(-0.313024 - 1.37145i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{2} + 5 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} + 8 q^{7} + 3 q^{8} - 6 q^{9}+O(q^{10}) $ 18 * q + 3 * q^2 + 5 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 + 8 * q^7 + 3 * q^8 - 6 * q^9	\( 18 q + 3 q^{2} + 5 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} + 8 q^{7} + 3 q^{8} - 6 q^{9} + 3 q^{10} + 5 q^{11} + 5 q^{12} + 22 q^{13} - 8 q^{14} - 2 q^{15} - 3 q^{16} + q^{17} + 13 q^{18} - 7 q^{19} - 3 q^{20} + 10 q^{21} - 5 q^{22} + 8 q^{23} + 2 q^{24} - 3 q^{25} - 22 q^{26} + 20 q^{27} + q^{28} - 6 q^{29} + 2 q^{30} - 5 q^{31} + 3 q^{32} + 39 q^{33} - q^{34} - 13 q^{35} + 8 q^{36} - 18 q^{37} - 7 q^{39} + 3 q^{40} + 16 q^{41} + 4 q^{42} - 13 q^{43} - 2 q^{44} - 13 q^{45} - 8 q^{46} - 36 q^{47} - 2 q^{48} - 14 q^{49} - 18 q^{50} - 30 q^{51} - 20 q^{52} - 18 q^{53} + 29 q^{54} + 5 q^{55} + 13 q^{56} + 29 q^{57} - 8 q^{58} - 4 q^{59} - 2 q^{60} + 42 q^{61} - 2 q^{62} - 29 q^{63} - 3 q^{64} + 8 q^{65} + 24 q^{66} - 19 q^{67} + q^{68} - 51 q^{69} + 13 q^{70} - 27 q^{71} + 13 q^{72} + 28 q^{73} + 4 q^{74} - 2 q^{75} + 42 q^{77} - 35 q^{78} - 26 q^{79} + 18 q^{80} - 4 q^{81} + 19 q^{82} + 62 q^{83} + 10 q^{84} - 6 q^{85} - 15 q^{86} - 66 q^{87} - 5 q^{88} - 12 q^{89} + 6 q^{90} - 22 q^{91} - 20 q^{92} - 6 q^{93} - 6 q^{94} - 7 q^{95} + 2 q^{96} + 71 q^{97} - 28 q^{98} + 59 q^{99}+O(q^{100}) \) 18 * q + 3 * q^2 + 5 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 + 8 * q^7 + 3 * q^8 - 6 * q^9 + 3 * q^10 + 5 * q^11 + 5 * q^12 + 22 * q^13 - 8 * q^14 - 2 * q^15 - 3 * q^16 + q^17 + 13 * q^18 - 7 * q^19 - 3 * q^20 + 10 * q^21 - 5 * q^22 + 8 * q^23 + 2 * q^24 - 3 * q^25 - 22 * q^26 + 20 * q^27 + q^28 - 6 * q^29 + 2 * q^30 - 5 * q^31 + 3 * q^32 + 39 * q^33 - q^34 - 13 * q^35 + 8 * q^36 - 18 * q^37 - 7 * q^39 + 3 * q^40 + 16 * q^41 + 4 * q^42 - 13 * q^43 - 2 * q^44 - 13 * q^45 - 8 * q^46 - 36 * q^47 - 2 * q^48 - 14 * q^49 - 18 * q^50 - 30 * q^51 - 20 * q^52 - 18 * q^53 + 29 * q^54 + 5 * q^55 + 13 * q^56 + 29 * q^57 - 8 * q^58 - 4 * q^59 - 2 * q^60 + 42 * q^61 - 2 * q^62 - 29 * q^63 - 3 * q^64 + 8 * q^65 + 24 * q^66 - 19 * q^67 + q^68 - 51 * q^69 + 13 * q^70 - 27 * q^71 + 13 * q^72 + 28 * q^73 + 4 * q^74 - 2 * q^75 + 42 * q^77 - 35 * q^78 - 26 * q^79 + 18 * q^80 - 4 * q^81 + 19 * q^82 + 62 * q^83 + 10 * q^84 - 6 * q^85 - 15 * q^86 - 66 * q^87 - 5 * q^88 - 12 * q^89 + 6 * q^90 - 22 * q^91 - 20 * q^92 - 6 * q^93 - 6 * q^94 - 7 * q^95 + 2 * q^96 + 71 * q^97 - 28 * q^98 + 59 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{6}{7}\right)$

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 $

$2$	0.900969	+	0.433884i	0.637081	+	0.306802i
$2$	0.900969	+	0.433884i	0.637081	+	0.306802i
$3$	−1.43931	+	0.693135i	−0.830986	+	0.400182i	−0.800485	−	0.599353i	$-0.795425\pi$
$3$	−1.43931	+	0.693135i	−0.830986	+	0.400182i	−0.0305010	+	0.999535i	$0.509710\pi$
$4$	0.623490	+	0.781831i	0.311745	+	0.390916i
$5$	−0.222521	−	0.974928i	−0.0995144	−	0.436001i
$5$	−0.222521	−	0.974928i	−0.0995144	−	0.436001i
$6$	−1.59751			−0.652182
$7$	−1.15014			−0.434711			−0.217356	−	0.976093i	$-0.569743\pi$
$7$	−1.15014			−0.434711			−0.217356	+	0.976093i	$0.569743\pi$
$8$	0.222521	+	0.974928i	0.0786730	+	0.344689i
$9$	−0.279294	+	0.350223i	−0.0930979	+	0.116741i
$10$	0.222521	−	0.974928i	0.0703673	−	0.308299i
$11$	−1.95796	+	2.45521i	−0.590349	+	0.740274i	−0.983839	−	0.179055i	$-0.942696\pi$
$11$	−1.95796	+	2.45521i	−0.590349	+	0.740274i	0.393490	+	0.919329i	$0.371267\pi$
$12$	−1.43931	−	0.693135i	−0.415493	−	0.200091i
$13$	1.16406	+	5.10009i	0.322853	+	1.41451i	0.832451	+	0.554098i	$0.186937\pi$
$13$	1.16406	+	5.10009i	0.322853	+	1.41451i	−0.509599	+	0.860412i	$0.670206\pi$
$14$	−1.03624	−	0.499026i	−0.276946	−	0.133370i
$15$	0.996033	+	1.24899i	0.257175	+	0.322487i
$16$	−0.222521	+	0.974928i	−0.0556302	+	0.243732i
$17$	−1.36118	+	5.96372i	−0.330135	+	1.44641i	0.488734	+	0.872433i	$0.337459\pi$
$17$	−1.36118	+	5.96372i	−0.330135	+	1.44641i	−0.818868	+	0.573982i	$0.805398\pi$
$18$	−0.403591	+	0.194359i	−0.0951273	+	0.0458109i
$19$	−2.57957	−	3.23468i	−0.591795	−	0.742087i	0.392279	−	0.919846i	$-0.371687\pi$
$19$	−2.57957	−	3.23468i	−0.591795	−	0.742087i	−0.984074	+	0.177759i	$0.943115\pi$
$20$	0.623490	−	0.781831i	0.139417	−	0.174823i
$21$	1.65540	−	0.797200i	0.361239	−	0.173963i
$22$	−2.82934	+	1.36254i	−0.603218	+	0.290494i
$23$	0.598721	−	0.750772i	0.124842	−	0.156547i	−0.715482	−	0.698631i	$-0.753793\pi$
$23$	0.598721	−	0.750772i	0.124842	−	0.156547i	0.840324	+	0.542084i	$0.182365\pi$
$24$	−0.996033	−	1.24899i	−0.203314	−	0.254948i
$25$	−0.900969	+	0.433884i	−0.180194	+	0.0867767i
$26$	−1.16406	+	5.10009i	−0.228291	+	1.00021i
$27$	1.22568	−	5.37005i	0.235882	−	1.03347i
$28$	−0.717099	−	0.899214i	−0.135519	−	0.169935i
$29$	−3.60662	−	1.73686i	−0.669733	−	0.322526i	0.0679354	−	0.997690i	$-0.478359\pi$
$29$	−3.60662	−	1.73686i	−0.669733	−	0.322526i	−0.737668	+	0.675163i	$0.764073\pi$
$30$	0.355480	+	1.55746i	0.0649015	+	0.284352i
$31$	−2.71659	−	1.30824i	−0.487914	−	0.234967i	0.173718	−	0.984795i	$-0.444422\pi$
$31$	−2.71659	−	1.30824i	−0.487914	−	0.234967i	−0.661632	+	0.749828i	$0.730136\pi$
$32$	−0.623490	+	0.781831i	−0.110218	+	0.138210i
$33$	1.11633	−	4.89094i	0.194327	−	0.851404i
$34$	−3.81394	+	4.78253i	−0.654086	+	0.820198i
$35$	0.255930	+	1.12130i	0.0432600	+	0.189534i
$36$	−0.447952			−0.0746587
$37$	1.44368			0.237339			0.118670	−	0.992934i	$-0.462137\pi$
$37$	1.44368			0.237339			0.118670	+	0.992934i	$0.462137\pi$
$38$	−0.920639	−	4.03358i	−0.149347	−	0.654334i
$39$	−5.21050	−	6.53376i	−0.834347	−	1.04624i
$40$	0.900969	−	0.433884i	0.142456	−	0.0686030i
$41$	10.3953	+	5.00613i	1.62348	+	0.781826i	1.00000		1.57983e-5i	$-5.02876e-6\pi$
$41$	10.3953	+	5.00613i	1.62348	+	0.781826i	0.623477	+	0.781841i	$0.285719\pi$
$42$	1.83736			0.283511
$43$	6.55623	+	0.126009i	0.999815	+	0.0192162i
$43$	6.55623	+	0.126009i	0.999815	+	0.0192162i
$44$	−3.14033			−0.473423
$45$	0.403591	+	0.194359i	0.0601638	+	0.0289734i
$46$	0.865177	−	0.416647i	0.127563	−	0.0614313i
$47$	2.08921	+	2.61978i	0.304742	+	0.382135i	0.910496	−	0.413517i	$-0.135700\pi$
$47$	2.08921	+	2.61978i	0.304742	+	0.382135i	−0.605754	+	0.795652i	$0.707128\pi$
$48$	−0.355480	−	1.55746i	−0.0513091	−	0.224800i
$49$	−5.67718			−0.811026
$50$	−1.00000			−0.141421
$51$	−2.17450	−	9.52712i	−0.304491	−	1.33406i
$52$	−3.26163	+	4.08995i	−0.452307	+	0.567175i
$53$	−2.89908	+	12.7017i	−0.398219	+	1.74471i	0.236182	+	0.971709i	$0.424104\pi$
$53$	−2.89908	+	12.7017i	−0.398219	+	1.74471i	−0.634401	+	0.773004i	$0.718753\pi$
$54$	3.43427	−	4.30644i	0.467346	−	0.586033i
$55$	2.82934	+	1.36254i	0.381508	+	0.183725i
$56$	−0.255930	−	1.12130i	−0.0342000	−	0.149840i
$57$	5.95488	+	2.86772i	0.788743	+	0.379839i
$58$	−2.49586	−	3.12971i	−0.327722	−	0.410951i
$59$	3.21743	−	14.0965i	0.418874	−	1.83521i	−0.119937	−	0.992781i	$-0.538269\pi$
$59$	3.21743	−	14.0965i	0.418874	−	1.83521i	0.538811	−	0.842426i	$-0.318874\pi$
$60$	−0.355480	+	1.55746i	−0.0458923	+	0.201067i
$61$	6.85497	−	3.30118i	0.877689	−	0.422673i	0.0599092	−	0.998204i	$-0.480919\pi$
$61$	6.85497	−	3.30118i	0.877689	−	0.422673i	0.817780	+	0.575531i	$0.195205\pi$
$62$	−1.87994	−	2.35737i	−0.238752	−	0.299386i
$63$	0.321226	−	0.402805i	0.0404707	−	0.0507486i
$64$	−0.900969	+	0.433884i	−0.112621	+	0.0542355i
$65$	4.71319	−	2.26975i	0.584599	−	0.281528i
$66$	3.12787	−	3.92223i	0.385015	−	0.482793i
$67$	6.04127	+	7.57551i	0.738059	+	0.925496i	0.999208	−	0.0398023i	$-0.0126728\pi$
$67$	6.04127	+	7.57551i	0.738059	+	0.925496i	−0.261149	+	0.965299i	$0.584101\pi$
$68$	−5.51131	+	2.65411i	−0.668344	+	0.321858i
$69$	−0.341358	+	1.49559i	−0.0410947	+	0.180048i
$70$	−0.255930	+	1.12130i	−0.0305894	+	0.134021i
$71$	3.84671	+	4.82362i	0.456520	+	0.572458i	0.955813	−	0.293975i	$-0.0949783\pi$
$71$	3.84671	+	4.82362i	0.456520	+	0.572458i	−0.499293	+	0.866433i	$0.666407\pi$
$72$	−0.403591	−	0.194359i	−0.0475636	−	0.0229054i
$73$	−1.03329	−	4.52714i	−0.120938	−	0.529862i	−0.998710	−	0.0507837i	$-0.983828\pi$
$73$	−1.03329	−	4.52714i	−0.120938	−	0.529862i	0.877772	−	0.479078i	$-0.159029\pi$
$74$	1.30071	+	0.626389i	0.151204	+	0.0728162i
$75$	0.996033	−	1.24899i	0.115012	−	0.144220i
$76$	0.920639	−	4.03358i	0.105605	−	0.462684i
$77$	2.25193	−	2.82383i	0.256631	−	0.321805i
$78$	−1.85960	−	8.14746i	−0.210559	−	0.922518i
$79$	−9.69659			−1.09095			−0.545476	−	0.838127i	$-0.683651\pi$
$79$	−9.69659			−1.09095			−0.545476	+	0.838127i	$0.683651\pi$
$80$	1.00000			0.111803
$81$	1.65900	+	7.26856i	0.184333	+	0.807618i
$82$	7.19379	+	9.02073i	0.794421	+	0.996173i
$83$	1.19476	−	0.575364i	0.131142	−	0.0631544i	−0.367162	−	0.930157i	$-0.619671\pi$
$83$	1.19476	−	0.575364i	0.131142	−	0.0631544i	0.498304	+	0.867002i	$0.333956\pi$
$84$	1.65540	+	0.797200i	0.180619	+	0.0869817i
$85$	6.11709			0.663491
$86$	5.85228	+	2.95817i	0.631068	+	0.318988i
$87$	6.39492			0.685608
$88$	−2.82934	−	1.36254i	−0.301609	−	0.145247i
$89$	3.63077	−	1.74849i	0.384861	−	0.185339i	−0.231441	−	0.972849i	$-0.574344\pi$
$89$	3.63077	−	1.74849i	0.384861	−	0.185339i	0.616303	+	0.787509i	$0.288630\pi$
$90$	0.279294	+	0.350223i	0.0294401	+	0.0369168i
$91$	−1.33883	−	5.86580i	−0.140348	−	0.614903i
$92$	0.960274			0.100115
$93$	4.81680			0.499479
$94$	0.745630	+	3.26682i	0.0769058	+	0.336947i
$95$	−2.57957	+	3.23468i	−0.264659	+	0.331872i
$96$	0.355480	−	1.55746i	0.0362810	−	0.158958i
$97$	7.10389	−	8.90799i	0.721290	−	0.904470i	−0.277120	−	0.960835i	$-0.589380\pi$
$97$	7.10389	−	8.90799i	0.721290	−	0.904470i	0.998410	+	0.0563658i	$0.0179513\pi$
$98$	−5.11497	−	2.46324i	−0.516690	−	0.248825i
$99$	−0.313024	−	1.37145i	−0.0314601	−	0.137836i
$100$	−0.900969	−	0.433884i	−0.0900969	−	0.0433884i
$101$	−2.20891	−	2.76988i	−0.219794	−	0.275613i	0.659693	−	0.751535i	$-0.270686\pi$
$101$	−2.20891	−	2.76988i	−0.219794	−	0.275613i	−0.879488	+	0.475921i	$0.842115\pi$
$102$	2.17450	−	9.52712i	0.215308	−	0.943326i
$103$	−0.873633	+	3.82763i	−0.0860816	+	0.377148i	−0.999558	−	0.0297447i	$-0.990531\pi$
$103$	−0.873633	+	3.82763i	−0.0860816	+	0.377148i	0.913476	+	0.406893i	$0.133388\pi$
$104$	−4.71319	+	2.26975i	−0.462166	+	0.222568i
$105$	−1.14557	−	1.43651i	−0.111797	−	0.140189i
$106$	−8.12304	+	10.1860i	−0.788980	+	0.989349i
$107$	−5.51287	+	2.65486i	−0.532949	+	0.256655i	−0.680947	−	0.732333i	$-0.738431\pi$
$107$	−5.51287	+	2.65486i	−0.532949	+	0.256655i	0.147998	+	0.988988i	$0.452717\pi$
$108$	4.96267	−	2.38990i	0.477533	−	0.229968i
$109$	10.9201	−	13.6933i	1.04595	−	1.31158i	0.0973009	−	0.995255i	$-0.468979\pi$
$109$	10.9201	−	13.6933i	1.04595	−	1.31158i	0.948650	−	0.316326i	$-0.102449\pi$
$110$	1.95796	+	2.45521i	0.186685	+	0.234095i
$111$	−2.07790	+	1.00066i	−0.197226	+	0.0949789i
$112$	0.255930	−	1.12130i	0.0241831	−	0.105953i
$113$	−1.24199	+	5.44153i	−0.116837	+	0.511896i	0.882313	+	0.470664i	$0.155985\pi$
$113$	−1.24199	+	5.44153i	−0.116837	+	0.511896i	−0.999150	+	0.0412322i	$0.986872\pi$
$114$	4.12090	+	5.16745i	0.385958	+	0.483976i
$115$	−0.865177	−	0.416647i	−0.0806781	−	0.0388525i
$116$	−0.890762	−	3.90268i	−0.0827052	−	0.362355i
$117$	−2.11128	−	1.01674i	−0.195188	−	0.0939977i
$118$	9.01505	−	11.3045i	0.829903	−	1.04066i
$119$	1.56554	−	6.85910i	0.143513	−	0.628772i
$120$	−0.996033	+	1.24899i	−0.0909250	+	0.114016i
$121$	0.253299	+	1.10978i	0.0230272	+	0.100889i
$122$	7.60844			0.688836
$123$	−18.4320			−1.66196
$124$	−0.670942	−	2.93959i	−0.0602524	−	0.263983i
$125$	0.623490	+	0.781831i	0.0557666	+	0.0699291i
$126$	0.464185	−	0.223540i	0.0413529	−	0.0199145i
$127$	−5.76787	−	2.77766i	−0.511816	−	0.246478i	0.160106	−	0.987100i	$-0.448817\pi$
$127$	−5.76787	−	2.77766i	−0.511816	−	0.246478i	−0.671922	+	0.740622i	$0.734531\pi$
$128$	−1.00000			−0.0883883
$129$	−9.52378	+	4.36298i	−0.838522	+	0.384139i
$130$	5.23125			0.458811
$131$	−0.770286	−	0.370950i	−0.0673002	−	0.0324101i	0.399931	−	0.916545i	$-0.369034\pi$
$131$	−0.770286	−	0.370950i	−0.0673002	−	0.0324101i	−0.467231	+	0.884135i	$0.654748\pi$
$132$	4.51991	−	2.17667i	0.393408	−	0.189455i
$133$	2.96686	+	3.72033i	0.257260	+	0.322594i
$134$	2.15610	+	9.44651i	0.186259	+	0.816054i
$135$	−5.50815			−0.474066
$136$	−6.11709			−0.524536
$137$	4.12137	+	18.0569i	0.352112	+	1.54270i	0.772295	+	0.635264i	$0.219109\pi$
$137$	4.12137	+	18.0569i	0.352112	+	1.54270i	−0.420183	+	0.907440i	$0.638034\pi$
$138$	−0.956464	+	1.19937i	−0.0814196	+	0.102097i
$139$	−2.60204	+	11.4003i	−0.220702	+	0.966961i	0.736249	+	0.676711i	$0.236595\pi$
$139$	−2.60204	+	11.4003i	−0.220702	+	0.966961i	−0.956951	+	0.290249i	$0.906262\pi$
$140$	−0.717099	+	0.899214i	−0.0606059	+	0.0759974i
$141$	−4.82288	−	2.32258i	−0.406160	−	0.195596i
$142$	1.37287	+	6.01495i	0.115209	+	0.504763i
$143$	−14.8010	−	7.12778i	−1.23772	−	0.596055i
$144$	−0.279294	−	0.350223i	−0.0232745	−	0.0291853i
$145$	−0.890762	+	3.90268i	−0.0739738	+	0.324100i
$146$	1.03329	−	4.52714i	0.0855158	−	0.374669i
$147$	8.17123	−	3.93505i	0.673951	−	0.324558i
$148$	0.900119	+	1.12871i	0.0739894	+	0.0927797i
$149$	−10.1666	+	12.7486i	−0.832883	+	1.04440i	0.165423	+	0.986223i	$0.447101\pi$
$149$	−10.1666	+	12.7486i	−0.832883	+	1.04440i	−0.998306	+	0.0581796i	$0.981470\pi$
$150$	1.43931	−	0.693135i	0.117519	−	0.0565942i
$151$	−10.4878	+	5.05068i	−0.853489	+	0.411019i	−0.808871	−	0.587986i	$-0.799921\pi$
$151$	−10.4878	+	5.05068i	−0.853489	+	0.411019i	−0.0446174	+	0.999004i	$0.514207\pi$
$152$	2.57957	−	3.23468i	0.209231	−	0.262368i
$153$	−1.70846	−	2.14235i	−0.138121	−	0.173198i
$154$	3.25413	−	1.56711i	0.262225	−	0.126281i
$155$	−0.670942	+	2.93959i	−0.0538914	+	0.236114i
$156$	1.85960	−	8.14746i	0.148888	−	0.652319i
$157$	−8.17259	−	10.2481i	−0.652244	−	0.817888i	0.340230	−	0.940342i	$-0.389495\pi$
$157$	−8.17259	−	10.2481i	−0.652244	−	0.817888i	−0.992474	+	0.122454i	$0.960924\pi$
$158$	−8.73632	−	4.20719i	−0.695024	−	0.334706i
$159$	−4.63132	−	20.2911i	−0.367288	−	1.60919i
$160$	0.900969	+	0.433884i	0.0712278	+	0.0343015i
$161$	−0.688611	+	0.863491i	−0.0542702	+	0.0680526i
$162$	−1.65900	+	7.26856i	−0.130343	+	0.571072i
$163$	5.44064	−	6.82235i	0.426144	−	0.534368i	−0.521689	−	0.853136i	$-0.674698\pi$
$163$	5.44064	−	6.82235i	0.426144	−	0.534368i	0.947833	+	0.318768i	$0.103269\pi$
$164$	2.56743	+	11.2487i	0.200483	+	0.878373i
$165$	−5.01672			−0.390551
$166$	1.32608			0.102924
$167$	4.78738	+	20.9749i	0.370458	+	1.62308i	0.725492	+	0.688230i	$0.241612\pi$
$167$	4.78738	+	20.9749i	0.370458	+	1.62308i	−0.355034	+	0.934853i	$0.615531\pi$
$168$	1.14557	+	1.43651i	0.0883830	+	0.110829i
$169$	−12.9433	+	6.23315i	−0.995637	+	0.479473i
$170$	5.51131	+	2.65411i	0.422698	+	0.203561i
$171$	1.85332			0.141727
$172$	3.98922	+	5.20443i	0.304175	+	0.396834i
$173$	3.59772			0.273529			0.136765	−	0.990604i	$-0.456330\pi$
$173$	3.59772			0.273529			0.136765	+	0.990604i	$0.456330\pi$
$174$	5.76163	+	2.77465i	0.436788	+	0.210346i
$175$	1.03624	−	0.499026i	0.0783322	−	0.0377228i
$176$	−1.95796	−	2.45521i	−0.147587	−	0.185068i
$177$	5.13989	+	22.5193i	0.386338	+	1.69266i
$178$	4.02986			0.302050
$179$	8.21482			0.614004			0.307002	−	0.951709i	$-0.400674\pi$
$179$	8.21482			0.614004			0.307002	+	0.951709i	$0.400674\pi$
$180$	0.0996787	+	0.436721i	0.00742961	+	0.0325513i
$181$	16.3824	−	20.5429i	1.21769	−	1.52694i	0.440399	−	0.897802i	$-0.354837\pi$
$181$	16.3824	−	20.5429i	1.21769	−	1.52694i	0.777295	−	0.629137i	$-0.216591\pi$
$182$	1.33883	−	5.86580i	0.0992408	−	0.434802i
$183$	−7.57826	+	9.50284i	−0.560201	+	0.702470i
$184$	0.865177	+	0.416647i	0.0637817	+	0.0307156i
$185$	−0.321249	−	1.40748i	−0.0236187	−	0.103480i
$186$	4.33979	+	2.08993i	0.318209	+	0.153241i
$187$	−11.9770	−	15.0187i	−0.875848	−	1.09828i
$188$	−0.745630	+	3.26682i	−0.0543806	+	0.238257i
$189$	−1.40970	+	6.17629i	−0.102540	+	0.449259i
$190$	−3.72759	+	1.79511i	−0.270428	+	0.130231i
$191$	−0.461205	−	0.578333i	−0.0333716	−	0.0418467i	0.764866	−	0.644190i	$-0.222805\pi$
$191$	−0.461205	−	0.578333i	−0.0333716	−	0.0418467i	−0.798237	+	0.602343i	$0.794234\pi$
$192$	0.996033	−	1.24899i	0.0718825	−	0.0901378i
$193$	17.8303	−	8.58661i	1.28345	−	0.618078i	0.337177	−	0.941441i	$-0.390528\pi$
$193$	17.8303	−	8.58661i	1.28345	−	0.618078i	0.946275	+	0.323364i	$0.104814\pi$
$194$	10.2654	−	4.94356i	0.737014	−	0.354927i
$195$	−5.21050	+	6.53376i	−0.373131	+	0.467892i
$196$	−3.53967	−	4.43860i	−0.252833	−	0.317043i
$197$	0.0208083	−	0.0100208i	0.00148253	−	0.000713950i	−0.433142	−	0.901326i	$-0.642595\pi$
$197$	0.0208083	−	0.0100208i	0.00148253	−	0.000713950i	0.434625	+	0.900612i	$0.356881\pi$
$198$	0.313024	−	1.37145i	0.0222457	−	0.0974646i
$199$	−0.643705	+	2.82026i	−0.0456310	+	0.199923i	−0.992605	−	0.121387i	$-0.961266\pi$
$199$	−0.643705	+	2.82026i	−0.0456310	+	0.199923i	0.946974	+	0.321309i	$0.104123\pi$
$200$	−0.623490	−	0.781831i	−0.0440874	−	0.0552838i
$201$	−13.9461	−	6.71609i	−0.983683	−	0.473717i
$202$	−0.788350	−	3.45398i	−0.0554681	−	0.243022i
$203$	4.14811	+	1.99762i	0.291140	+	0.140206i
$204$	6.09282	−	7.64016i	0.426583	−	0.534918i
$205$	2.56743	−	11.2487i	0.179317	−	0.785641i
$206$	−2.44786	+	3.06952i	−0.170551	+	0.213864i
$207$	0.0957189	+	0.419372i	0.00665292	+	0.0291483i
$208$	−5.23125			−0.362722
$209$	12.9925			0.898713
$210$	−0.408851	−	1.79129i	−0.0282134	−	0.123611i
$211$	9.32540	+	11.6937i	0.641987	+	0.805026i	0.991250	−	0.131998i	$-0.0421394\pi$
$211$	9.32540	+	11.6937i	0.641987	+	0.805026i	−0.349263	+	0.937025i	$0.613568\pi$
$212$	−11.7381	+	5.65279i	−0.806179	+	0.388235i
$213$	−8.88002	−	4.27639i	−0.608449	−	0.293013i
$214$	−6.11882			−0.418274
$215$	−1.33605	−	6.41989i	−0.0911177	−	0.437833i
$216$	5.50815			0.374782
$217$	3.12445	+	1.50466i	0.212102	+	0.102143i
$218$	15.7799	−	7.59921i	1.06875	−	0.514684i
$219$	4.62515	+	5.79975i	0.312538	+	0.391911i
$220$	0.698790	+	3.06160i	0.0471124	+	0.206413i
$221$	−32.0000			−2.15255
$222$	−2.30630			−0.154788
$223$	−1.68364	−	7.37651i	−0.112745	−	0.493968i	−0.999497	−	0.0317219i	$-0.989901\pi$
$223$	−1.68364	−	7.37651i	−0.112745	−	0.493968i	0.886752	−	0.462246i	$-0.152956\pi$
$224$	0.717099	−	0.899214i	0.0479132	−	0.0600812i
$225$	0.0996787	−	0.436721i	0.00664525	−	0.0291147i
$226$	−3.47999	+	4.36377i	−0.231485	+	0.290273i
$227$	−14.2790	−	6.87639i	−0.947728	−	0.456402i	−0.104839	−	0.994489i	$-0.533433\pi$
$227$	−14.2790	−	6.87639i	−0.947728	−	0.456402i	−0.842889	+	0.538087i	$0.819147\pi$
$228$	1.47073	+	6.44370i	0.0974017	+	0.426745i
$229$	0.368062	+	0.177249i	0.0243222	+	0.0117130i	0.446005	−	0.895030i	$-0.352846\pi$
$229$	0.368062	+	0.177249i	0.0243222	+	0.0117130i	−0.421683	+	0.906743i	$0.638561\pi$
$230$	−0.598721	−	0.750772i	−0.0394785	−	0.0495045i
$231$	−1.28393	+	5.62525i	−0.0844762	+	0.370115i
$232$	0.890762	−	3.90268i	0.0584814	−	0.256224i
$233$	−18.5751	+	8.94527i	−1.21689	+	0.586024i	−0.928444	−	0.371471i	$-0.878853\pi$
$233$	−18.5751	+	8.94527i	−1.21689	+	0.586024i	−0.288448	+	0.957496i	$0.593139\pi$
$234$	−1.46105	−	1.83210i	−0.0955121	−	0.119768i
$235$	2.08921	−	2.61978i	0.136285	−	0.170896i
$236$	13.0271	−	6.27353i	0.847994	−	0.408372i
$237$	13.9564	−	6.72104i	0.906565	−	0.436579i
$238$	4.38656	−	5.50057i	0.284338	−	0.356549i
$239$	−5.72665	−	7.18100i	−0.370426	−	0.464500i	0.561326	−	0.827595i	$-0.310291\pi$
$239$	−5.72665	−	7.18100i	−0.370426	−	0.464500i	−0.931752	+	0.363095i	$0.881720\pi$
$240$	−1.43931	+	0.693135i	−0.0929070	+	0.0447417i
$241$	−5.85324	+	25.6447i	−0.377040	+	1.65192i	0.329432	+	0.944179i	$0.393143\pi$
$241$	−5.85324	+	25.6447i	−0.377040	+	1.65192i	−0.706472	+	0.707741i	$0.749714\pi$
$242$	−0.253299	+	1.10978i	−0.0162827	+	0.0713391i
$243$	2.87692	+	3.60754i	0.184554	+	0.231424i
$244$	6.85497	+	3.30118i	0.438845	+	0.211336i
$245$	1.26329	+	5.53485i	0.0807088	+	0.353608i
$246$	−16.6067	−	7.99735i	−1.05880	−	0.509893i
$247$	13.4944	−	16.9214i	0.858628	−	1.07669i
$248$	0.670942	−	2.93959i	0.0426049	−	0.186664i
$249$	−1.32082	+	1.65625i	−0.0837035	+	0.104961i
$250$	0.222521	+	0.974928i	0.0140735	+	0.0616599i
$251$	−14.1021			−0.890114			−0.445057	−	0.895502i	$-0.646817\pi$
$251$	−14.1021			−0.890114			−0.445057	+	0.895502i	$0.646817\pi$
$252$	0.515206			0.0324550
$253$	0.671029	+	2.93997i	0.0421872	+	0.184834i
$254$	−3.99149	−	5.00517i	−0.250448	−	0.314052i
$255$	−8.80438	+	4.23997i	−0.551352	+	0.265517i
$256$	−0.900969	−	0.433884i	−0.0563106	−	0.0271177i
$257$	14.9507			0.932596			0.466298	−	0.884628i	$-0.345587\pi$
$257$	14.9507			0.932596			0.466298	+	0.884628i	$0.345587\pi$
$258$	−10.4737	−	0.201301i	−0.652062	−	0.0125324i
$259$	−1.66043			−0.103174
$260$	4.71319	+	2.26975i	0.292300	+	0.140764i
$261$	1.61559	−	0.778029i	0.100003	−	0.0481588i
$262$	−0.533054	−	0.668429i	−0.0329322	−	0.0412957i
$263$	3.95789	+	17.3407i	0.244054	+	1.06927i	0.937287	+	0.348558i	$0.113329\pi$
$263$	3.95789	+	17.3407i	0.244054	+	1.06927i	−0.693233	+	0.720714i	$0.743814\pi$
$264$	5.01672			0.308758
$265$	13.0284			0.800325
$266$	1.05886	+	4.63918i	0.0649230	+	0.284446i
$267$	−4.01387	+	5.03323i	−0.245645	+	0.308029i
$268$	−2.15610	+	9.44651i	−0.131705	+	0.577037i
$269$	−3.67656	+	4.61026i	−0.224164	+	0.281093i	−0.881177	−	0.472786i	$-0.843248\pi$
$269$	−3.67656	+	4.61026i	−0.224164	+	0.281093i	0.657013	+	0.753879i	$0.271820\pi$
$270$	−4.96267	−	2.38990i	−0.302018	−	0.145444i
$271$	1.31563	+	5.76415i	0.0799188	+	0.350147i	0.999039	−	0.0438302i	$-0.0139561\pi$
$271$	1.31563	+	5.76415i	0.0799188	+	0.350147i	−0.919120	+	0.393977i	$0.871099\pi$
$272$	−5.51131	−	2.65411i	−0.334172	−	0.160929i
$273$	5.99279	+	7.51472i	0.362700	+	0.454811i
$274$	−4.12137	+	18.0569i	−0.248981	+	1.09086i
$275$	0.698790	−	3.06160i	0.0421386	−	0.184621i
$276$	−1.38213	+	0.665599i	−0.0831945	+	0.0400644i
$277$	2.42988	+	3.04697i	0.145997	+	0.183075i	0.849453	−	0.527664i	$-0.176932\pi$
$277$	2.42988	+	3.04697i	0.145997	+	0.183075i	−0.703456	+	0.710739i	$0.748361\pi$
$278$	−7.29076	+	9.14233i	−0.437271	+	0.548320i
$279$	1.21690	−	0.586029i	0.0728540	−	0.0350847i
$280$	−1.03624	+	0.499026i	−0.0619271	+	0.0298225i
$281$	2.93646	−	3.68220i	0.175174	−	0.219662i	−0.686491	−	0.727138i	$-0.740850\pi$
$281$	2.93646	−	3.68220i	0.175174	−	0.219662i	0.861666	+	0.507476i	$0.169421\pi$
$282$	−3.33754	−	4.18514i	−0.198747	−	0.249221i
$283$	10.3341	−	4.97665i	0.614299	−	0.295831i	−0.100743	−	0.994913i	$-0.532122\pi$
$283$	10.3341	−	4.97665i	0.614299	−	0.295831i	0.715042	+	0.699082i	$0.246408\pi$
$284$	−1.37287	+	6.01495i	−0.0814650	+	0.356922i
$285$	1.47073	−	6.44370i	0.0871187	−	0.381692i
$286$	−10.2426	−	12.8438i	−0.605658	−	0.759471i
$287$	−11.9561	−	5.75773i	−0.705744	−	0.339868i
$288$	−0.0996787	−	0.436721i	−0.00587363	−	0.0257340i
$289$	−18.3967	−	8.85937i	−1.08216	−	0.521140i
$290$	−2.49586	+	3.12971i	−0.146562	+	0.183783i
$291$	−4.05025	+	17.7453i	−0.237430	+	1.04025i
$292$	2.89522	−	3.63049i	0.169430	−	0.212458i
$293$	−1.70858	−	7.48579i	−0.0998164	−	0.437324i	−0.999998	−	0.00181029i	$-0.999424\pi$
$293$	−1.70858	−	7.48579i	−0.0998164	−	0.437324i	0.900182	−	0.435514i	$-0.143433\pi$
$294$	9.06938			0.528937
$295$	−14.4590			−0.841837
$296$	0.321249	+	1.40748i	0.0186722	+	0.0818083i
$297$	10.7848	+	13.5237i	0.625795	+	0.784723i
$298$	−14.6912	+	7.07491i	−0.851039	+	0.409839i
$299$	4.52595	+	2.17958i	0.261743	+	0.126049i
$300$	1.59751			0.0922325
$301$	−7.54056	−	0.144928i	−0.434631	−	0.00835348i
$302$	−11.6406			−0.669843
$303$	5.09920	+	2.45565i	0.292941	+	0.141073i
$304$	3.72759	−	1.79511i	0.213792	−	0.102957i
$305$	−4.74379	−	5.94852i	−0.271629	−	0.340611i
$306$	−0.609744	−	2.67146i	−0.0348567	−	0.152717i
$307$	−20.3038			−1.15880			−0.579401	−	0.815043i	$-0.696713\pi$
$307$	−20.3038			−1.15880			−0.579401	+	0.815043i	$0.696713\pi$
$308$	3.61181			0.205802
$309$	−1.39564	−	6.11470i	−0.0793951	−	0.347853i
$310$	−1.87994	+	2.35737i	−0.106773	+	0.133890i
$311$	−6.56013	+	28.7418i	−0.371991	+	1.62980i	0.349191	+	0.937052i	$0.386456\pi$
$311$	−6.56013	+	28.7418i	−0.371991	+	1.62980i	−0.721182	+	0.692746i	$0.756401\pi$
$312$	5.21050	−	6.53376i	0.294986	−	0.369901i
$313$	21.4403	+	10.3251i	1.21188	+	0.583611i	0.927039	−	0.374964i	$-0.122345\pi$
$313$	21.4403	+	10.3251i	1.21188	+	0.583611i	0.284841	+	0.958575i	$0.408059\pi$
$314$	−2.91677	−	12.7792i	−0.164603	−	0.721171i
$315$	−0.464185	−	0.223540i	−0.0261539	−	0.0125950i
$316$	−6.04572	−	7.58110i	−0.340098	−	0.426470i
$317$	−0.821662	+	3.59994i	−0.0461491	+	0.202193i	−0.992747	−	0.120225i	$-0.961638\pi$
$317$	−0.821662	+	3.59994i	−0.0461491	+	0.202193i	0.946598	+	0.322418i	$0.104496\pi$
$318$	4.63132	−	20.2911i	0.259711	−	1.13787i
$319$	11.3260	−	5.45431i	0.634134	−	0.305383i
$320$	0.623490	+	0.781831i	0.0348541	+	0.0437057i
$321$	6.09455	−	7.64232i	0.340164	−	0.426553i
$322$	−0.995072	+	0.479201i	−0.0554532	+	0.0267048i
$323$	22.8020	−	10.9809i	1.26874	−	0.610992i
$324$	−4.64842	+	5.82893i	−0.258245	+	0.323829i
$325$	−3.26163	−	4.08995i	−0.180923	−	0.226870i
$326$	7.86196	−	3.78612i	0.435434	−	0.209694i
$327$	−6.22602	+	27.2780i	−0.344300	+	1.50848i
$328$	−2.56743	+	11.2487i	−0.141763	+	0.621104i
$329$	−2.40288	−	3.01311i	−0.132475	−	0.166118i
$330$	−4.51991	−	2.17667i	−0.248813	−	0.119822i
$331$	−0.327907	−	1.43666i	−0.0180234	−	0.0789658i	0.965116	−	0.261821i	$-0.0843231\pi$
$331$	−0.327907	−	1.43666i	−0.0180234	−	0.0789658i	−0.983140	+	0.182856i	$0.941466\pi$
$332$	1.19476	+	0.575364i	0.0655708	+	0.0315772i
$333$	−0.403210	+	0.505610i	−0.0220958	+	0.0277072i
$334$	−4.78738	+	20.9749i	−0.261954	+	1.14769i
$335$	6.04127	−	7.57551i	0.330070	−	0.413894i
$336$	0.408851	+	1.79129i	0.0223046	+	0.0977230i
$337$	−25.7780			−1.40422			−0.702109	−	0.712069i	$-0.747758\pi$
$337$	−25.7780			−1.40422			−0.702109	+	0.712069i	$0.747758\pi$
$338$	−14.3660			−0.781405
$339$	−1.98410	−	8.69291i	−0.107762	−	0.472134i
$340$	3.81394	+	4.78253i	0.206840	+	0.259369i
$341$	8.53099	−	4.10831i	0.461979	−	0.222477i
$342$	1.66978	+	0.804125i	0.0902915	+	0.0434821i
$343$	14.5805			0.787273
$344$	1.33605	+	6.41989i	0.0720349	+	0.346137i
$345$	1.53405			0.0825905
$346$	3.24143	+	1.56099i	0.174260	+	0.0839194i
$347$	−17.1263	+	8.24758i	−0.919386	+	0.442753i	−0.832852	−	0.553496i	$-0.813294\pi$
$347$	−17.1263	+	8.24758i	−0.919386	+	0.442753i	−0.0865343	+	0.996249i	$0.527579\pi$
$348$	3.98717	+	4.99975i	0.213735	+	0.268015i
$349$	−2.87264	−	12.5858i	−0.153769	−	0.673704i	−0.991770	−	0.128036i	$-0.959133\pi$
$349$	−2.87264	−	12.5858i	−0.153769	−	0.673704i	0.838001	−	0.545669i	$-0.183724\pi$
$350$	1.15014			0.0614774
$351$	28.8145			1.53800
$352$	−0.698790	−	3.06160i	−0.0372456	−	0.163184i
$353$	−2.25163	+	2.82346i	−0.119842	+	0.150278i	−0.838134	−	0.545465i	$-0.816353\pi$
$353$	−2.25163	+	2.82346i	−0.119842	+	0.150278i	0.718291	+	0.695743i	$0.244925\pi$
$354$	−5.13989	+	22.5193i	−0.273182	+	1.19689i
$355$	3.84671	−	4.82362i	0.204162	−	0.256011i
$356$	3.63077	+	1.74849i	0.192431	+	0.0926697i
$357$	2.50098	+	10.9575i	0.132366	+	0.579932i
$358$	7.40129	+	3.56427i	0.391170	+	0.188378i
$359$	19.0669	+	23.9091i	1.00631	+	1.26187i	0.964869	+	0.262733i	$0.0846238\pi$
$359$	19.0669	+	23.9091i	1.00631	+	1.26187i	0.0414421	+	0.999141i	$0.486805\pi$
$360$	−0.0996787	+	0.436721i	−0.00525353	+	0.0230172i
$361$	0.418922	−	1.83542i	0.0220485	−	0.0966008i
$362$	23.6732	−	11.4004i	1.24424	−	0.599193i
$363$	−1.13380	−	1.42174i	−0.0595091	−	0.0746220i
$364$	3.75132	−	4.70401i	0.196623	−	0.246557i
$365$	−4.18371	+	2.01477i	−0.218985	+	0.105458i
$366$	−10.9509	+	5.27368i	−0.572413	+	0.275660i
$367$	20.8948	−	26.2013i	1.09070	−	1.36770i	0.166389	−	0.986060i	$-0.446789\pi$
$367$	20.8948	−	26.2013i	1.09070	−	1.36770i	0.924313	−	0.381636i	$-0.124639\pi$
$368$	0.598721	+	0.750772i	0.0312105	+	0.0391367i
$369$	−4.65661	+	2.24250i	−0.242413	+	0.116740i
$370$	0.321249	−	1.40748i	0.0167009	−	0.0731716i
$371$	3.33434	−	14.6087i	0.173110	−	0.758446i
$372$	3.00323	+	3.76593i	0.155710	+	0.195254i
$373$	−22.1846	−	10.6835i	−1.14867	−	0.553172i	−0.240039	−	0.970763i	$-0.577160\pi$
$373$	−22.1846	−	10.6835i	−1.14867	−	0.553172i	−0.908635	+	0.417591i	$0.862874\pi$
$374$	−4.27456	−	18.7281i	−0.221032	−	0.968405i
$375$	−1.43931	−	0.693135i	−0.0743256	−	0.0357933i
$376$	−2.08921	+	2.61978i	−0.107743	+	0.135105i
$377$	4.65980	−	20.4159i	0.239992	−	1.05147i
$378$	−3.94989	+	4.95300i	−0.203160	+	0.254755i
$379$	−5.28881	−	23.1718i	−0.271668	−	1.19025i	−0.908044	−	0.418875i	$-0.862424\pi$
$379$	−5.28881	−	23.1718i	−0.271668	−	1.19025i	0.636376	−	0.771379i	$-0.280433\pi$
$380$	−4.13732			−0.212240
$381$	10.2270			0.523948
$382$	−0.164602	−	0.721170i	−0.00842178	−	0.0368982i
$383$	13.0770	+	16.3981i	0.668205	+	0.837903i	0.994209	−	0.107466i	$-0.0342736\pi$
$383$	13.0770	+	16.3981i	0.668205	+	0.837903i	−0.326004	+	0.945369i	$0.605702\pi$
$384$	1.43931	−	0.693135i	0.0734495	−	0.0353714i
$385$	−3.25413	−	1.56711i	−0.165846	−	0.0798672i
$386$	19.7901			1.00729
$387$	−1.87524	+	2.26095i	−0.0953240	+	0.114930i
$388$	11.3937			0.578430
$389$	−3.36164	−	1.61888i	−0.170442	−	0.0820806i	0.346717	−	0.937970i	$-0.387296\pi$
$389$	−3.36164	−	1.61888i	−0.170442	−	0.0820806i	−0.517159	+	0.855889i	$0.673011\pi$
$390$	−7.52938	+	3.62596i	−0.381265	+	0.183608i
$391$	3.66243	+	4.59254i	0.185217	+	0.232255i
$392$	−1.26329	−	5.53485i	−0.0638059	−	0.279552i
$393$	1.36580			0.0688954
$394$	0.0230955			0.00116354
$395$	2.15769	+	9.45347i	0.108565	+	0.475656i
$396$	0.877075	−	1.09982i	0.0440747	−	0.0552679i
$397$	4.26002	−	18.6644i	0.213804	−	0.936738i	−0.748150	−	0.663529i	$-0.769058\pi$
$397$	4.26002	−	18.6644i	0.213804	−	0.936738i	0.961955	−	0.273209i	$-0.0880851\pi$
$398$	−1.80362	+	2.26167i	−0.0904074	+	0.113367i
$399$	−6.84893	−	3.29827i	−0.342875	−	0.165120i
$400$	−0.222521	−	0.974928i	−0.0111260	−	0.0487464i
$401$	20.3960	+	9.82218i	1.01853	+	0.490496i	0.867185	−	0.497985i	$-0.165927\pi$
$401$	20.3960	+	9.82218i	1.01853	+	0.490496i	0.151341	+	0.988482i	$0.451641\pi$
$402$	−9.65101	−	12.1020i	−0.481348	−	0.603592i
$403$	3.50987	−	15.3777i	0.174839	−	0.766019i
$404$	0.788350	−	3.45398i	0.0392219	−	0.171842i
$405$	6.71716	−	3.23481i	0.333778	−	0.160739i
$406$	2.87058	+	3.59960i	0.142465	+	0.178645i
$407$	−2.82667	+	3.54454i	−0.140113	+	0.175696i
$408$	8.80438	−	4.23997i	0.435882	−	0.209910i
$409$	8.32991	−	4.01148i	0.411888	−	0.198355i	−0.216453	−	0.976293i	$-0.569449\pi$
$409$	8.32991	−	4.01148i	0.411888	−	0.198355i	0.628341	+	0.777938i	$0.283734\pi$
$410$	7.19379	−	9.02073i	0.355276	−	0.445502i
$411$	−18.4478	−	23.1328i	−0.909962	−	1.14106i
$412$	−3.53727	+	1.70346i	−0.174269	+	0.0839233i
$413$	−3.70049	+	16.2129i	−0.182089	+	0.797785i
$414$	−0.0957189	+	0.419372i	−0.00470433	+	0.0206110i
$415$	−0.826797	−	1.03677i	−0.0405859	−	0.0508931i
$416$	−4.71319	−	2.26975i	−0.231083	−	0.111284i
$417$	−4.15680	−	18.2121i	−0.203559	−	0.891852i
$418$	11.7059	+	5.63725i	0.572553	+	0.275727i
$419$	21.4132	−	26.8513i	1.04610	−	1.31177i	0.0975254	−	0.995233i	$-0.468907\pi$
$419$	21.4132	−	26.8513i	1.04610	−	1.31177i	0.948579	−	0.316540i	$-0.102521\pi$
$420$	0.408851	−	1.79129i	0.0199499	−	0.0874061i
$421$	12.1245	−	15.2036i	0.590911	−	0.740979i	−0.393020	−	0.919530i	$-0.628570\pi$
$421$	12.1245	−	15.2036i	0.590911	−	0.740979i	0.983931	+	0.178551i	$0.0571411\pi$
$422$	3.32820	+	14.5818i	0.162014	+	0.709830i
$423$	−1.50101			−0.0729817
$424$	−13.0284			−0.632713
$425$	−1.36118	−	5.96372i	−0.0660269	−	0.289283i
$426$	−6.14516	−	7.70579i	−0.297734	−	0.373347i
$427$	−7.88416	+	3.79681i	−0.381541	+	0.183741i
$428$	−5.51287	−	2.65486i	−0.266474	−	0.128327i
$429$	26.2437			1.26706
$430$	1.58175	−	6.36381i	0.0762786	−	0.306890i
$431$	7.95675			0.383263			0.191631	−	0.981467i	$-0.438622\pi$
$431$	7.95675			0.383263			0.191631	+	0.981467i	$0.438622\pi$
$432$	4.96267	+	2.38990i	0.238767	+	0.114984i
$433$	15.1480	−	7.29489i	0.727966	−	0.350570i	−0.0329176	−	0.999458i	$-0.510480\pi$
$433$	15.1480	−	7.29489i	0.727966	−	0.350570i	0.760884	+	0.648888i	$0.224766\pi$
$434$	2.16219	+	2.71130i	0.103788	+	0.130146i
$435$	−1.42300	−	6.23459i	−0.0682278	−	0.298926i
$436$	17.5144			0.838788
$437$	−3.97296			−0.190052
$438$	1.65070	+	7.23217i	0.0788733	+	0.345567i
$439$	11.4613	−	14.3721i	0.547020	−	0.685941i	−0.429079	−	0.903267i	$-0.641162\pi$
$439$	11.4613	−	14.3721i	0.547020	−	0.685941i	0.976099	+	0.217325i	$0.0697333\pi$
$440$	−0.698790	+	3.06160i	−0.0333135	+	0.145956i
$441$	1.58560	−	1.98828i	0.0755048	−	0.0946800i
$442$	−28.8310	−	13.8843i	−1.37135	−	0.660408i
$443$	1.44686	+	6.33912i	0.0687425	+	0.301181i	0.997599	−	0.0692601i	$-0.0220638\pi$
$443$	1.44686	+	6.33912i	0.0687425	+	0.301181i	−0.928856	+	0.370441i	$0.879207\pi$
$444$	−2.07790	−	1.00066i	−0.0986128	−	0.0474894i
$445$	−2.51257	−	3.15067i	−0.119107	−	0.149356i
$446$	1.68364	−	7.37651i	0.0797227	−	0.349288i
$447$	5.79646	−	25.3960i	0.274163	−	1.20119i
$448$	1.03624	−	0.499026i	0.0489576	−	0.0235768i
$449$	16.2270	+	20.3480i	0.765798	+	0.960281i	0.999929	−	0.0119245i	$-0.00379578\pi$
$449$	16.2270	+	20.3480i	0.765798	+	0.960281i	−0.234131	+	0.972205i	$0.575224\pi$
$450$	0.279294	−	0.350223i	0.0131660	−	0.0165097i
$451$	−32.6448	+	15.7209i	−1.53718	+	0.740268i
$452$	−5.02873	+	2.42171i	−0.236531	+	0.113908i
$453$	11.5945	−	14.5390i	0.544755	−	0.683101i
$454$	−9.88135	−	12.3908i	−0.463755	−	0.581530i
$455$	−5.42082	+	2.61053i	−0.254132	+	0.122383i
$456$	−1.47073	+	6.44370i	−0.0688734	+	0.301754i
$457$	−6.31985	+	27.6891i	−0.295630	+	1.29524i	0.580932	+	0.813952i	$0.302688\pi$
$457$	−6.31985	+	27.6891i	−0.295630	+	1.29524i	−0.876562	+	0.481288i	$0.840169\pi$
$458$	0.254707	+	0.319392i	0.0119017	+	0.0149242i
$459$	30.3571	+	14.6192i	1.41695	+	0.682366i
$460$	−0.213681	−	0.936198i	−0.00996293	−	0.0436504i
$461$	30.2047	+	14.5458i	1.40677	+	0.677467i	0.974523	−	0.224286i	$-0.0720051\pi$
$461$	30.2047	+	14.5458i	1.40677	+	0.677467i	0.432251	+	0.901753i	$0.357719\pi$
$462$	−3.59748	+	4.51110i	−0.167370	+	0.209876i
$463$	−0.136493	+	0.598016i	−0.00634338	+	0.0277922i	−0.978001	−	0.208602i	$-0.933109\pi$
$463$	−0.136493	+	0.598016i	−0.00634338	+	0.0277922i	0.971657	+	0.236394i	$0.0759657\pi$
$464$	2.49586	−	3.12971i	0.115867	−	0.145293i
$465$	−1.07184	−	4.69603i	−0.0497054	−	0.217773i
$466$	−20.6168			−0.955053
$467$	31.3484			1.45063			0.725316	−	0.688416i	$-0.241693\pi$
$467$	31.3484			1.45063			0.725316	+	0.688416i	$0.241693\pi$
$468$	−0.521444	−	2.28460i	−0.0241038	−	0.105605i
$469$	−6.94829	−	8.71288i	−0.320842	−	0.402323i
$470$	3.01899	−	1.45387i	0.139256	−	0.0670621i
$471$	18.8662	+	9.08549i	0.869309	+	0.418637i
$472$	14.4590			0.665530
$473$	−13.1462	+	15.8502i	−0.604465	+	0.728793i
$474$	15.4904			0.711499
$475$	3.72759	+	1.79511i	0.171034	+	0.0823655i
$476$	6.33876	−	3.05259i	0.290537	−	0.139915i
$477$	−3.63873	−	4.56283i	−0.166606	−	0.208918i
$478$	−2.04382	−	8.95455i	−0.0934821	−	0.409572i
$479$	−13.1680			−0.601661			−0.300831	−	0.953678i	$-0.597264\pi$
$479$	−13.1680			−0.601661			−0.300831	+	0.953678i	$0.597264\pi$
$480$	−1.59751			−0.0729162
$481$	1.68053	+	7.36289i	0.0766257	+	0.335719i
$482$	−16.4004	+	20.5655i	−0.747018	+	0.936731i
$483$	0.392609	−	1.72013i	0.0178643	−	0.0782687i
$484$	−0.709728	+	0.889971i	−0.0322604	+	0.0404532i
$485$	−10.2654	−	4.94356i	−0.466128	−	0.224476i
$486$	1.02676	+	4.49853i	0.0465748	+	0.204057i
$487$	−37.5704	−	18.0929i	−1.70248	−	0.819869i	−0.993395	−	0.114743i	$-0.963396\pi$
$487$	−37.5704	−	18.0929i	−1.70248	−	0.819869i	−0.709081	−	0.705127i	$-0.750890\pi$
$488$	4.74379	+	5.94852i	0.214741	+	0.269277i
$489$	−3.10196	+	13.5906i	−0.140275	+	0.614587i
$490$	−1.26329	+	5.53485i	−0.0570697	+	0.250039i
$491$	17.7962	−	8.57018i	0.803129	−	0.386767i	0.0131602	−	0.999913i	$-0.495811\pi$
$491$	17.7962	−	8.57018i	0.803129	−	0.386767i	0.789969	+	0.613147i	$0.210097\pi$
$492$	−11.4922	−	14.4107i	−0.518107	−	0.649686i
$493$	15.2674	−	19.1447i	0.687609	−	0.862234i
$494$	19.5000	−	9.39069i	0.877345	−	0.422507i
$495$	−1.26741	+	0.610352i	−0.0569658	+	0.0274333i
$496$	1.87994	−	2.35737i	0.0844117	−	0.105849i
$497$	−4.42424	−	5.54782i	−0.198454	−	0.248854i
$498$	−1.90864	+	0.919152i	−0.0855281	+	0.0411882i
$499$	−1.20399	+	5.27503i	−0.0538981	+	0.236143i	−0.994701	−	0.102812i	$-0.967216\pi$
$499$	−1.20399	+	5.27503i	−0.0538981	+	0.236143i	0.940803	+	0.338954i	$0.110073\pi$
$500$	−0.222521	+	0.974928i	−0.00995144	+	0.0436001i
$501$	−21.4289	−	26.8710i	−0.957374	−	1.20051i
$502$	−12.7055	−	6.11865i	−0.567075	−	0.273089i
$503$	−9.35157	−	40.9719i	−0.416966	−	1.82685i	−0.549280	−	0.835638i	$-0.685098\pi$
$503$	−9.35157	−	40.9719i	−0.416966	−	1.82685i	0.132314	−	0.991208i	$-0.457759\pi$
$504$	0.464185	+	0.223540i	0.0206764	+	0.00995725i
$505$	−2.20891	+	2.76988i	−0.0982950	+	0.123258i
$506$	−0.671029	+	2.93997i	−0.0298309	+	0.130698i
$507$	14.3090	−	17.9429i	0.635484	−	0.796871i
$508$	−1.42455	−	6.24135i	−0.0632040	−	0.276915i
$509$	13.7725			0.610453			0.305227	−	0.952280i	$-0.401268\pi$
$509$	13.7725			0.610453			0.305227	+	0.952280i	$0.401268\pi$
$510$	−9.77213			−0.432717
$511$	1.18843	+	5.20684i	0.0525729	+	0.230337i
$512$	−0.623490	−	0.781831i	−0.0275546	−	0.0345524i
$513$	−20.5321	+	9.88775i	−0.906516	+	0.436555i
$514$	13.4701	+	6.48684i	0.594139	+	0.286122i
$515$	3.92607			0.173003
$516$	−9.34910	−	4.72572i	−0.411571	−	0.208038i
$517$	−10.5227			−0.462789
$518$	−1.49600	−	0.720433i	−0.0657303	−	0.0316540i
$519$	−5.17823	+	2.49370i	−0.227299	+	0.109461i
$520$	3.26163	+	4.08995i	0.143032	+	0.179356i
$521$	−7.55461	−	33.0989i	−0.330973	−	1.45009i	−0.817249	−	0.576284i	$-0.804502\pi$
$521$	−7.55461	−	33.0989i	−0.330973	−	1.45009i	0.486276	−	0.873805i	$-0.338355\pi$
$522$	1.79317			0.0784851
$523$	1.67794			0.0733713			0.0366857	−	0.999327i	$-0.488320\pi$
$523$	1.67794			0.0733713			0.0366857	+	0.999327i	$0.488320\pi$
$524$	−0.190245	−	0.833517i	−0.00831089	−	0.0364124i
$525$	−1.14557	+	1.43651i	−0.0499970	+	0.0626942i
$526$	−3.95789	+	17.3407i	−0.172572	+	0.756089i
$527$	11.4998	−	14.4202i	0.500937	−	0.628155i
$528$	4.51991	+	2.17667i	0.196704	+	0.0947276i
$529$	4.91279	+	21.5243i	0.213600	+	0.935841i
$530$	11.7381	+	5.65279i	0.509872	+	0.245541i
$531$	4.03831	+	5.06388i	0.175248	+	0.219754i
$532$	−1.05886	+	4.63918i	−0.0459075	+	0.201134i
$533$	−13.4309	+	58.8445i	−0.581756	+	2.54884i
$534$	−5.80021	+	2.79323i	−0.251000	+	0.120875i
$535$	3.81502	+	4.78389i	0.164938	+	0.206825i
$536$	−6.04127	+	7.57551i	−0.260943	+	0.327212i
$537$	−11.8237	+	5.69398i	−0.510229	+	0.245713i
$538$	−5.31279	+	2.55850i	−0.229051	+	0.110305i
$539$	11.1157	−	13.9387i	0.478788	−	0.600381i
$540$	−3.43427	−	4.30644i	−0.147788	−	0.185320i
$541$	10.0319	−	4.83113i	0.431307	−	0.207707i	−0.205618	−	0.978632i	$-0.565920\pi$
$541$	10.0319	−	4.83113i	0.431307	−	0.207707i	0.636925	+	0.770926i	$0.280206\pi$
$542$	−1.31563	+	5.76415i	−0.0565111	+	0.247591i
$543$	−9.34035	+	40.9227i	−0.400833	+	1.75616i
$544$	−3.81394	−	4.78253i	−0.163521	−	0.205049i
$545$	−15.7799	−	7.59921i	−0.675938	−	0.325515i
$546$	2.13880	+	9.37070i	0.0915322	+	0.401029i
$547$	16.8594	+	8.11906i	0.720856	+	0.347146i	0.758080	−	0.652161i	$-0.226137\pi$
$547$	16.8594	+	8.11906i	0.720856	+	0.347146i	−0.0372246	+	0.999307i	$0.511852\pi$
$548$	−11.5478	+	14.4805i	−0.493298	+	0.618576i
$549$	−0.758400	+	3.32277i	−0.0323677	+	0.141812i
$550$	1.95796	−	2.45521i	0.0834879	−	0.104691i
$551$	3.68536	+	16.1466i	0.157002	+	0.687870i
$552$	−1.53405			−0.0652935
$553$	11.1524			0.474248
$554$	0.867214	+	3.79951i	0.0368444	+	0.161426i
$555$	1.43795	+	1.80314i	0.0610377	+	0.0765388i
$556$	−10.5355	+	5.07361i	−0.446803	+	0.215169i
$557$	−21.1439	−	10.1824i	−0.895895	−	0.431440i	−0.0714902	−	0.997441i	$-0.522775\pi$
$557$	−21.1439	−	10.1824i	−0.895895	−	0.431440i	−0.824404	+	0.566001i	$0.808490\pi$
$558$	1.35066			0.0571780
$559$	6.98920	+	33.5840i	0.295612	+	1.42045i
$560$	−1.15014			−0.0486022
$561$	27.6487	+	13.3149i	1.16733	+	0.562156i
$562$	4.24331	−	2.04347i	0.178993	−	0.0861985i
$563$	8.56793	+	10.7438i	0.361095	+	0.452799i	0.928882	−	0.370377i	$-0.120771\pi$
$563$	8.56793	+	10.7438i	0.361095	+	0.452799i	−0.567786	+	0.823176i	$0.692200\pi$
$564$	−1.19115	−	5.21878i	−0.0501566	−	0.219750i
$565$	5.58147			0.234814
$566$	11.4700			0.482120
$567$	−1.90808	−	8.35984i	−0.0801318	−	0.351080i
$568$	−3.84671	+	4.82362i	−0.161404	+	0.202394i
$569$	−2.28187	+	9.99751i	−0.0956608	+	0.419117i	−0.999970	−	0.00776087i	$-0.997530\pi$
$569$	−2.28187	+	9.99751i	−0.0956608	+	0.419117i	0.904309	+	0.426878i	$0.140387\pi$
$570$	4.12090	−	5.16745i	0.172606	−	0.216441i
$571$	23.5907	+	11.3607i	0.987240	+	0.475430i	0.856589	−	0.515999i	$-0.172579\pi$
$571$	23.5907	+	11.3607i	0.987240	+	0.475430i	0.130651	+	0.991428i	$0.458293\pi$
$572$	−3.65554	−	16.0160i	−0.152846	−	0.669662i
$573$	1.06468	+	0.512723i	0.0444776	+	0.0214193i
$574$	−8.27385	−	10.3751i	−0.345344	−	0.433047i
$575$	−0.213681	+	0.936198i	−0.00891111	+	0.0390421i
$576$	0.0996787	−	0.436721i	0.00415328	−	0.0181967i
$577$	−23.5324	+	11.3326i	−0.979668	+	0.471783i	−0.853991	−	0.520288i	$-0.825825\pi$
$577$	−23.5324	+	11.3326i	−0.979668	+	0.471783i	−0.125677	+	0.992071i	$0.540110\pi$
$578$	−12.7309	−	15.9640i	−0.529535	−	0.664016i
$579$	−19.7116	+	24.7176i	−0.819186	+	1.02723i
$580$	−3.60662	+	1.73686i	−0.149757	+	0.0721191i
$581$	−1.37413	+	0.661748i	−0.0570087	+	0.0274539i
$582$	−11.3486	+	14.2306i	−0.470413	+	0.589879i
$583$	−25.5091	−	31.9873i	−1.05648	−	1.32478i
$584$	4.18371	−	2.01477i	0.173123	−	0.0833717i
$585$	−0.521444	+	2.28460i	−0.0215591	+	0.0944564i
$586$	1.70858	−	7.48579i	0.0705809	−	0.309235i
$587$	−22.5021	−	28.2167i	−0.928761	−	1.16463i	−0.986080	−	0.166273i	$-0.946827\pi$
$587$	−22.5021	−	28.2167i	−0.928761	−	1.16463i	0.0573191	−	0.998356i	$-0.481745\pi$
$588$	8.17123	+	3.93505i	0.336976	+	0.162279i
$589$	2.77590	+	12.1620i	0.114379	+	0.501127i
$590$	−13.0271	−	6.27353i	−0.536318	−	0.258277i
$591$	−0.0230039	+	0.0288460i	−0.000946254	+	0.00118657i
$592$	−0.321249	+	1.40748i	−0.0132032	+	0.0578472i
$593$	−10.2642	+	12.8710i	−0.421502	+	0.528547i	−0.946564	−	0.322517i	$-0.895471\pi$
$593$	−10.2642	+	12.8710i	−0.421502	+	0.528547i	0.525061	+	0.851064i	$0.324042\pi$
$594$	3.84904	+	16.8637i	0.157928	+	0.691927i
$595$	−7.03549			−0.288427
$596$	−16.3060			−0.667920
$597$	−1.02833	−	4.50539i	−0.0420866	−	0.184394i
$598$	3.13206	+	3.92748i	0.128079	+	0.160606i
$599$	−23.5867	+	11.3588i	−0.963728	+	0.464107i	−0.848479	−	0.529229i	$-0.822481\pi$
$599$	−23.5867	+	11.3588i	−0.963728	+	0.464107i	−0.115250	+	0.993337i	$0.536767\pi$
$600$	1.43931	+	0.693135i	0.0587596	+	0.0282971i
$601$	−4.09902			−0.167203			−0.0836013	−	0.996499i	$-0.526642\pi$
$601$	−4.09902			−0.167203			−0.0836013	+	0.996499i	$0.526642\pi$
$602$	−6.73093	−	3.40230i	−0.274332	−	0.138667i
$603$	−4.34041			−0.176755
$604$	−10.4878	−	5.05068i	−0.426744	−	0.205509i
$605$	1.02559	−	0.493897i	0.0416961	−	0.0200798i
$606$	3.52876	+	4.42492i	0.143346	+	0.179750i
$607$	3.58249	+	15.6959i	0.145409	+	0.637078i	0.994126	+	0.108230i	$0.0345184\pi$
$607$	3.58249	+	15.6959i	0.145409	+	0.637078i	−0.848717	+	0.528847i	$0.822624\pi$
$608$	4.13732			0.167790
$609$	−7.35504			−0.298041
$610$	−1.69304	−	7.41769i	−0.0685491	−	0.300333i
$611$	−10.9292	+	13.7047i	−0.442147	+	0.554435i
$612$	0.609744	−	2.67146i	0.0246474	−	0.107987i
$613$	6.88351	−	8.63165i	0.278022	−	0.348629i	−0.623140	−	0.782110i	$-0.714143\pi$
$613$	6.88351	−	8.63165i	0.278022	−	0.348629i	0.901163	+	0.433481i	$0.142715\pi$
$614$	−18.2931	−	8.80951i	−0.738251	−	0.355523i
$615$	4.10151	+	17.9699i	0.165389	+	0.724616i
$616$	3.25413	+	1.56711i	0.131113	+	0.0631405i
$617$	−8.36251	−	10.4863i	−0.336662	−	0.422161i	0.584468	−	0.811417i	$-0.301303\pi$
$617$	−8.36251	−	10.4863i	−0.336662	−	0.422161i	−0.921129	+	0.389256i	$0.872732\pi$
$618$	1.39564	−	6.11470i	0.0561408	−	0.245969i
$619$	−9.02156	+	39.5260i	−0.362607	+	1.58869i	0.383943	+	0.923357i	$0.374566\pi$
$619$	−9.02156	+	39.5260i	−0.362607	+	1.58869i	−0.746550	+	0.665329i	$0.768291\pi$
$620$	−2.71659	+	1.30824i	−0.109101	+	0.0525402i
$621$	−3.29784	−	4.13536i	−0.132338	−	0.165946i
$622$	−18.3811	+	23.0491i	−0.737014	+	0.924186i
$623$	−4.17589	+	2.01100i	−0.167303	+	0.0805691i
$624$	7.52938	−	3.62596i	0.301417	−	0.145155i
$625$	0.623490	−	0.781831i	0.0249396	−	0.0312733i
$626$	14.8372	+	18.6052i	0.593013	+	0.743615i
$627$	−18.7003	+	9.00559i	−0.746818	+	0.359648i
$628$	2.91677	−	12.7792i	0.116392	−	0.509945i
$629$	−1.96511	+	8.60970i	−0.0783540	+	0.343291i
$630$	−0.321226	−	0.402805i	−0.0127979	−	0.0160481i
$631$	−29.3898	−	14.1534i	−1.16999	−	0.563438i	−0.255011	−	0.966938i	$-0.582079\pi$
$631$	−29.3898	−	14.1534i	−1.16999	−	0.563438i	−0.914980	+	0.403500i	$0.867793\pi$
$632$	−2.15769	−	9.45347i	−0.0858284	−	0.376039i
$633$	−21.5274	−	10.3671i	−0.855639	−	0.412054i
$634$	−2.30224	+	2.88692i	−0.0914338	+	0.114654i
$635$	−1.42455	+	6.24135i	−0.0565314	+	0.247680i
$636$	12.9767	−	16.2722i	0.514558	−	0.645236i
$637$	−6.60860	−	28.9541i	−0.261842	−	1.14721i
$638$	12.5709			0.497687
$639$	−2.76370			−0.109330
$640$	0.222521	+	0.974928i	0.00879591	+	0.0385374i
$641$	−13.2386	−	16.6006i	−0.522891	−	0.655685i	0.448329	−	0.893869i	$-0.352019\pi$
$641$	−13.2386	−	16.6006i	−0.522891	−	0.655685i	−0.971220	+	0.238184i	$0.923448\pi$
$642$	8.80687	−	4.24117i	0.347580	−	0.167386i
$643$	25.3424	+	12.2042i	0.999405	+	0.481288i	0.860736	−	0.509051i	$-0.170004\pi$
$643$	25.3424	+	12.2042i	0.999405	+	0.481288i	0.138668	+	0.990339i	$0.455718\pi$
$644$	−1.10445			−0.0435213
$645$	6.37284	+	8.31415i	0.250930	+	0.327369i
$646$	25.3083			0.995743
$647$	−28.5500	−	13.7490i	−1.12242	−	0.540528i	−0.221779	−	0.975097i	$-0.571186\pi$
$647$	−28.5500	−	13.7490i	−1.12242	−	0.540528i	−0.900639	+	0.434569i	$0.856901\pi$
$648$	−6.71716	+	3.23481i	−0.263875	+	0.127075i
$649$	28.3102	+	35.4999i	1.11127	+	1.39349i
$650$	−1.16406	−	5.10009i	−0.0456583	−	0.200042i
$651$	−5.53998			−0.217129
$652$	8.72611			0.341741
$653$	−9.01625	−	39.5028i	−0.352833	−	1.54586i	−0.770607	−	0.637311i	$-0.780047\pi$
$653$	−9.01625	−	39.5028i	−0.352833	−	1.54586i	0.417774	−	0.908551i	$-0.362810\pi$
$654$	−17.4449	+	21.8752i	−0.682151	+	0.855390i
$655$	−0.190245	+	0.833517i	−0.00743348	+	0.0325682i
$656$	−7.19379	+	9.02073i	−0.280870	+	0.352200i
$657$	1.87410	+	0.902520i	0.0731157	+	0.0352107i
$658$	−0.857577	−	3.75729i	−0.0334318	−	0.146474i
$659$	21.0730	+	10.1482i	0.820888	+	0.395319i	0.796690	−	0.604388i	$-0.206582\pi$
$659$	21.0730	+	10.1482i	0.820888	+	0.395319i	0.0241981	+	0.999707i	$0.492297\pi$
$660$	−3.12787	−	3.92223i	−0.121752	−	0.152673i
$661$	6.05422	−	26.5253i	0.235482	−	1.03171i	−0.709529	−	0.704676i	$-0.751092\pi$
$661$	6.05422	−	26.5253i	0.235482	−	1.03171i	0.945011	−	0.327038i	$-0.106051\pi$
$662$	0.327907	−	1.43666i	0.0127445	−	0.0558372i
$663$	46.0579	−	22.1803i	1.78874	−	0.861412i
$664$	0.826797	+	1.03677i	0.0320859	+	0.0402345i
$665$	2.96686	−	3.72033i	0.115050	−	0.144268i
$666$	−0.582656	+	0.280592i	−0.0225775	+	0.0108727i
$667$	−3.46334	+	1.66786i	−0.134101	+	0.0645797i
$668$	−13.4139	+	16.8205i	−0.519001	+	0.650806i
$669$	7.53620	+	9.45009i	0.291366	+	0.365362i
$670$	8.72989	−	4.20409i	0.337265	−	0.162418i
$671$	−5.31670	+	23.2940i	−0.205249	+	0.899255i
$672$	−0.408851	+	1.79129i	−0.0157718	+	0.0691006i
$673$	−0.835462	−	1.04764i	−0.0322047	−	0.0403834i	0.765468	−	0.643474i	$-0.222507\pi$
$673$	−0.835462	−	1.04764i	−0.0322047	−	0.0403834i	−0.797673	+	0.603090i	$0.793936\pi$
$674$	−23.2252	−	11.1847i	−0.894601	−	0.430817i
$675$	1.22568	+	5.37005i	0.0471764	+	0.206693i
$676$	−12.9433	−	6.23315i	−0.497818	−	0.239737i
$677$	7.53823	−	9.45264i	0.289718	−	0.363294i	−0.615578	−	0.788076i	$-0.711078\pi$
$677$	7.53823	−	9.45264i	0.289718	−	0.363294i	0.905296	+	0.424781i	$0.139649\pi$
$678$	1.98410	−	8.69291i	0.0761989	−	0.333849i
$679$	−8.17045	+	10.2454i	−0.313553	+	0.393183i
$680$	1.36118	+	5.96372i	0.0521989	+	0.228698i
$681$	25.3181			0.970192
$682$	9.46869			0.362575
$683$	2.32996	+	10.2082i	0.0891534	+	0.390606i	0.999742	−	0.0227071i	$-0.00722851\pi$
$683$	2.32996	+	10.2082i	0.0891534	+	0.390606i	−0.910589	+	0.413313i	$0.864371\pi$
$684$	1.15553	+	1.44898i	0.0441826	+	0.0554033i
$685$	16.6871	−	8.03607i	0.637580	−	0.307042i
$686$	13.1366	+	6.32624i	0.501557	+	0.241537i
$687$	−0.652613			−0.0248988
$688$	−1.58175	+	6.36381i	−0.0603036	+	0.242618i
$689$	−68.1545			−2.59648
$690$	1.38213	+	0.665599i	0.0526168	+	0.0253389i
$691$	−10.1655	+	4.89543i	−0.386713	+	0.186231i	−0.617131	−	0.786861i	$-0.711705\pi$
$691$	−10.1655	+	4.89543i	−0.386713	+	0.186231i	0.230418	+	0.973092i	$0.425991\pi$
$692$	2.24314	+	2.81281i	0.0852714	+	0.106927i
$693$	0.360021	+	1.57735i	0.0136761	+	0.0599187i
$694$	−19.0087			−0.721561
$695$	11.6935			0.443559
$696$	1.42300	+	6.23459i	0.0539388	+	0.236321i
$697$	−44.0050	+	55.1806i	−1.66681	+	2.09011i
$698$	2.87264	−	12.5858i	0.108731	−	0.476381i
$699$	20.5350	−	25.7500i	0.776704	−	0.973956i
$700$	1.03624	+	0.499026i	0.0391661	+	0.0188614i
$701$	−7.68183	−	33.6563i	−0.290139	−	1.27118i	−0.884332	−	0.466859i	$-0.845386\pi$
$701$	−7.68183	−	33.6563i	−0.290139	−	1.27118i	0.594193	−	0.804323i	$-0.297472\pi$
$702$	25.9610	+	12.5021i	0.979833	+	0.471863i
$703$	−3.72408	−	4.66985i	−0.140456	−	0.176127i
$704$	0.698790	−	3.06160i	0.0263366	−	0.115388i
$705$	−1.19115	+	5.21878i	−0.0448614	+	0.196551i
$706$	−3.25371	+	1.56690i	−0.122455	+	0.0589711i
$707$	2.54055	+	3.18574i	0.0955470	+	0.119812i
$708$	−14.4017	+	18.0591i	−0.541248	+	0.678703i
$709$	37.3231	−	17.9739i	1.40170	−	0.675022i	0.428193	−	0.903687i	$-0.359150\pi$
$709$	37.3231	−	17.9739i	1.40170	−	0.675022i	0.973505	+	0.228665i	$0.0734360\pi$
$710$	5.55865	−	2.67690i	0.208612	−	0.100462i
$711$	2.70819	−	3.39597i	0.101565	−	0.127359i
$712$	2.51257	+	3.15067i	0.0941627	+	0.118076i
$713$	−2.60867	+	1.25627i	−0.0976955	+	0.0470477i
$714$	−2.50098	+	10.9575i	−0.0935967	+	0.410074i
$715$	−3.65554	+	16.0160i	−0.136710	+	0.598963i
$716$	5.12185	+	6.42260i	0.191413	+	0.240024i
$717$	13.2198	+	6.36633i	0.493703	+	0.237755i
$718$	6.80489	+	29.8142i	0.253956	+	1.11265i
$719$	32.7009	+	15.7479i	1.21954	+	0.587299i	0.929183	−	0.369620i	$-0.120512\pi$
$719$	32.7009	+	15.7479i	1.21954	+	0.587299i	0.290355	+	0.956919i	$0.406227\pi$
$720$	−0.279294	+	0.350223i	−0.0104087	+	0.0130520i
$721$	1.00480	−	4.40230i	0.0374206	−	0.163950i
$722$	1.17379	−	1.47189i	0.0436840	−	0.0547780i
$723$	−9.35062	−	40.9677i	−0.347753	−	1.52361i
$724$	26.2753			0.976514
$725$	4.00305			0.148669
$726$	−0.404649	−	1.77288i	−0.0150179	−	0.0657978i
$727$	18.7883	+	23.5598i	0.696819	+	0.873783i	0.996781	−	0.0801676i	$-0.0255455\pi$
$727$	18.7883	+	23.5598i	0.696819	+	0.873783i	−0.299962	+	0.953951i	$0.596974\pi$
$728$	5.42082	−	2.61053i	0.200909	−	0.0967526i
$729$	−26.7928	−	12.9027i	−0.992324	−	0.477878i
$730$	−4.64357			−0.171866
$731$	−9.67569	+	38.9280i	−0.357868	+	1.43980i
$732$	−12.1546			−0.449247
$733$	15.3975	+	7.41507i	0.568721	+	0.273882i	0.696067	−	0.717977i	$-0.254932\pi$
$733$	15.3975	+	7.41507i	0.568721	+	0.273882i	−0.127346	+	0.991858i	$0.540646\pi$
$734$	30.1939	−	14.5406i	1.11448	−	0.536704i
$735$	−5.65466	−	7.09072i	−0.208575	−	0.261545i
$736$	0.213681	+	0.936198i	0.00787639	+	0.0345087i
$737$	−30.4281			−1.12083
$738$	−5.16845			−0.190253
$739$	−2.01507	−	8.82860i	−0.0741256	−	0.324765i	0.924247	−	0.381795i	$-0.124694\pi$
$739$	−2.01507	−	8.82860i	−0.0741256	−	0.324765i	−0.998372	+	0.0570300i	$0.981837\pi$
$740$	0.900119	−	1.12871i	0.0330890	−	0.0414924i
$741$	−7.69377	+	33.7086i	−0.282638	+	1.23832i
$742$	9.34262	−	11.7153i	0.342978	−	0.430081i
$743$	−26.2685	−	12.6502i	−0.963698	−	0.464092i	−0.115230	−	0.993339i	$-0.536760\pi$
$743$	−26.2685	−	12.6502i	−0.963698	−	0.464092i	−0.848468	+	0.529246i	$0.822475\pi$
$744$	1.07184	+	4.69603i	0.0392955	+	0.172165i
$745$	14.6912	+	7.07491i	0.538244	+	0.259205i
$746$	−15.3522	−	19.2510i	−0.562084	−	0.704831i
$747$	−0.132182	+	0.579127i	−0.00483628	+	0.0211891i
$748$	4.27456	−	18.7281i	0.156293	−	0.684766i
$749$	6.34055	−	3.05345i	0.231679	−	0.111571i
$750$	−0.996033	−	1.24899i	−0.0363700	−	0.0456065i
$751$	26.6298	−	33.3927i	0.971734	−	1.21852i	−0.00409814	−	0.999992i	$-0.501304\pi$
$751$	26.6298	−	33.3927i	0.971734	−	1.21852i	0.975832	−	0.218524i	$-0.0701241\pi$
$752$	−3.01899	+	1.45387i	−0.110091	+	0.0530172i
$753$	20.2972	−	9.77463i	0.739672	−	0.356207i
$754$	13.0565	−	16.3723i	0.475488	−	0.596243i
$755$	7.25781	+	9.10101i	0.264139	+	0.331220i
$756$	−5.70775	+	2.74871i	−0.207589	+	0.0999696i
$757$	−8.45404	+	37.0396i	−0.307267	+	1.34623i	0.551634	+	0.834086i	$0.314004\pi$
$757$	−8.45404	+	37.0396i	−0.307267	+	1.34623i	−0.858902	+	0.512140i	$0.828853\pi$
$758$	5.28881	−	23.1718i	0.192098	−	0.841637i
$759$	−3.00362	−	3.76641i	−0.109024	−	0.136712i
$760$	−3.72759	−	1.79511i	−0.135214	−	0.0651156i
$761$	−3.60455	−	15.7926i	−0.130665	−	0.572480i	−0.997293	−	0.0735260i	$-0.976575\pi$
$761$	−3.60455	−	15.7926i	−0.130665	−	0.572480i	0.866628	−	0.498954i	$-0.166282\pi$
$762$	9.21425	+	4.43735i	0.333797	+	0.160748i
$763$	−12.5596	+	15.7492i	−0.454687	+	0.570159i
$764$	0.164602	−	0.721170i	0.00595510	−	0.0260910i
$765$	−1.70846	+	2.14235i	−0.0617696	+	0.0774567i
$766$	4.66714	+	20.4481i	0.168631	+	0.738819i
$767$	75.6387			2.73116
$768$	1.59751			0.0576453
$769$	3.40883	+	14.9351i	0.122926	+	0.538572i	0.998463	+	0.0554219i	$0.0176504\pi$
$769$	3.40883	+	14.9351i	0.122926	+	0.538572i	−0.875537	+	0.483150i	$0.839492\pi$
$770$	−2.25193	−	2.82383i	−0.0811539	−	0.101764i
$771$	−21.5186	+	10.3628i	−0.774974	+	0.373208i
$772$	17.8303	+	8.58661i	0.641726	+	0.309039i
$773$	−45.9864			−1.65402			−0.827008	−	0.562190i	$-0.809959\pi$
$773$	−45.9864			−1.65402			−0.827008	+	0.562190i	$0.809959\pi$
$774$	−2.67053	+	1.22341i	−0.0959900	+	0.0439744i
$775$	3.01519			0.108309
$776$	10.2654	+	4.94356i	0.368507	+	0.177464i
$777$	2.38987	−	1.15090i	0.0857362	−	0.0412884i
$778$	−2.32633	−	2.91712i	−0.0834029	−	0.104584i
$779$	−10.6223	−	46.5393i	−0.380583	−	1.66744i
$780$	−8.35699			−0.299228
$781$	−19.3747			−0.693281
$782$	1.30711	+	5.72680i	0.0467420	+	0.204790i
$783$	−13.7476	+	17.2389i	−0.491298	+	0.616068i
$784$	1.26329	−	5.53485i	0.0451176	−	0.197673i
$785$	−8.17259	+	10.2481i	−0.291692	+	0.365771i
$786$	1.23054	+	0.592598i	0.0438920	+	0.0211373i
$787$	−2.94451	−	12.9007i	−0.104960	−	0.459861i	−0.999906	−	0.0136869i	$-0.995643\pi$
$787$	−2.94451	−	12.9007i	−0.104960	−	0.459861i	0.894946	−	0.446175i	$-0.147214\pi$
$788$	0.0208083	+	0.0100208i	0.000741267	+	0.000356975i
$789$	−17.7161	−	22.2152i	−0.630708	−	0.790883i
$790$	−2.15769	+	9.45347i	−0.0767673	+	0.336339i
$791$	1.42846	−	6.25850i	0.0507903	−	0.222527i
$792$	1.26741	−	0.610352i	0.0450354	−	0.0216879i
$793$	24.8159	+	31.1182i	0.881240	+	1.10504i
$794$	11.9363	−	14.9677i	0.423604	−	0.531183i
$795$	−18.7518	+	9.03040i	−0.665059	+	0.320275i
$796$	−2.60631	+	1.25513i	−0.0923781	+	0.0444870i
$797$	7.72299	−	9.68433i	0.273563	−	0.343037i	−0.626004	−	0.779820i	$-0.715311\pi$
$797$	7.72299	−	9.68433i	0.273563	−	0.343037i	0.899567	+	0.436783i	$0.143882\pi$
$798$	−4.73960	−	5.94328i	−0.167780	−	0.210390i
$799$	−18.4675	+	8.89346i	−0.653331	+	0.314628i
$800$	0.222521	−	0.974928i	0.00786730	−	0.0344689i
$801$	−0.401691	+	1.75992i	−0.0141930	+	0.0621838i
$802$	14.1144	+	17.6990i	0.498399	+	0.624972i
$803$	13.1382	+	6.32704i	0.463638	+	0.223276i
$804$	−3.44440	−	15.0909i	−0.121475	−	0.532216i
$805$	0.995072	+	0.479201i	0.0350717	+	0.0168896i
$806$	9.83443	−	12.3320i	0.346403	−	0.434375i
$807$	2.09618	−	9.18395i	0.0737889	−	0.323290i
$808$	2.20891	−	2.76988i	0.0777091	−	0.0974441i
$809$	−0.480542	−	2.10539i	−0.0168949	−	0.0740216i	0.965778	−	0.259371i	$-0.0835153\pi$
$809$	−0.480542	−	2.10539i	−0.0168949	−	0.0740216i	−0.982673	+	0.185350i	$0.940658\pi$
$810$	7.45548			0.261959
$811$	−30.4646			−1.06976			−0.534879	−	0.844929i	$-0.679643\pi$
$811$	−30.4646			−1.06976			−0.534879	+	0.844929i	$0.679643\pi$
$812$	1.02450	+	4.48862i	0.0359529	+	0.157520i
$813$	−5.88893	−	7.38448i	−0.206534	−	0.258985i
$814$	−4.08466	+	1.96707i	−0.143167	+	0.0689457i
$815$	−7.86196	−	3.78612i	−0.275392	−	0.132622i
$816$	9.77213			0.342093
$817$	−16.5047	−	21.5324i	−0.577426	−	0.753322i
$818$	9.24551			0.323262
$819$	2.42827	+	1.16939i	0.0848505	+	0.0408619i
$820$	10.3953	−	5.00613i	0.363021	−	0.174822i
$821$	−2.84390	−	3.56613i	−0.0992527	−	0.124459i	0.729725	−	0.683741i	$-0.239648\pi$
$821$	−2.84390	−	3.56613i	−0.0992527	−	0.124459i	−0.828977	+	0.559282i	$0.811077\pi$
$822$	−6.58394	−	28.8461i	−0.229641	−	1.00612i
$823$	−31.3835			−1.09396			−0.546980	−	0.837146i	$-0.684223\pi$
$823$	−31.3835			−1.09396			−0.546980	+	0.837146i	$0.684223\pi$
$824$	−3.92607			−0.136771
$825$	1.11633	+	4.89094i	0.0388655	+	0.170281i
$826$	−10.3685	+	13.0017i	−0.360768	+	0.452389i
$827$	1.54165	−	6.75443i	0.0536086	−	0.234874i	−0.941025	−	0.338338i	$-0.890135\pi$
$827$	1.54165	−	6.75443i	0.0536086	−	0.234874i	0.994633	+	0.103463i	$0.0329925\pi$
$828$	−0.268198	+	0.336310i	−0.00932053	+	0.0116876i
$829$	6.80695	+	3.27805i	0.236415	+	0.113852i	0.548341	−	0.836255i	$-0.315260\pi$
$829$	6.80695	+	3.27805i	0.236415	+	0.113852i	−0.311926	+	0.950107i	$0.600974\pi$
$830$	−0.295080	−	1.29283i	−0.0102424	−	0.0448748i
$831$	−5.60931	−	2.70130i	−0.194585	−	0.0937071i
$832$	−3.26163	−	4.08995i	−0.113077	−	0.141794i
$833$	7.72767	−	33.8571i	0.267748	−	1.17308i
$834$	4.15680	−	18.2121i	0.143938	−	0.630634i
$835$	19.3837	−	9.33469i	0.670800	−	0.323040i
$836$	8.10072	+	10.1580i	0.280169	+	0.351321i
$837$	−10.3550	+	12.9847i	−0.357921	+	0.448818i
$838$	30.9430	−	14.9014i	1.06891	−	0.514759i
$839$	44.2252	−	21.2978i	1.52682	−	0.735280i	0.532987	−	0.846123i	$-0.321069\pi$
$839$	44.2252	−	21.2978i	1.52682	−	0.735280i	0.993838	+	0.110843i	$0.0353552\pi$
$840$	1.14557	−	1.43651i	0.0395261	−	0.0495641i
$841$	−8.09016	−	10.1447i	−0.278971	−	0.349818i
$842$	17.5204	−	8.43737i	0.603792	−	0.290771i
$843$	−1.67421	+	7.33519i	−0.0576628	+	0.252637i
$844$	−3.32820	+	14.5818i	−0.114561	+	0.501926i
$845$	8.95703	+	11.2318i	0.308131	+	0.386384i
$846$	−1.35236	−	0.651265i	−0.0464953	−	0.0223909i
$847$	−0.291329	−	1.27639i	−0.0100102	−	0.0438574i
$848$	−11.7381	−	5.65279i	−0.403089	−	0.194118i
$849$	−11.4245	+	14.3259i	−0.392088	+	0.491663i
$850$	1.36118	−	5.96372i	0.0466881	−	0.204554i
$851$	0.864361	−	1.08387i	0.0296299	−	0.0371547i
$852$	−2.19318	−	9.60896i	−0.0751372	−	0.329198i
$853$	−35.2029			−1.20532			−0.602662	−	0.797996i	$-0.705893\pi$
$853$	−35.2029			−1.20532			−0.602662	+	0.797996i	$0.705893\pi$
$854$	−8.75076			−0.299445
$855$	−0.412402	−	1.80685i	−0.0141039	−	0.0617931i
$856$	−3.81502	−	4.78389i	−0.130395	−	0.163510i
$857$	38.2709	−	18.4303i	1.30731	−	0.629566i	0.355046	−	0.934849i	$-0.384465\pi$
$857$	38.2709	−	18.4303i	1.30731	−	0.629566i	0.952262	+	0.305283i	$0.0987510\pi$
$858$	23.6448	+	11.3867i	0.807219	+	0.388736i
$859$	−25.3236			−0.864030			−0.432015	−	0.901866i	$-0.642197\pi$
$859$	−25.3236			−0.864030			−0.432015	+	0.901866i	$0.642197\pi$
$860$	4.18626	−	5.04730i	0.142750	−	0.172112i
$861$	21.1993			0.722472
$862$	7.16878	+	3.45230i	0.244170	+	0.117586i
$863$	−4.56751	+	2.19960i	−0.155480	+	0.0748751i	−0.510005	−	0.860171i	$-0.670357\pi$
$863$	−4.56751	+	2.19960i	−0.155480	+	0.0748751i	0.354526	+	0.935046i	$0.384642\pi$
$864$	3.43427	+	4.30644i	0.116836	+	0.146508i
$865$	−0.800568	−	3.50752i	−0.0272201	−	0.119259i
$866$	16.8130			0.571329
$867$	32.6193			1.10781
$868$	0.771676	+	3.38093i	0.0261924	+	0.114756i
$869$	18.9856	−	23.8072i	0.644041	−	0.807602i
$870$	1.42300	−	6.23459i	0.0482444	−	0.211372i
$871$	−31.6034	+	39.6294i	−1.07084	+	1.34279i
$872$	15.7799	+	7.59921i	0.534376	+	0.257342i
$873$	1.13571	+	4.97589i	0.0384381	+	0.168408i
$874$	−3.57951	−	1.72380i	−0.121079	−	0.0583084i
$875$	−0.717099	−	0.899214i	−0.0242424	−	0.0303990i
$876$	−1.65070	+	7.23217i	−0.0557718	+	0.244352i
$877$	−5.26560	+	23.0701i	−0.177807	+	0.779021i	0.804834	+	0.593500i	$0.202254\pi$
$877$	−5.26560	+	23.0701i	−0.177807	+	0.779021i	−0.982640	+	0.185521i	$0.940603\pi$
$878$	16.5621	−	7.97590i	0.558944	−	0.269173i
$879$	7.64784	+	9.59009i	0.257955	+	0.323466i
$880$	−1.95796	+	2.45521i	−0.0660030	+	0.0827651i
$881$	6.98147	−	3.36210i	0.235212	−	0.113272i	−0.312566	−	0.949896i	$-0.601188\pi$
$881$	6.98147	−	3.36210i	0.235212	−	0.113272i	0.547777	+	0.836624i	$0.315474\pi$
$882$	2.29126	−	1.10341i	0.0771507	−	0.0371538i
$883$	−3.95097	+	4.95436i	−0.132961	+	0.166727i	−0.843855	−	0.536572i	$-0.819719\pi$
$883$	−3.95097	+	4.95436i	−0.132961	+	0.166727i	0.710894	+	0.703299i	$0.248291\pi$
$884$	−19.9517	−	25.0186i	−0.671048	−	0.841467i
$885$	20.8110	−	10.0220i	0.699554	−	0.336888i
$886$	−1.44686	+	6.33912i	−0.0486083	+	0.212967i
$887$	−2.26467	+	9.92216i	−0.0760401	+	0.333153i	−0.998612	−	0.0526721i	$-0.983226\pi$
$887$	−2.26467	+	9.92216i	−0.0760401	+	0.333153i	0.922572	+	0.385826i	$0.126083\pi$
$888$	−1.43795	−	1.80314i	−0.0482545	−	0.0605093i
$889$	6.63385	+	3.19469i	0.222492	+	0.107147i
$890$	−0.896727	−	3.92882i	−0.0300584	−	0.131694i
$891$	−21.0941	−	10.1584i	−0.706679	−	0.340319i
$892$	4.71746	−	5.91550i	0.157952	−	0.198066i
$893$	3.08491	−	13.5159i	0.103232	−	0.452291i
$894$	16.2413	−	20.3660i	0.543191	−	0.681140i
$895$	−1.82797	−	8.00885i	−0.0611022	−	0.267706i
$896$	1.15014			0.0384234
$897$	−8.02499			−0.267947
$898$	5.79134	+	25.3735i	0.193260	+	0.846725i
$899$	7.52549	+	9.43666i	0.250989	+	0.314730i
$900$	0.403591	−	0.194359i	0.0134530	−	0.00647864i
$901$	−71.8032	−	34.5786i	−2.39211	−	1.15198i
$902$	−36.2330			−1.20643
$903$	10.9537	−	5.01803i	0.364515	−	0.166990i
$904$	−5.58147			−0.185637
$905$	−23.6732	−	11.4004i	−0.786925	−	0.378963i
$906$	16.7545	−	8.06853i	0.556630	−	0.268059i
$907$	18.4123	+	23.0884i	0.611372	+	0.766636i	0.987102	−	0.160093i	$-0.0511794\pi$
$907$	18.4123	+	23.0884i	0.611372	+	0.766636i	−0.375730	+	0.926729i	$0.622608\pi$
$908$	−3.52661	−	15.4511i	−0.117035	−	0.512763i
$909$	1.58701			0.0526378
$910$	−6.01665			−0.199450
$911$	−12.0289	−	52.7022i	−0.398536	−	1.74610i	−0.633166	−	0.774016i	$-0.718245\pi$
$911$	−12.0289	−	52.7022i	−0.398536	−	1.74610i	0.234629	−	0.972085i	$-0.424612\pi$
$912$	−4.12090	+	5.16745i	−0.136457	+	0.171111i
$913$	−0.926650	+	4.05992i	−0.0306677	+	0.134364i
$914$	−17.7078	+	22.2049i	−0.585723	+	0.734473i
$915$	10.9509	+	5.27368i	0.362026	+	0.174342i
$916$	0.0909039	+	0.398276i	0.00300355	+	0.0131594i
$917$	0.885934	+	0.426643i	0.0292561	+	0.0140890i
$918$	21.0078	+	26.3429i	0.693359	+	0.869445i
$919$	9.19765	−	40.2975i	0.303402	−	1.32929i	−0.561552	−	0.827442i	$-0.689795\pi$
$919$	9.19765	−	40.2975i	0.303402	−	1.32929i	0.864954	−	0.501851i	$-0.167347\pi$
$920$	0.213681	−	0.936198i	0.00704485	−	0.0308655i
$921$	29.2235	−	14.0733i	0.962947	−	0.463731i
$922$	20.9023	+	26.2107i	0.688381	+	0.863203i
$923$	−20.1231	+	25.2335i	−0.662359	+	0.830572i
$924$	−5.19852	+	2.50347i	−0.171019	+	0.0823582i
$925$	−1.30071	+	0.626389i	−0.0427671	+	0.0205955i
$926$	−0.382446	+	0.479572i	−0.0125679	+	0.0157597i
$927$	−1.09653	−	1.37500i	−0.0360146	−	0.0451609i
$928$	3.60662	−	1.73686i	0.118393	−	0.0570151i
$929$	−7.43303	+	32.5662i	−0.243870	+	1.06846i	0.693590	+	0.720370i	$0.256028\pi$
$929$	−7.43303	+	32.5662i	−0.243870	+	1.06846i	−0.937460	+	0.348094i	$0.886829\pi$
$930$	1.07184	−	4.69603i	0.0351470	−	0.153989i
$931$	14.6447	+	18.3639i	0.479961	+	0.601852i
$932$	−18.5751	−	8.94527i	−0.608446	−	0.293012i
$933$	−10.4799	−	45.9154i	−0.343096	−	1.50320i
$934$	28.2440	+	13.6016i	0.924171	+	0.445057i
$935$	−11.9770	+	15.0187i	−0.391691	+	0.491165i
$936$	0.521444	−	2.28460i	0.0170439	−	0.0746744i
$937$	24.3052	−	30.4778i	0.794017	−	0.995666i	−0.205837	−	0.978586i	$-0.565992\pi$
$937$	24.3052	−	30.4778i	0.794017	−	0.995666i	0.999854	−	0.0170798i	$-0.00543695\pi$
$938$	−2.47982	−	10.8648i	−0.0809689	−	0.354748i
$939$	−38.0160			−1.24061
$940$	3.35083			0.109292
$941$	−10.6164	−	46.5137i	−0.346086	−	1.51630i	−0.785979	−	0.618253i	$-0.787841\pi$
$941$	−10.6164	−	46.5137i	−0.346086	−	1.51630i	0.439893	−	0.898050i	$-0.355016\pi$
$942$	13.0558	+	16.3715i	0.425382	+	0.533412i
$943$	9.98236	−	4.80725i	0.325070	−	0.156546i
$944$	13.0271	+	6.27353i	0.423997	+	0.204186i
$945$	6.33513			0.206082
$946$	−18.7215	+	8.57659i	−0.608688	+	0.278849i
$947$	45.1162			1.46608			0.733039	−	0.680187i	$-0.238101\pi$
$947$	45.1162			1.46608			0.733039	+	0.680187i	$0.238101\pi$
$948$	13.9564	+	6.72104i	0.453282	+	0.218289i
$949$	21.8860	−	10.5398i	0.710450	−	0.342135i
$950$	2.57957	+	3.23468i	0.0836924	+	0.104947i
$951$	−1.31262	−	5.75094i	−0.0425645	−	0.186487i
$952$	7.03549			0.228022
$953$	18.2616			0.591550			0.295775	−	0.955258i	$-0.404422\pi$
$953$	18.2616			0.591550			0.295775	+	0.955258i	$0.404422\pi$
$954$	−1.29865	−	5.68975i	−0.0420453	−	0.184213i
$955$	−0.461205	+	0.578333i	−0.0149243	+	0.0187144i
$956$	2.04382	−	8.95455i	0.0661018	−	0.289611i
$957$	−12.5210	+	15.7009i	−0.404747	+	0.507537i
$958$	−11.8640	−	5.71338i	−0.383307	−	0.184591i
$959$	−4.74014	−	20.7679i	−0.153067	−	0.670630i
$960$	−1.43931	−	0.693135i	−0.0464535	−	0.0223708i
$961$	−13.6598	−	17.1289i	−0.440639	−	0.552544i
$962$	−1.68053	+	7.36289i	−0.0541825	+	0.237389i
$963$	0.609916	−	2.67222i	0.0196543	−	0.0861110i
$964$	−23.6993	+	11.4130i	−0.763302	+	0.367587i
$965$	−12.3389	−	15.4725i	−0.397204	−	0.498078i
$966$	1.10007	−	1.37944i	0.0353940	−	0.0443827i
$967$	−6.93153	+	3.33805i	−0.222903	+	0.107344i	−0.542003	−	0.840377i	$-0.682334\pi$
$967$	−6.93153	+	3.33805i	−0.222903	+	0.107344i	0.319100	+	0.947721i	$0.396619\pi$
$968$	−1.02559	+	0.493897i	−0.0329636	+	0.0158744i
$969$	−25.2079	+	31.6097i	−0.809795	+	1.01545i
$970$	−7.10389	−	8.90799i	−0.228092	−	0.286018i
$971$	−34.8920	+	16.8031i	−1.11974	+	0.539237i	−0.899811	−	0.436279i	$-0.856296\pi$
$971$	−34.8920	+	16.8031i	−1.11974	+	0.539237i	−0.219927	+	0.975516i	$0.570582\pi$
$972$	−1.02676	+	4.49853i	−0.0329333	+	0.144290i
$973$	2.99271	−	13.1119i	0.0959418	−	0.420348i
$974$	−25.9995	−	32.6024i	−0.833078	−	1.04465i
$975$	7.52938	+	3.62596i	0.241133	+	0.116124i
$976$	1.69304	+	7.41769i	0.0541928	+	0.237434i
$977$	11.3581	+	5.46978i	0.363378	+	0.174994i	0.606659	−	0.794962i	$-0.292509\pi$
$977$	11.3581	+	5.46978i	0.363378	+	0.174994i	−0.243281	+	0.969956i	$0.578224\pi$
$978$	−8.69150	+	10.8988i	−0.277923	+	0.348505i
$979$	−2.81602	+	12.3378i	−0.0900004	+	0.394318i
$980$	−3.53967	+	4.43860i	−0.113070	+	0.141786i
$981$	1.74581	+	7.64891i	0.0557395	+	0.244211i
$982$	19.7522			0.630319
$983$	−18.3019			−0.583741			−0.291870	−	0.956458i	$-0.594278\pi$
$983$	−18.3019			−0.583741			−0.291870	+	0.956458i	$0.594278\pi$
$984$	−4.10151	−	17.9699i	−0.130751	−	0.572859i
$985$	−0.0143998	−	0.0180568i	−0.000458816	−	0.000575338i
$986$	22.0620	−	10.6245i	0.702598	−	0.338353i
$987$	5.54698	+	2.67128i	0.176562	+	0.0850279i
$988$	21.6433			0.688566
$989$	4.01995	−	4.84679i	0.127827	−	0.154119i
$990$	−1.40672			−0.0447084
$991$	13.8682	+	6.67857i	0.440537	+	0.212152i	0.640986	−	0.767553i	$-0.278526\pi$
$991$	13.8682	+	6.67857i	0.440537	+	0.212152i	−0.200449	+	0.979704i	$0.564240\pi$
$992$	2.71659	−	1.30824i	0.0862518	−	0.0415367i
$993$	1.46776	+	1.84051i	0.0465778	+	0.0584068i
$994$	−1.57899	−	6.91802i	−0.0500826	−	0.219426i
$995$	2.89278			0.0917074
$996$	−2.11843			−0.0671250
$997$	9.55878	+	41.8798i	0.302730	+	1.32635i	0.865988	+	0.500064i	$0.166690\pi$
$997$	9.55878	+	41.8798i	0.302730	+	1.32635i	−0.563259	+	0.826281i	$0.690453\pi$
$998$	−3.37351	+	4.23025i	−0.106787	+	0.133906i
$999$	1.76949	−	7.75263i	0.0559841	−	0.245282i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.k.c.21.1	✓	18
43.41	even	7	inner	430.2.k.c.41.1	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.k.c.21.1	✓	18	1.1	even	1	trivial
430.2.k.c.41.1	yes	18	43.41	even	7	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.900969 + 0.433884i) q^{2} +(-1.43931 + 0.693135i) q^{3} +(0.623490 + 0.781831i) q^{4} +(-0.222521 - 0.974928i) q^{5} -1.59751 q^{6} -1.15014 q^{7} +(0.222521 + 0.974928i) q^{8} +(-0.279294 + 0.350223i) q^{9} +O(q^{10})\)	\(q+(0.900969 + 0.433884i) q^{2} +(-1.43931 + 0.693135i) q^{3} +(0.623490 + 0.781831i) q^{4} +(-0.222521 - 0.974928i) q^{5} -1.59751 q^{6} -1.15014 q^{7} +(0.222521 + 0.974928i) q^{8} +(-0.279294 + 0.350223i) q^{9} +(0.222521 - 0.974928i) q^{10} +(-1.95796 + 2.45521i) q^{11} +(-1.43931 - 0.693135i) q^{12} +(1.16406 + 5.10009i) q^{13} +(-1.03624 - 0.499026i) q^{14} +(0.996033 + 1.24899i) q^{15} +(-0.222521 + 0.974928i) q^{16} +(-1.36118 + 5.96372i) q^{17} +(-0.403591 + 0.194359i) q^{18} +(-2.57957 - 3.23468i) q^{19} +(0.623490 - 0.781831i) q^{20} +(1.65540 - 0.797200i) q^{21} +(-2.82934 + 1.36254i) q^{22} +(0.598721 - 0.750772i) q^{23} +(-0.996033 - 1.24899i) q^{24} +(-0.900969 + 0.433884i) q^{25} +(-1.16406 + 5.10009i) q^{26} +(1.22568 - 5.37005i) q^{27} +(-0.717099 - 0.899214i) q^{28} +(-3.60662 - 1.73686i) q^{29} +(0.355480 + 1.55746i) q^{30} +(-2.71659 - 1.30824i) q^{31} +(-0.623490 + 0.781831i) q^{32} +(1.11633 - 4.89094i) q^{33} +(-3.81394 + 4.78253i) q^{34} +(0.255930 + 1.12130i) q^{35} -0.447952 q^{36} +1.44368 q^{37} +(-0.920639 - 4.03358i) q^{38} +(-5.21050 - 6.53376i) q^{39} +(0.900969 - 0.433884i) q^{40} +(10.3953 + 5.00613i) q^{41} +1.83736 q^{42} +(6.55623 + 0.126009i) q^{43} -3.14033 q^{44} +(0.403591 + 0.194359i) q^{45} +(0.865177 - 0.416647i) q^{46} +(2.08921 + 2.61978i) q^{47} +(-0.355480 - 1.55746i) q^{48} -5.67718 q^{49} -1.00000 q^{50} +(-2.17450 - 9.52712i) q^{51} +(-3.26163 + 4.08995i) q^{52} +(-2.89908 + 12.7017i) q^{53} +(3.43427 - 4.30644i) q^{54} +(2.82934 + 1.36254i) q^{55} +(-0.255930 - 1.12130i) q^{56} +(5.95488 + 2.86772i) q^{57} +(-2.49586 - 3.12971i) q^{58} +(3.21743 - 14.0965i) q^{59} +(-0.355480 + 1.55746i) q^{60} +(6.85497 - 3.30118i) q^{61} +(-1.87994 - 2.35737i) q^{62} +(0.321226 - 0.402805i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(4.71319 - 2.26975i) q^{65} +(3.12787 - 3.92223i) q^{66} +(6.04127 + 7.57551i) q^{67} +(-5.51131 + 2.65411i) q^{68} +(-0.341358 + 1.49559i) q^{69} +(-0.255930 + 1.12130i) q^{70} +(3.84671 + 4.82362i) q^{71} +(-0.403591 - 0.194359i) q^{72} +(-1.03329 - 4.52714i) q^{73} +(1.30071 + 0.626389i) q^{74} +(0.996033 - 1.24899i) q^{75} +(0.920639 - 4.03358i) q^{76} +(2.25193 - 2.82383i) q^{77} +(-1.85960 - 8.14746i) q^{78} -9.69659 q^{79} +1.00000 q^{80} +(1.65900 + 7.26856i) q^{81} +(7.19379 + 9.02073i) q^{82} +(1.19476 - 0.575364i) q^{83} +(1.65540 + 0.797200i) q^{84} +6.11709 q^{85} +(5.85228 + 2.95817i) q^{86} +6.39492 q^{87} +(-2.82934 - 1.36254i) q^{88} +(3.63077 - 1.74849i) q^{89} +(0.279294 + 0.350223i) q^{90} +(-1.33883 - 5.86580i) q^{91} +0.960274 q^{92} +4.81680 q^{93} +(0.745630 + 3.26682i) q^{94} +(-2.57957 + 3.23468i) q^{95} +(0.355480 - 1.55746i) q^{96} +(7.10389 - 8.90799i) q^{97} +(-5.11497 - 2.46324i) q^{98} +(-0.313024 - 1.37145i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{2} + 5 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} + 8 q^{7} + 3 q^{8} - 6 q^{9}+O(q^{10}) \) 18 * q + 3 * q^2 + 5 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 + 8 * q^7 + 3 * q^8 - 6 * q^9	\( 18 q + 3 q^{2} + 5 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} + 8 q^{7} + 3 q^{8} - 6 q^{9} + 3 q^{10} + 5 q^{11} + 5 q^{12} + 22 q^{13} - 8 q^{14} - 2 q^{15} - 3 q^{16} + q^{17} + 13 q^{18} - 7 q^{19} - 3 q^{20} + 10 q^{21} - 5 q^{22} + 8 q^{23} + 2 q^{24} - 3 q^{25} - 22 q^{26} + 20 q^{27} + q^{28} - 6 q^{29} + 2 q^{30} - 5 q^{31} + 3 q^{32} + 39 q^{33} - q^{34} - 13 q^{35} + 8 q^{36} - 18 q^{37} - 7 q^{39} + 3 q^{40} + 16 q^{41} + 4 q^{42} - 13 q^{43} - 2 q^{44} - 13 q^{45} - 8 q^{46} - 36 q^{47} - 2 q^{48} - 14 q^{49} - 18 q^{50} - 30 q^{51} - 20 q^{52} - 18 q^{53} + 29 q^{54} + 5 q^{55} + 13 q^{56} + 29 q^{57} - 8 q^{58} - 4 q^{59} - 2 q^{60} + 42 q^{61} - 2 q^{62} - 29 q^{63} - 3 q^{64} + 8 q^{65} + 24 q^{66} - 19 q^{67} + q^{68} - 51 q^{69} + 13 q^{70} - 27 q^{71} + 13 q^{72} + 28 q^{73} + 4 q^{74} - 2 q^{75} + 42 q^{77} - 35 q^{78} - 26 q^{79} + 18 q^{80} - 4 q^{81} + 19 q^{82} + 62 q^{83} + 10 q^{84} - 6 q^{85} - 15 q^{86} - 66 q^{87} - 5 q^{88} - 12 q^{89} + 6 q^{90} - 22 q^{91} - 20 q^{92} - 6 q^{93} - 6 q^{94} - 7 q^{95} + 2 q^{96} + 71 q^{97} - 28 q^{98} + 59 q^{99}+O(q^{100}) \) 18 * q + 3 * q^2 + 5 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 + 8 * q^7 + 3 * q^8 - 6 * q^9 + 3 * q^10 + 5 * q^11 + 5 * q^12 + 22 * q^13 - 8 * q^14 - 2 * q^15 - 3 * q^16 + q^17 + 13 * q^18 - 7 * q^19 - 3 * q^20 + 10 * q^21 - 5 * q^22 + 8 * q^23 + 2 * q^24 - 3 * q^25 - 22 * q^26 + 20 * q^27 + q^28 - 6 * q^29 + 2 * q^30 - 5 * q^31 + 3 * q^32 + 39 * q^33 - q^34 - 13 * q^35 + 8 * q^36 - 18 * q^37 - 7 * q^39 + 3 * q^40 + 16 * q^41 + 4 * q^42 - 13 * q^43 - 2 * q^44 - 13 * q^45 - 8 * q^46 - 36 * q^47 - 2 * q^48 - 14 * q^49 - 18 * q^50 - 30 * q^51 - 20 * q^52 - 18 * q^53 + 29 * q^54 + 5 * q^55 + 13 * q^56 + 29 * q^57 - 8 * q^58 - 4 * q^59 - 2 * q^60 + 42 * q^61 - 2 * q^62 - 29 * q^63 - 3 * q^64 + 8 * q^65 + 24 * q^66 - 19 * q^67 + q^68 - 51 * q^69 + 13 * q^70 - 27 * q^71 + 13 * q^72 + 28 * q^73 + 4 * q^74 - 2 * q^75 + 42 * q^77 - 35 * q^78 - 26 * q^79 + 18 * q^80 - 4 * q^81 + 19 * q^82 + 62 * q^83 + 10 * q^84 - 6 * q^85 - 15 * q^86 - 66 * q^87 - 5 * q^88 - 12 * q^89 + 6 * q^90 - 22 * q^91 - 20 * q^92 - 6 * q^93 - 6 * q^94 - 7 * q^95 + 2 * q^96 + 71 * q^97 - 28 * q^98 + 59 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more