LMFDB - Embedded newform 731.2.m.b.87.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (of order $8$, degree $4$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$29$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			87.20
Character	$\chi$	$=$	731.87
Dual form			731.2.m.b.689.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.629885 + 0.629885i) q^{2} +(-0.623684 + 0.258339i) q^{3} -1.20649i q^{4} +(1.24172 + 2.99777i) q^{5} +(-0.555573 - 0.230126i) q^{6} +(1.05484 - 2.54660i) q^{7} +(2.01972 - 2.01972i) q^{8} +(-1.79908 + 1.79908i) q^{9} +O(q^{10})$	\(q+(0.629885 + 0.629885i) q^{2} +(-0.623684 + 0.258339i) q^{3} -1.20649i q^{4} +(1.24172 + 2.99777i) q^{5} +(-0.555573 - 0.230126i) q^{6} +(1.05484 - 2.54660i) q^{7} +(2.01972 - 2.01972i) q^{8} +(-1.79908 + 1.79908i) q^{9} +(-1.10611 + 2.67039i) q^{10} +(2.43813 + 1.00991i) q^{11} +(0.311683 + 0.752468i) q^{12} +3.90919i q^{13} +(2.26850 - 0.939641i) q^{14} +(-1.54888 - 1.54888i) q^{15} +0.131406 q^{16} +(2.39130 - 3.35882i) q^{17} -2.26642 q^{18} +(-1.97187 - 1.97187i) q^{19} +(3.61677 - 1.49812i) q^{20} +1.86078i q^{21} +(0.899616 + 2.17187i) q^{22} +(6.55748 + 2.71620i) q^{23} +(-0.737897 + 1.78144i) q^{24} +(-3.90922 + 3.90922i) q^{25} +(-2.46234 + 2.46234i) q^{26} +(1.43230 - 3.45788i) q^{27} +(-3.07245 - 1.27265i) q^{28} +(3.24782 + 7.84093i) q^{29} -1.95123i q^{30} +(3.88493 - 1.60919i) q^{31} +(-3.95667 - 3.95667i) q^{32} -1.78152 q^{33} +(3.62192 - 0.609432i) q^{34} +8.94393 q^{35} +(2.17057 + 2.17057i) q^{36} +(-4.07323 + 1.68719i) q^{37} -2.48411i q^{38} +(-1.00989 - 2.43810i) q^{39} +(8.56257 + 3.54673i) q^{40} +(-0.278939 + 0.673418i) q^{41} +(-1.17208 + 1.17208i) q^{42} +(0.707107 - 0.707107i) q^{43} +(1.21844 - 2.94157i) q^{44} +(-7.62716 - 3.15927i) q^{45} +(2.41957 + 5.84136i) q^{46} +2.63427i q^{47} +(-0.0819561 + 0.0339473i) q^{48} +(-0.422760 - 0.422760i) q^{49} -4.92472 q^{50} +(-0.623700 + 2.71261i) q^{51} +4.71639 q^{52} +(-0.467704 - 0.467704i) q^{53} +(3.08025 - 1.27588i) q^{54} +8.56295i q^{55} +(-3.01295 - 7.27390i) q^{56} +(1.73924 + 0.720415i) q^{57} +(-2.89313 + 6.98464i) q^{58} +(-2.64678 + 2.64678i) q^{59} +(-1.86870 + 1.86870i) q^{60} +(-3.25823 + 7.86606i) q^{61} +(3.46066 + 1.43345i) q^{62} +(2.68380 + 6.47927i) q^{63} -5.24731i q^{64} +(-11.7188 + 4.85410i) q^{65} +(-1.12215 - 1.12215i) q^{66} +3.57275 q^{67} +(-4.05239 - 2.88507i) q^{68} -4.79150 q^{69} +(5.63365 + 5.63365i) q^{70} +(0.942201 - 0.390273i) q^{71} +7.26726i q^{72} +(-5.06462 - 12.2271i) q^{73} +(-3.62840 - 1.50293i) q^{74} +(1.42822 - 3.44802i) q^{75} +(-2.37904 + 2.37904i) q^{76} +(5.14366 - 5.14366i) q^{77} +(0.899606 - 2.17184i) q^{78} +(-5.51905 - 2.28607i) q^{79} +(0.163169 + 0.393926i) q^{80} -5.10619i q^{81} +(-0.599876 + 0.248477i) q^{82} +(1.82439 + 1.82439i) q^{83} +2.24501 q^{84} +(13.0383 + 2.99784i) q^{85} +0.890792 q^{86} +(-4.05123 - 4.05123i) q^{87} +(6.96406 - 2.88461i) q^{88} -14.0451i q^{89} +(-2.81425 - 6.79421i) q^{90} +(9.95515 + 4.12356i) q^{91} +(3.27706 - 7.91153i) q^{92} +(-2.00725 + 2.00725i) q^{93} +(-1.65929 + 1.65929i) q^{94} +(3.46271 - 8.35972i) q^{95} +(3.48987 + 1.44555i) q^{96} +(0.343547 + 0.829395i) q^{97} -0.532581i q^{98} +(-6.20328 + 2.56948i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 8 q^{6}+O(q^{10}) $ 116 * q - 8 * q^6	$ 116 q - 8 q^{6} - 8 q^{10} + 8 q^{14} + 4 q^{15} - 68 q^{16} - 4 q^{17} - 44 q^{18} + 12 q^{19} + 8 q^{20} - 16 q^{22} - 28 q^{23} - 12 q^{24} - 4 q^{25} - 8 q^{26} + 24 q^{28} + 80 q^{33} + 32 q^{34} - 112 q^{35} + 160 q^{36} - 20 q^{37} + 8 q^{39} - 112 q^{40} + 8 q^{41} + 4 q^{42} + 32 q^{44} - 52 q^{45} - 40 q^{46} + 40 q^{48} + 8 q^{49} + 100 q^{50} - 32 q^{51} - 152 q^{52} + 28 q^{53} - 36 q^{54} + 124 q^{56} - 104 q^{57} - 32 q^{58} - 36 q^{59} - 24 q^{60} + 52 q^{61} - 68 q^{62} + 20 q^{63} + 20 q^{65} - 60 q^{66} + 64 q^{67} - 128 q^{69} + 188 q^{70} + 52 q^{73} - 104 q^{74} + 36 q^{75} - 112 q^{76} + 28 q^{77} + 56 q^{78} - 108 q^{79} - 44 q^{80} + 52 q^{82} - 52 q^{83} + 120 q^{84} + 12 q^{85} - 20 q^{86} + 56 q^{87} + 36 q^{88} + 144 q^{90} - 16 q^{92} - 176 q^{93} - 8 q^{94} + 164 q^{95} - 164 q^{96} - 8 q^{97} - 24 q^{99}+O(q^{100}) $ 116 * q - 8 * q^6 - 8 * q^10 + 8 * q^14 + 4 * q^15 - 68 * q^16 - 4 * q^17 - 44 * q^18 + 12 * q^19 + 8 * q^20 - 16 * q^22 - 28 * q^23 - 12 * q^24 - 4 * q^25 - 8 * q^26 + 24 * q^28 + 80 * q^33 + 32 * q^34 - 112 * q^35 + 160 * q^36 - 20 * q^37 + 8 * q^39 - 112 * q^40 + 8 * q^41 + 4 * q^42 + 32 * q^44 - 52 * q^45 - 40 * q^46 + 40 * q^48 + 8 * q^49 + 100 * q^50 - 32 * q^51 - 152 * q^52 + 28 * q^53 - 36 * q^54 + 124 * q^56 - 104 * q^57 - 32 * q^58 - 36 * q^59 - 24 * q^60 + 52 * q^61 - 68 * q^62 + 20 * q^63 + 20 * q^65 - 60 * q^66 + 64 * q^67 - 128 * q^69 + 188 * q^70 + 52 * q^73 - 104 * q^74 + 36 * q^75 - 112 * q^76 + 28 * q^77 + 56 * q^78 - 108 * q^79 - 44 * q^80 + 52 * q^82 - 52 * q^83 + 120 * q^84 + 12 * q^85 - 20 * q^86 + 56 * q^87 + 36 * q^88 + 144 * q^90 - 16 * q^92 - 176 * q^93 - 8 * q^94 + 164 * q^95 - 164 * q^96 - 8 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

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 $

$2$	0.629885	+	0.629885i	0.445396	+	0.445396i	0.893821	−	0.448425i	$-0.148015\pi$
$2$	0.629885	+	0.629885i	0.445396	+	0.445396i	−0.448425	+	0.893821i	$0.648015\pi$
$3$	−0.623684	+	0.258339i	−0.360084	+	0.149152i	−0.555389	−	0.831591i	$-0.687431\pi$
$3$	−0.623684	+	0.258339i	−0.360084	+	0.149152i	0.195304	+	0.980743i	$0.437431\pi$
$4$		−	1.20649i		−	0.603244i
$5$	1.24172	+	2.99777i	0.555312	+	1.34064i	0.913441	+	0.406970i	$0.133415\pi$
$5$	1.24172	+	2.99777i	0.555312	+	1.34064i	−0.358129	+	0.933672i	$0.616585\pi$
$6$	−0.555573	−	0.230126i	−0.226812	−	0.0939486i
$7$	1.05484	−	2.54660i	0.398691	−	0.962526i	−0.589286	−	0.807925i	$-0.700591\pi$
$7$	1.05484	−	2.54660i	0.398691	−	0.962526i	0.987977	−	0.154601i	$-0.0494092\pi$
$8$	2.01972	−	2.01972i	0.714079	−	0.714079i
$9$	−1.79908	+	1.79908i	−0.599692	+	0.599692i
$10$	−1.10611	+	2.67039i	−0.349783	+	0.844451i
$11$	2.43813	+	1.00991i	0.735123	+	0.304498i	0.718655	−	0.695366i	$-0.244758\pi$
$11$	2.43813	+	1.00991i	0.735123	+	0.304498i	0.0164677	+	0.999864i	$0.494758\pi$
$12$	0.311683	+	0.752468i	0.0899750	+	0.217219i
$13$			3.90919i			1.08421i	0.840310	+	0.542107i	$0.182373\pi$
$13$			3.90919i			1.08421i	−0.840310	+	0.542107i	$0.817627\pi$
$14$	2.26850	−	0.939641i	0.606281	−	0.251130i
$15$	−1.54888	−	1.54888i	−0.399919	−	0.399919i
$16$	0.131406			0.0328516
$17$	2.39130	−	3.35882i	0.579974	−	0.814635i
$17$	2.39130	−	3.35882i	0.579974	−	0.814635i
$18$	−2.26642			−0.534201
$19$	−1.97187	−	1.97187i	−0.452378	−	0.452378i	0.443765	−	0.896143i	$-0.353643\pi$
$19$	−1.97187	−	1.97187i	−0.452378	−	0.452378i	−0.896143	+	0.443765i	$0.853643\pi$
$20$	3.61677	−	1.49812i	0.808735	−	0.334989i
$21$			1.86078i			0.406056i
$22$	0.899616	+	2.17187i	0.191799	+	0.463043i
$23$	6.55748	+	2.71620i	1.36733	+	0.566367i	0.941063	−	0.338231i	$-0.109828\pi$
$23$	6.55748	+	2.71620i	1.36733	+	0.566367i	0.426267	+	0.904598i	$0.359828\pi$
$24$	−0.737897	+	1.78144i	−0.150623	+	0.363635i
$25$	−3.90922	+	3.90922i	−0.781843	+	0.781843i
$26$	−2.46234	+	2.46234i	−0.482905	+	0.482905i
$27$	1.43230	−	3.45788i	0.275646	−	0.665469i
$28$	−3.07245	−	1.27265i	−0.580638	−	0.240508i
$29$	3.24782	+	7.84093i	0.603105	+	1.45602i	0.870369	+	0.492400i	$0.163880\pi$
$29$	3.24782	+	7.84093i	0.603105	+	1.45602i	−0.267264	+	0.963623i	$0.586120\pi$
$30$		−	1.95123i		−	0.356244i
$31$	3.88493	−	1.60919i	0.697754	−	0.289019i	−0.00547274	−	0.999985i	$-0.501742\pi$
$31$	3.88493	−	1.60919i	0.697754	−	0.289019i	0.703226	+	0.710966i	$0.251742\pi$
$32$	−3.95667	−	3.95667i	−0.699447	−	0.699447i
$33$	−1.78152			−0.310123
$34$	3.62192	−	0.609432i	0.621154	−	0.104517i
$35$	8.94393			1.51180
$36$	2.17057	+	2.17057i	0.361761	+	0.361761i
$37$	−4.07323	+	1.68719i	−0.669634	+	0.277372i	−0.691486	−	0.722390i	$-0.743044\pi$
$37$	−4.07323	+	1.68719i	−0.669634	+	0.277372i	0.0218521	+	0.999761i	$0.493044\pi$
$38$		−	2.48411i		−	0.402975i
$39$	−1.00989	−	2.43810i	−0.161712	−	0.390408i
$40$	8.56257	+	3.54673i	1.35386	+	0.560788i
$41$	−0.278939	+	0.673418i	−0.0435629	+	0.105170i	−0.944163	−	0.329478i	$-0.893127\pi$
$41$	−0.278939	+	0.673418i	−0.0435629	+	0.105170i	0.900600	+	0.434648i	$0.143127\pi$
$42$	−1.17208	+	1.17208i	−0.180856	+	0.180856i
$43$	0.707107	−	0.707107i	0.107833	−	0.107833i
$43$	0.707107	−	0.707107i	0.107833	−	0.107833i
$44$	1.21844	−	2.94157i	0.183687	−	0.443459i
$45$	−7.62716	−	3.15927i	−1.13699	−	0.470956i
$46$	2.41957	+	5.84136i	0.356746	+	0.861261i
$47$			2.63427i			0.384248i	0.981371	+	0.192124i	$0.0615375\pi$
$47$			2.63427i			0.384248i	−0.981371	+	0.192124i	$0.938462\pi$
$48$	−0.0819561	+	0.0339473i	−0.0118293	+	0.00489987i
$49$	−0.422760	−	0.422760i	−0.0603943	−	0.0603943i
$50$	−4.92472			−0.696460
$51$	−0.623700	+	2.71261i	−0.0873355	+	0.379842i
$52$	4.71639			0.654046
$53$	−0.467704	−	0.467704i	−0.0642440	−	0.0642440i	0.674255	−	0.738499i	$-0.264465\pi$
$53$	−0.467704	−	0.467704i	−0.0642440	−	0.0642440i	−0.738499	+	0.674255i	$0.764465\pi$
$54$	3.08025	−	1.27588i	0.419169	−	0.173626i
$55$			8.56295i			1.15463i
$56$	−3.01295	−	7.27390i	−0.402622	−	0.972016i
$57$	1.73924	+	0.720415i	0.230368	+	0.0954213i
$58$	−2.89313	+	6.98464i	−0.379887	+	0.917128i
$59$	−2.64678	+	2.64678i	−0.344582	+	0.344582i	−0.858087	−	0.513505i	$-0.828347\pi$
$59$	−2.64678	+	2.64678i	−0.344582	+	0.344582i	0.513505	+	0.858087i	$0.328347\pi$
$60$	−1.86870	+	1.86870i	−0.241249	+	0.241249i
$61$	−3.25823	+	7.86606i	−0.417174	+	1.00715i	0.565989	+	0.824413i	$0.308494\pi$
$61$	−3.25823	+	7.86606i	−0.417174	+	1.00715i	−0.983163	+	0.182733i	$0.941506\pi$
$62$	3.46066	+	1.43345i	0.439505	+	0.182049i
$63$	2.68380	+	6.47927i	0.338127	+	0.816311i
$64$		−	5.24731i		−	0.655914i
$65$	−11.7188	+	4.85410i	−1.45354	+	0.602077i
$66$	−1.12215	−	1.12215i	−0.138128	−	0.138128i
$67$	3.57275			0.436480			0.218240	−	0.975895i	$-0.429968\pi$
$67$	3.57275			0.436480			0.218240	+	0.975895i	$0.429968\pi$
$68$	−4.05239	−	2.88507i	−0.491424	−	0.349866i
$69$	−4.79150			−0.576829
$70$	5.63365	+	5.63365i	0.673350	+	0.673350i
$71$	0.942201	−	0.390273i	0.111819	−	0.0463168i	−0.326073	−	0.945345i	$-0.605725\pi$
$71$	0.942201	−	0.390273i	0.111819	−	0.0463168i	0.437891	+	0.899028i	$0.355725\pi$
$72$			7.26726i			0.856455i
$73$	−5.06462	−	12.2271i	−0.592769	−	1.43107i	−0.880818	−	0.473454i	$-0.843007\pi$
$73$	−5.06462	−	12.2271i	−0.592769	−	1.43107i	0.288050	−	0.957615i	$-0.406993\pi$
$74$	−3.62840	−	1.50293i	−0.421793	−	0.174712i
$75$	1.42822	−	3.44802i	0.164916	−	0.398143i
$76$	−2.37904	+	2.37904i	−0.272895	+	0.272895i
$77$	5.14366	−	5.14366i	0.586174	−	0.586174i
$78$	0.899606	−	2.17184i	0.101860	−	0.245913i
$79$	−5.51905	−	2.28607i	−0.620942	−	0.257203i	0.0499570	−	0.998751i	$-0.484092\pi$
$79$	−5.51905	−	2.28607i	−0.620942	−	0.257203i	−0.670899	+	0.741549i	$0.734092\pi$
$80$	0.163169	+	0.393926i	0.0182429	+	0.0440422i
$81$		−	5.10619i		−	0.567355i
$82$	−0.599876	+	0.248477i	−0.0662452	+	0.0274397i
$83$	1.82439	+	1.82439i	0.200253	+	0.200253i	0.800108	−	0.599855i	$-0.204775\pi$
$83$	1.82439	+	1.82439i	0.200253	+	0.200253i	−0.599855	+	0.800108i	$0.704775\pi$
$84$	2.24501			0.244951
$85$	13.0383	+	2.99784i	1.41420	+	0.325162i
$86$	0.890792			0.0960566
$87$	−4.05123	−	4.05123i	−0.434337	−	0.434337i
$88$	6.96406	−	2.88461i	0.742372	−	0.307500i
$89$		−	14.0451i		−	1.48878i	−0.667744	−	0.744391i	$-0.732740\pi$
$89$		−	14.0451i		−	1.48878i	0.667744	−	0.744391i	$-0.267260\pi$
$90$	−2.81425	−	6.79421i	−0.296648	−	0.716173i
$91$	9.95515	+	4.12356i	1.04358	+	0.432266i
$92$	3.27706	−	7.91153i	0.341658	−	0.824834i
$93$	−2.00725	+	2.00725i	−0.208142	+	0.208142i
$94$	−1.65929	+	1.65929i	−0.171142	+	0.171142i
$95$	3.46271	−	8.35972i	0.355266	−	0.857689i
$96$	3.48987	+	1.44555i	0.356184	+	0.147536i
$97$	0.343547	+	0.829395i	0.0348819	+	0.0842123i	0.940360	−	0.340180i	$-0.110488\pi$
$97$	0.343547	+	0.829395i	0.0348819	+	0.0842123i	−0.905479	+	0.424392i	$0.860488\pi$
$98$		−	0.532581i		−	0.0537988i
$99$	−6.20328	+	2.56948i	−0.623453	+	0.258243i
$100$	4.71643	+	4.71643i	0.471643	+	0.471643i
$101$	4.35259			0.433099			0.216549	−	0.976272i	$-0.430520\pi$
$101$	4.35259			0.433099			0.216549	+	0.976272i	$0.430520\pi$
$102$	−2.10149	+	1.31577i	−0.208079	+	0.130281i
$103$	0.256588			0.0252824			0.0126412	−	0.999920i	$-0.495976\pi$
$103$	0.256588			0.0252824			0.0126412	+	0.999920i	$0.495976\pi$
$104$	7.89547	+	7.89547i	0.774214	+	0.774214i
$105$	−5.57819	+	2.31056i	−0.544376	+	0.225488i
$106$		−	0.589199i		−	0.0572281i
$107$	−7.41317	−	17.8970i	−0.716658	−	1.73017i	−0.682652	−	0.730743i	$-0.739174\pi$
$107$	−7.41317	−	17.8970i	−0.716658	−	1.73017i	−0.0340057	−	0.999422i	$-0.510826\pi$
$108$	−4.17190	−	1.72806i	−0.401441	−	0.166282i
$109$	2.26953	−	5.47913i	0.217382	−	0.524806i	−0.777141	−	0.629326i	$-0.783331\pi$
$109$	2.26953	−	5.47913i	0.217382	−	0.524806i	0.994523	+	0.104521i	$0.0333309\pi$
$110$	−5.39368	+	5.39368i	−0.514267	+	0.514267i
$111$	2.10454	−	2.10454i	0.199754	−	0.199754i
$112$	0.138612	−	0.334640i	0.0130976	−	0.0316205i
$113$	−18.0797	−	7.48885i	−1.70079	−	0.704492i	−0.700832	−	0.713326i	$-0.747188\pi$
$113$	−18.0797	−	7.48885i	−1.70079	−	0.704492i	−0.999961	+	0.00883459i	$0.997188\pi$
$114$	0.641740	+	1.54930i	0.0601045	+	0.145105i
$115$			23.0306i			2.14761i
$116$	9.45999	−	3.91846i	0.878338	−	0.363820i
$117$	−7.03293	−	7.03293i	−0.650194	−	0.650194i
$118$	−3.33434			−0.306951
$119$	−6.03117	−	9.63270i	−0.552876	−	0.883028i
$120$	−6.25660			−0.571147
$121$	−2.85362	−	2.85362i	−0.259420	−	0.259420i
$122$	−7.00703	+	2.90241i	−0.634387	+	0.262772i
$123$		−	0.492061i		−	0.0443676i
$124$	−1.94147	−	4.68712i	−0.174349	−	0.420916i
$125$	−1.58422	−	0.656205i	−0.141697	−	0.0586928i
$126$	−2.39071	+	5.77168i	−0.212981	+	0.514182i
$127$	−1.42243	+	1.42243i	−0.126220	+	0.126220i	−0.767395	−	0.641175i	$-0.778447\pi$
$127$	−1.42243	+	1.42243i	−0.126220	+	0.126220i	0.641175	+	0.767395i	$0.278447\pi$
$128$	−4.60814	+	4.60814i	−0.407306	+	0.407306i
$129$	−0.258339	+	0.623684i	−0.0227454	+	0.0549124i
$130$	−10.4390	−	4.32400i	−0.915565	−	0.379239i
$131$	−5.09328	−	12.2963i	−0.445002	−	1.07433i	−0.974171	−	0.225813i	$-0.927496\pi$
$131$	−5.09328	−	12.2963i	−0.445002	−	1.07433i	0.529168	−	0.848517i	$-0.322504\pi$
$132$			2.14938i			0.187080i
$133$	−7.10158	+	2.94157i	−0.615785	+	0.255067i
$134$	2.25042	+	2.25042i	0.194407	+	0.194407i
$135$	12.1444			1.04523
$136$	−1.95414	−	11.6136i	−0.167566	−	0.995861i
$137$	10.7505			0.918480			0.459240	−	0.888312i	$-0.348122\pi$
$137$	10.7505			0.918480			0.459240	+	0.888312i	$0.348122\pi$
$138$	−3.01810	−	3.01810i	−0.256917	−	0.256917i
$139$	−17.9171	+	7.42152i	−1.51971	+	0.629486i	−0.977534	−	0.210778i	$-0.932400\pi$
$139$	−17.9171	+	7.42152i	−1.51971	+	0.629486i	−0.542178	+	0.840263i	$0.682400\pi$
$140$		−	10.7908i		−	0.911986i
$141$	−0.680533	−	1.64295i	−0.0573112	−	0.138362i
$142$	0.839306	+	0.347652i	0.0704330	+	0.0291743i
$143$	−3.94791	+	9.53110i	−0.330141	+	0.797030i
$144$	−0.236410	+	0.236410i	−0.0197008	+	0.0197008i
$145$	−19.4724	+	19.4724i	−1.61710	+	1.61710i
$146$	4.51152	−	10.8918i	0.373376	−	0.901410i
$147$	0.372884	+	0.154454i	0.0307550	+	0.0127391i
$148$	2.03557	+	4.91430i	0.167323	+	0.403953i
$149$			0.537485i			0.0440325i	0.999758	+	0.0220162i	$0.00700855\pi$
$149$			0.537485i			0.0440325i	−0.999758	+	0.0220162i	$0.992991\pi$
$150$	3.07147	−	1.27224i	0.250784	−	0.103878i
$151$	0.285668	+	0.285668i	0.0232473	+	0.0232473i	0.718635	−	0.695388i	$-0.244767\pi$
$151$	0.285668	+	0.285668i	0.0232473	+	0.0232473i	−0.695388	+	0.718635i	$0.744767\pi$
$152$	−7.96526			−0.646068
$153$	1.74066	+	10.3449i	0.140724	+	0.836336i
$154$	6.47983			0.522160
$155$	9.64795	+	9.64795i	0.774942	+	0.774942i
$156$	−2.94154	+	1.21843i	−0.235512	+	0.0975521i
$157$			8.91954i			0.711857i	0.934513	+	0.355929i	$0.115835\pi$
$157$			8.91954i			0.711857i	−0.934513	+	0.355929i	$0.884165\pi$
$158$	−2.03641	−	4.91633i	−0.162008	−	0.391122i
$159$	0.412525	+	0.170874i	0.0327154	+	0.0135512i
$160$	6.94812	−	16.7742i	0.549297	−	1.32612i
$161$	13.8342	−	13.8342i	1.09028	−	1.09028i
$162$	3.21631	−	3.21631i	0.252698	−	0.252698i
$163$	9.55247	−	23.0617i	0.748207	−	1.80633i	0.179566	−	0.983746i	$-0.442531\pi$
$163$	9.55247	−	23.0617i	0.748207	−	1.80633i	0.568641	−	0.822586i	$-0.307469\pi$
$164$	0.812471	+	0.336537i	0.0634434	+	0.0262791i
$165$	−2.21214	−	5.34058i	−0.172215	−	0.415764i
$166$			2.29832i			0.178384i
$167$	−17.0245	+	7.05179i	−1.31740	+	0.545684i	−0.927034	−	0.374977i	$-0.877651\pi$
$167$	−17.0245	+	7.05179i	−1.31740	+	0.545684i	−0.390363	+	0.920661i	$0.627651\pi$
$168$	3.75826	+	3.75826i	0.289956	+	0.289956i
$169$	−2.28175			−0.175519
$170$	6.32433	+	10.1009i	0.485054	+	0.774705i
$171$	7.09510			0.542576
$172$	−0.853117	−	0.853117i	−0.0650495	−	0.0650495i
$173$	−16.8933	+	6.99744i	−1.28438	+	0.532006i	−0.917304	−	0.398187i	$-0.869640\pi$
$173$	−16.8933	+	6.99744i	−1.28438	+	0.532006i	−0.367071	+	0.930193i	$0.619640\pi$
$174$		−	5.10362i		−	0.386904i
$175$	5.83164	+	14.0788i	0.440830	+	1.06426i
$176$	0.320385	+	0.132708i	0.0241500	+	0.0100032i
$177$	0.966991	−	2.33452i	0.0726835	−	0.175473i
$178$	8.84682	−	8.84682i	0.663098	−	0.663098i
$179$	−13.1765	+	13.1765i	−0.984857	+	0.984857i	−0.999887	−	0.0150300i	$-0.995216\pi$
$179$	−13.1765	+	13.1765i	−0.984857	+	0.984857i	0.0150300	+	0.999887i	$0.495216\pi$
$180$	−3.81163	+	9.20208i	−0.284102	+	0.685882i
$181$	1.08104	+	0.447781i	0.0803529	+	0.0332833i	0.422498	−	0.906364i	$-0.361153\pi$
$181$	1.08104	+	0.447781i	0.0803529	+	0.0332833i	−0.342145	+	0.939647i	$0.611153\pi$
$182$	3.67323	+	8.86797i	0.272278	+	0.657338i
$183$		−	5.74767i		−	0.424880i
$184$	18.7302	−	7.75832i	1.38081	−	0.571951i
$185$	−10.1156	−	10.1156i	−0.743712	−	0.743712i
$186$	−2.52868			−0.185412
$187$	9.22238	−	5.77426i	0.674407	−	0.422256i
$188$	3.17822			0.231795
$189$	−7.29501	−	7.29501i	−0.530634	−	0.530634i
$190$	7.44677	−	3.08455i	0.540246	−	0.223777i
$191$		−	7.89404i		−	0.571193i	−0.958350	−	0.285596i	$-0.907808\pi$
$191$		−	7.89404i		−	0.571193i	0.958350	−	0.285596i	$-0.0921917\pi$
$192$	1.35558	+	3.27267i	0.0978307	+	0.236184i
$193$	4.58904	+	1.90084i	0.330326	+	0.136826i	0.541682	−	0.840584i	$-0.317788\pi$
$193$	4.58904	+	1.90084i	0.330326	+	0.136826i	−0.211355	+	0.977409i	$0.567788\pi$
$194$	−0.306029	+	0.738819i	−0.0219716	+	0.0530441i
$195$	6.05485	−	6.05485i	0.433597	−	0.433597i
$196$	−0.510056	+	0.510056i	−0.0364326	+	0.0364326i
$197$	6.76019	−	16.3205i	0.481644	−	1.16279i	−0.477184	−	0.878803i	$-0.658343\pi$
$197$	6.76019	−	16.3205i	0.481644	−	1.16279i	0.958828	−	0.283987i	$-0.0916574\pi$
$198$	−5.52583	−	2.28887i	−0.392704	−	0.162663i
$199$	−6.09580	−	14.7166i	−0.432120	−	1.04323i	−0.978603	−	0.205760i	$-0.934034\pi$
$199$	−6.09580	−	14.7166i	−0.432120	−	1.04323i	0.546482	−	0.837471i	$-0.315966\pi$
$200$			15.7910i			1.11660i
$201$	−2.22827	+	0.922978i	−0.157170	+	0.0651018i
$202$	2.74163	+	2.74163i	0.192901	+	0.192901i
$203$	23.3937			1.64191
$204$	3.27274	+	0.752487i	0.229137	+	0.0526846i
$205$	−2.36511			−0.165187
$206$	0.161621	+	0.161621i	0.0112607	+	0.0112607i
$207$	−16.6841	+	6.91077i	−1.15962	+	0.480332i
$208$			0.513692i			0.0356181i
$209$	−2.81627	−	6.79908i	−0.194806	−	0.470302i
$210$	−4.96901	−	2.05823i	−0.342894	−	0.142032i
$211$	7.05381	−	17.0294i	0.485604	−	1.17235i	−0.471307	−	0.881969i	$-0.656218\pi$
$211$	7.05381	−	17.0294i	0.485604	−	1.17235i	0.956911	−	0.290382i	$-0.0937825\pi$
$212$	−0.564279	+	0.564279i	−0.0387549	+	0.0387549i
$213$	−0.486814	+	0.486814i	−0.0333559	+	0.0333559i
$214$	6.60359	−	15.9425i	0.451412	−	1.08981i
$215$	2.99777	+	1.24172i	0.204446	+	0.0846843i
$216$	−4.09110	−	9.87680i	−0.278364	−	0.672031i
$217$		−	11.5908i		−	0.786835i
$218$	4.88077	−	2.02168i	0.330567	−	0.136925i
$219$	6.31745	+	6.31745i	0.426893	+	0.426893i
$220$	10.3311			0.696523
$221$	13.1303	+	9.34802i	0.883238	+	0.628816i
$222$	2.65124			0.177940
$223$	−5.73854	−	5.73854i	−0.384281	−	0.384281i	0.488361	−	0.872642i	$-0.337595\pi$
$223$	−5.73854	−	5.73854i	−0.384281	−	0.384281i	−0.872642	+	0.488361i	$0.837595\pi$
$224$	−14.2497	+	5.90243i	−0.952099	+	0.394372i
$225$		−	14.0660i		−	0.937731i
$226$	−6.67101	−	16.1052i	−0.443749	−	1.07130i
$227$	15.5245	+	6.43044i	1.03039	+	0.426804i	0.832855	−	0.553491i	$-0.186705\pi$
$227$	15.5245	+	6.43044i	1.03039	+	0.426804i	0.197540	+	0.980295i	$0.436705\pi$
$228$	0.869173	−	2.09837i	0.0575624	−	0.138968i
$229$	−12.4636	+	12.4636i	−0.823615	+	0.823615i	−0.986624	−	0.163010i	$-0.947880\pi$
$229$	−12.4636	+	12.4636i	−0.823615	+	0.823615i	0.163010	+	0.986624i	$0.447880\pi$
$230$	−14.5066	+	14.5066i	−0.956537	+	0.956537i
$231$	−1.87921	+	4.53683i	−0.123643	+	0.298501i
$232$	22.3962	+	9.27680i	1.47038	+	0.609051i
$233$	2.01535	+	4.86550i	0.132030	+	0.318749i	0.976044	−	0.217572i	$-0.0698136\pi$
$233$	2.01535	+	4.86550i	0.132030	+	0.318749i	−0.844014	+	0.536321i	$0.819814\pi$
$234$		−	8.85988i		−	0.579188i
$235$	−7.89692	+	3.27101i	−0.515139	+	0.213377i
$236$	3.19331	+	3.19331i	0.207867	+	0.207867i
$237$	4.03273			0.261954
$238$	2.26855	−	9.86644i	0.147048	−	0.639546i
$239$	2.49148			0.161160			0.0805801	−	0.996748i	$-0.474323\pi$
$239$	2.49148			0.161160			0.0805801	+	0.996748i	$0.474323\pi$
$240$	−0.203532	−	0.203532i	−0.0131380	−	0.0131380i
$241$	1.74125	−	0.721248i	0.112163	−	0.0464596i	−0.325896	−	0.945406i	$-0.605666\pi$
$241$	1.74125	−	0.721248i	0.112163	−	0.0464596i	0.438059	+	0.898946i	$0.355666\pi$
$242$		−	3.59490i		−	0.231089i
$243$	5.61603	+	13.5583i	0.360268	+	0.869765i
$244$	9.49032	+	3.93102i	0.607555	+	0.251658i
$245$	0.742389	−	1.79229i	0.0474295	−	0.114505i
$246$	0.309942	−	0.309942i	0.0197612	−	0.0197612i
$247$	7.70842	−	7.70842i	0.490475	−	0.490475i
$248$	4.59635	−	11.0966i	0.291869	−	0.704634i
$249$	−1.60916	−	0.666534i	−0.101976	−	0.0422399i
$250$	−0.584542	−	1.41121i	−0.0369697	−	0.0892528i
$251$			28.4100i			1.79323i	0.442815	+	0.896613i	$0.353980\pi$
$251$			28.4100i			1.79323i	−0.442815	+	0.896613i	$0.646020\pi$
$252$	7.81717	−	3.23798i	0.492435	−	0.203973i
$253$	13.2449	+	13.2449i	0.832698	+	0.832698i
$254$	−1.79194			−0.112436
$255$	−8.90623	+	1.49858i	−0.557730	+	0.0938450i
$256$	−16.2998			−1.01874
$257$	−9.48300	−	9.48300i	−0.591533	−	0.591533i	0.346512	−	0.938045i	$-0.387366\pi$
$257$	−9.48300	−	9.48300i	−0.591533	−	0.591533i	−0.938045	+	0.346512i	$0.887366\pi$
$258$	−0.555573	+	0.230126i	−0.0345885	+	0.0143270i
$259$			12.1526i			0.755126i
$260$	5.85642	+	14.1386i	0.363200	+	0.876841i
$261$	−19.9495	−	8.26336i	−1.23484	−	0.511489i
$262$	4.53706	−	10.9534i	0.280300	−	0.676705i
$263$	0.633387	−	0.633387i	0.0390563	−	0.0390563i	−0.687309	−	0.726365i	$-0.741208\pi$
$263$	0.633387	−	0.633387i	0.0390563	−	0.0390563i	0.726365	+	0.687309i	$0.241208\pi$
$264$	−3.59817	+	3.59817i	−0.221452	+	0.221452i
$265$	0.821312	−	1.98282i	0.0504528	−	0.121804i
$266$	−6.32603	−	2.62033i	−0.387874	−	0.160663i
$267$	3.62840	+	8.75973i	0.222055	+	0.536087i
$268$		−	4.31048i		−	0.263304i
$269$	−8.55421	+	3.54327i	−0.521559	+	0.216037i	−0.627902	−	0.778293i	$-0.716086\pi$
$269$	−8.55421	+	3.54327i	−0.521559	+	0.216037i	0.106342	+	0.994330i	$0.466086\pi$
$270$	7.64960	+	7.64960i	0.465540	+	0.465540i
$271$	−5.80760			−0.352787			−0.176393	−	0.984320i	$-0.556443\pi$
$271$	−5.80760			−0.352787			−0.176393	+	0.984320i	$0.556443\pi$
$272$	0.314231	−	0.441371i	0.0190531	−	0.0267620i
$273$	−7.27415			−0.440251
$274$	6.77160	+	6.77160i	0.409088	+	0.409088i
$275$	−13.4791	+	5.58323i	−0.812821	+	0.336681i
$276$			5.78089i			0.347969i
$277$	12.1794	+	29.4036i	0.731787	+	1.76669i	0.636549	+	0.771237i	$0.280361\pi$
$277$	12.1794	+	29.4036i	0.731787	+	1.76669i	0.0952388	+	0.995454i	$0.469639\pi$
$278$	−15.9605	−	6.61104i	−0.957245	−	0.396504i
$279$	−4.09423	+	9.88434i	−0.245115	+	0.591760i
$280$	18.0642	−	18.0642i	1.07955	−	1.07955i
$281$	14.5779	−	14.5779i	0.869642	−	0.869642i	−0.122790	−	0.992433i	$-0.539184\pi$
$281$	14.5779	−	14.5779i	0.869642	−	0.869642i	0.992433	+	0.122790i	$0.0391843\pi$
$282$	0.606214	−	1.46353i	0.0360995	−	0.0871519i
$283$	5.12839	+	2.12425i	0.304851	+	0.126273i	0.529865	−	0.848082i	$-0.322243\pi$
$283$	5.12839	+	2.12425i	0.304851	+	0.126273i	−0.225014	+	0.974356i	$0.572243\pi$
$284$	−0.470859	−	1.13676i	−0.0279404	−	0.0674540i
$285$			6.10838i			0.361829i
$286$	−8.49023	+	3.51677i	−0.502038	+	0.207951i
$287$	1.42069	+	1.42069i	0.0838609	+	0.0838609i
$288$	14.2367			0.838906
$289$	−5.56341	−	16.0639i	−0.327259	−	0.944935i
$290$	−24.5308			−1.44050
$291$	−0.428529	−	0.428529i	−0.0251208	−	0.0251208i
$292$	−14.7518	+	6.11040i	−0.863285	+	0.357584i
$293$			16.6179i			0.970831i	0.874284	+	0.485415i	$0.161332\pi$
$293$			16.6179i			0.970831i	−0.874284	+	0.485415i	$0.838668\pi$
$294$	0.137586	+	0.332163i	0.00802419	+	0.0193721i
$295$	−11.2210	−	4.64789i	−0.653311	−	0.270610i
$296$	−4.81913	+	11.6344i	−0.280106	+	0.676237i
$297$	6.98427	−	6.98427i	0.405268	−	0.405268i
$298$	−0.338554	+	0.338554i	−0.0196119	+	0.0196119i
$299$	−10.6181	+	25.6344i	−0.614062	+	1.48248i
$300$	−4.16000	−	1.72313i	−0.240178	−	0.0994848i
$301$	−1.05484	−	2.54660i	−0.0607998	−	0.146784i
$302$			0.359876i			0.0207085i
$303$	−2.71464	+	1.12444i	−0.155952	+	0.0645975i
$304$	−0.259116	−	0.259116i	−0.0148613	−	0.0148613i
$305$	−27.6264			−1.58188
$306$	−5.41969	+	7.61252i	−0.309823	+	0.435179i
$307$	14.7193			0.840077			0.420039	−	0.907506i	$-0.362017\pi$
$307$	14.7193			0.840077			0.420039	+	0.907506i	$0.362017\pi$
$308$	−6.20577	−	6.20577i	−0.353606	−	0.353606i
$309$	−0.160030	+	0.0662867i	−0.00910380	+	0.00377092i
$310$			12.1542i			0.690313i
$311$	0.201087	+	0.485467i	0.0114026	+	0.0275283i	0.929478	−	0.368877i	$-0.120258\pi$
$311$	0.201087	+	0.485467i	0.0114026	+	0.0275283i	−0.918076	+	0.396405i	$0.870258\pi$
$312$	−6.96398	−	2.88458i	−0.394258	−	0.163307i
$313$	−2.86152	+	6.90832i	−0.161743	+	0.390482i	−0.983885	−	0.178800i	$-0.942779\pi$
$313$	−2.86152	+	6.90832i	−0.161743	+	0.390482i	0.822143	+	0.569281i	$0.192779\pi$
$314$	−5.61829	+	5.61829i	−0.317058	+	0.317058i
$315$	−16.0908	+	16.0908i	−0.906615	+	0.906615i
$316$	−2.75811	+	6.65868i	−0.155156	+	0.374580i
$317$	2.74567	+	1.13730i	0.154212	+	0.0638769i	0.458455	−	0.888718i	$-0.348403\pi$
$317$	2.74567	+	1.13730i	0.154212	+	0.0638769i	−0.304242	+	0.952595i	$0.598403\pi$
$318$	0.152213	+	0.367474i	0.00853568	+	0.0206069i
$319$			22.3972i			1.25400i
$320$	15.7302	−	6.51567i	0.879345	−	0.364237i
$321$	9.24695	+	9.24695i	0.516115	+	0.516115i
$322$	17.4279			0.971217
$323$	−11.3385	+	1.90784i	−0.630891	+	0.106155i
$324$	−6.16056			−0.342254
$325$	−15.2819	−	15.2819i	−0.847685	−	0.847685i
$326$	20.5432	−	8.50927i	1.13778	−	0.471285i
$327$			4.00356i			0.221397i
$328$	0.796738	+	1.92349i	0.0439925	+	0.106207i
$329$	6.70844	+	2.77873i	0.369848	+	0.153196i
$330$	1.97056	−	4.75735i	0.108476	−	0.261883i
$331$	−5.28203	+	5.28203i	−0.290327	+	0.290327i	−0.837209	−	0.546883i	$-0.815814\pi$
$331$	−5.28203	+	5.28203i	−0.290327	+	0.290327i	0.546883	+	0.837209i	$0.315814\pi$
$332$	2.20111	−	2.20111i	0.120802	−	0.120802i
$333$	4.29267	−	10.3634i	0.235237	−	0.567912i
$334$	−15.1653	−	6.28168i	−0.829809	−	0.343718i
$335$	4.43633	+	10.7103i	0.242383	+	0.585164i
$336$			0.244519i			0.0133396i
$337$	13.8963	−	5.75605i	0.756982	−	0.313552i	0.0293952	−	0.999568i	$-0.490642\pi$
$337$	13.8963	−	5.75605i	0.756982	−	0.313552i	0.727587	+	0.686016i	$0.240642\pi$
$338$	−1.43724	−	1.43724i	−0.0781755	−	0.0781755i
$339$	13.2107			0.717505
$340$	3.61686	−	15.7305i	0.196152	−	0.853109i
$341$	11.0971			0.600941
$342$	4.46910	+	4.46910i	0.241661	+	0.241661i
$343$	16.3037	−	6.75321i	0.880316	−	0.364639i
$344$		−	2.85632i		−	0.154002i
$345$	−5.94968	−	14.3638i	−0.320320	−	0.773321i
$346$	−15.0484	−	6.23327i	−0.809009	−	0.335103i
$347$	−13.5845	+	32.7959i	−0.729254	+	1.76058i	−0.0841868	+	0.996450i	$0.526829\pi$
$347$	−13.5845	+	32.7959i	−0.729254	+	1.76058i	−0.645067	+	0.764126i	$0.723171\pi$
$348$	−4.88776	+	4.88776i	−0.262012	+	0.262012i
$349$	2.40942	−	2.40942i	0.128973	−	0.128973i	−0.639673	−	0.768647i	$-0.720930\pi$
$349$	2.40942	−	2.40942i	0.128973	−	0.128973i	0.768647	+	0.639673i	$0.220930\pi$
$350$	−5.19478	+	12.5413i	−0.277672	+	0.670361i
$351$	13.5175	+	5.59913i	0.721511	+	0.298860i
$352$	−5.65100	−	13.6427i	−0.301199	−	0.727160i
$353$		−	1.90609i		−	0.101451i	−0.998713	−	0.0507253i	$-0.983847\pi$
$353$		−	1.90609i		−	0.101451i	0.998713	−	0.0507253i	$-0.0161533\pi$
$354$	2.07958	−	0.861388i	0.110528	−	0.0457823i
$355$	2.33989	+	2.33989i	0.124189	+	0.124189i
$356$	−16.9453			−0.898099
$357$	6.25004	+	4.44968i	0.330787	+	0.235502i
$358$	−16.5994			−0.877303
$359$	10.2598	+	10.2598i	0.541491	+	0.541491i	0.923966	−	0.382475i	$-0.124928\pi$
$359$	10.2598	+	10.2598i	0.541491	+	0.541491i	−0.382475	+	0.923966i	$0.624928\pi$
$360$	−21.7856	+	9.02388i	−1.14820	+	0.475600i
$361$		−	11.2234i		−	0.590707i
$362$	0.398879	+	0.962980i	0.0209646	+	0.0506131i
$363$	2.51696	+	1.04256i	0.132106	+	0.0547201i
$364$	4.97503	−	12.0108i	0.260762	−	0.629536i
$365$	30.3651	−	30.3651i	1.58938	−	1.58938i
$366$	3.62037	−	3.62037i	0.189240	−	0.189240i
$367$	−7.21659	+	17.4224i	−0.376703	+	0.909441i	0.615877	+	0.787843i	$0.288802\pi$
$367$	−7.21659	+	17.4224i	−0.376703	+	0.909441i	−0.992579	+	0.121598i	$0.961198\pi$
$368$	0.861695	+	0.356926i	0.0449189	+	0.0186060i
$369$	−0.709698	−	1.71336i	−0.0369454	−	0.0891941i
$370$		−	12.7433i		−	0.662493i
$371$	−1.68441	+	0.697704i	−0.0874501	+	0.0362230i
$372$	2.42173	+	2.42173i	0.125561	+	0.125561i
$373$	8.45965			0.438024			0.219012	−	0.975722i	$-0.429717\pi$
$373$	8.45965			0.438024			0.219012	+	0.975722i	$0.429717\pi$
$374$	9.44616	+	2.17192i	0.488449	+	0.112307i
$375$	1.15758			0.0597770
$376$	5.32049	+	5.32049i	0.274383	+	0.274383i
$377$	−30.6517	+	12.6963i	−1.57864	+	0.653894i
$378$		−	9.19004i		−	0.472684i
$379$	2.76644	+	6.67878i	0.142103	+	0.343066i	0.978867	−	0.204497i	$-0.0655558\pi$
$379$	2.76644	+	6.67878i	0.142103	+	0.343066i	−0.836765	+	0.547563i	$0.815556\pi$
$380$	−10.0859	−	4.17772i	−0.517396	−	0.214312i
$381$	0.519680	−	1.25462i	0.0266240	−	0.0642760i
$382$	4.97234	−	4.97234i	0.254407	−	0.254407i
$383$	−0.409393	+	0.409393i	−0.0209190	+	0.0209190i	−0.717489	−	0.696570i	$-0.754709\pi$
$383$	−0.409393	+	0.409393i	−0.0209190	+	0.0209190i	0.696570	+	0.717489i	$0.254709\pi$
$384$	1.68356	−	4.06448i	0.0859140	−	0.207415i
$385$	21.8065	+	9.03253i	1.11136	+	0.460340i
$386$	1.69326	+	4.08788i	0.0861845	+	0.208068i
$387$			2.54428i			0.129333i
$388$	1.00066	−	0.414485i	0.0508006	−	0.0210423i
$389$	−22.9501	−	22.9501i	−1.16362	−	1.16362i	−0.983677	−	0.179941i	$-0.942409\pi$
$389$	−22.9501	−	22.9501i	−1.16362	−	1.16362i	−0.179941	−	0.983677i	$-0.557591\pi$
$390$	7.62773			0.386245
$391$	24.8041	−	15.5302i	1.25440	−	0.785396i
$392$	−1.70772			−0.0862527
$393$	6.35320	+	6.35320i	0.320477	+	0.320477i
$394$	14.5382	−	6.02193i	0.732425	−	0.303380i
$395$		−	19.3835i		−	0.975289i
$396$	3.10005	+	7.48418i	0.155783	+	0.376094i
$397$	−28.2767	−	11.7126i	−1.41917	−	0.587839i	−0.464517	−	0.885564i	$-0.653772\pi$
$397$	−28.2767	−	11.7126i	−1.41917	−	0.587839i	−0.954652	+	0.297725i	$0.903772\pi$
$398$	5.43010	−	13.1094i	0.272186	−	0.657115i
$399$	3.66922	−	3.66922i	0.183691	−	0.183691i
$400$	−0.513696	+	0.513696i	−0.0256848	+	0.0256848i
$401$	11.8904	−	28.7061i	0.593780	−	1.43351i	−0.286045	−	0.958216i	$-0.592341\pi$
$401$	11.8904	−	28.7061i	0.593780	−	1.43351i	0.879826	−	0.475297i	$-0.157659\pi$
$402$	−1.98492	−	0.822182i	−0.0989989	−	0.0410067i
$403$	6.29062	+	15.1869i	0.313358	+	0.756514i
$404$		−	5.25135i		−	0.261265i
$405$	15.3072	−	6.34044i	0.760620	−	0.315059i
$406$	14.7353	+	14.7353i	0.731302	+	0.731302i
$407$	−11.6349			−0.576723
$408$	4.21902	+	6.73842i	0.208872	+	0.333601i
$409$	−16.1036			−0.796272			−0.398136	−	0.917326i	$-0.630343\pi$
$409$	−16.1036			−0.796272			−0.398136	+	0.917326i	$0.630343\pi$
$410$	−1.48975	−	1.48975i	−0.0735735	−	0.0735735i
$411$	−6.70494	+	2.77728i	−0.330730	+	0.136993i
$412$		−	0.309571i		−	0.0152515i
$413$	3.94838	+	9.53223i	0.194287	+	0.469050i
$414$	−14.8620	−	6.15606i	−0.730429	−	0.302554i
$415$	−3.20373	+	7.73448i	−0.157265	+	0.379671i
$416$	15.4674	−	15.4674i	0.758350	−	0.758350i
$417$	9.25738	−	9.25738i	0.453336	−	0.453336i
$418$	2.50871	−	6.05657i	0.122705	−	0.296236i
$419$	−9.76141	−	4.04331i	−0.476876	−	0.197528i	0.131281	−	0.991345i	$-0.458091\pi$
$419$	−9.76141	−	4.04331i	−0.476876	−	0.197528i	−0.608157	+	0.793817i	$0.708091\pi$
$420$	2.78767	+	6.73003i	0.136024	+	0.328392i
$421$		−	6.63714i		−	0.323474i	−0.986834	−	0.161737i	$-0.948290\pi$
$421$		−	6.63714i		−	0.323474i	0.986834	−	0.161737i	$-0.0517097\pi$
$422$	15.1697	−	6.28348i	0.738447	−	0.305875i
$423$	−4.73925	−	4.73925i	−0.230430	−	0.230430i
$424$	−1.88926			−0.0917506
$425$	3.78228	+	22.4785i	0.183468	+	1.09037i
$426$	−0.613274			−0.0297132
$427$	16.5948	+	16.5948i	0.803081	+	0.803081i
$428$	−21.5925	+	8.94390i	−1.04371	+	0.432320i
$429$		−	6.96429i		−	0.336239i
$430$	1.10611	+	2.67039i	0.0533414	+	0.128778i
$431$	33.0545	+	13.6916i	1.59218	+	0.659502i	0.990282	−	0.139071i	$-0.0444118\pi$
$431$	33.0545	+	13.6916i	1.59218	+	0.659502i	0.601897	+	0.798574i	$0.294412\pi$
$432$	0.188213	−	0.454387i	0.00905542	−	0.0218617i
$433$	−2.62686	+	2.62686i	−0.126239	+	0.126239i	−0.767403	−	0.641165i	$-0.778452\pi$
$433$	−2.62686	+	2.62686i	−0.126239	+	0.126239i	0.641165	+	0.767403i	$0.278452\pi$
$434$	7.30088	−	7.30088i	0.350453	−	0.350453i
$435$	7.11416	−	17.1751i	0.341098	−	0.823484i
$436$	−6.61051	−	2.73816i	−0.316586	−	0.131134i
$437$	−7.57452	−	18.2865i	−0.362339	−	0.874763i
$438$			7.95853i			0.380273i
$439$	−15.8034	+	6.54598i	−0.754255	+	0.312423i	−0.726476	−	0.687191i	$-0.758843\pi$
$439$	−15.8034	+	6.54598i	−0.754255	+	0.312423i	−0.0277787	+	0.999614i	$0.508843\pi$
$440$	17.2948	+	17.2948i	0.824496	+	0.824496i
$441$	1.52116			0.0724360
$442$	2.38239	+	14.1588i	0.113319	+	0.673463i
$443$	31.1120			1.47817			0.739087	−	0.673610i	$-0.235257\pi$
$443$	31.1120			1.47817			0.739087	+	0.673610i	$0.235257\pi$
$444$	−2.53911	−	2.53911i	−0.120501	−	0.120501i
$445$	42.1040	−	17.4401i	1.99592	−	0.826739i
$446$		−	7.22924i		−	0.342315i
$447$	−0.138853	−	0.335221i	−0.00656752	−	0.0158554i
$448$	−13.3628	−	5.53506i	−0.631334	−	0.261507i
$449$	−2.18150	+	5.26661i	−0.102951	+	0.248547i	−0.966959	−	0.254932i	$-0.917947\pi$
$449$	−2.18150	+	5.26661i	−0.102951	+	0.248547i	0.864008	+	0.503479i	$0.167947\pi$
$450$	8.85994	−	8.85994i	0.417662	−	0.417662i
$451$	−1.36018	+	1.36018i	−0.0640482	+	0.0640482i
$452$	−9.03521	+	21.8129i	−0.424981	+	1.02599i
$453$	−0.251966	−	0.104368i	−0.0118384	−	0.00490362i
$454$	5.72819	+	13.8291i	0.268837	+	0.649031i
$455$			34.9635i			1.63911i
$456$	4.96781	−	2.05773i	0.232639	−	0.0963622i
$457$	18.2674	+	18.2674i	0.854514	+	0.854514i	0.990685	−	0.136171i	$-0.0434796\pi$
$457$	18.2674	+	18.2674i	0.854514	+	0.854514i	−0.136171	+	0.990685i	$0.543480\pi$
$458$	−15.7012			−0.733670
$459$	−8.18936	−	13.0797i	−0.382247	−	0.610506i
$460$	27.7861			1.29553
$461$	29.4286	+	29.4286i	1.37063	+	1.37063i	0.859511	+	0.511117i	$0.170768\pi$
$461$	29.4286	+	29.4286i	1.37063	+	1.37063i	0.511117	+	0.859511i	$0.329232\pi$
$462$	−4.04137	+	1.67399i	−0.188022	+	0.0778811i
$463$			28.5116i			1.32505i	0.749041	+	0.662524i	$0.230515\pi$
$463$			28.5116i			1.32505i	−0.749041	+	0.662524i	$0.769485\pi$
$464$	0.426784	+	1.03035i	0.0198129	+	0.0478327i
$465$	−8.50972	−	3.52484i	−0.394629	−	0.163461i
$466$	−1.79526	+	4.33415i	−0.0831639	+	0.200775i
$467$	11.2473	−	11.2473i	0.520465	−	0.520465i	−0.397247	−	0.917712i	$-0.630034\pi$
$467$	11.2473	−	11.2473i	0.520465	−	0.520465i	0.917712	+	0.397247i	$0.130034\pi$
$468$	−8.48515	+	8.48515i	−0.392226	+	0.392226i
$469$	3.76867	−	9.09837i	0.174021	−	0.420124i
$470$	−7.03452	−	2.91379i	−0.324478	−	0.134403i
$471$	−2.30426	−	5.56298i	−0.106175	−	0.256329i
$472$			10.6915i			0.492117i
$473$	2.43813	−	1.00991i	0.112105	−	0.0464355i
$474$	2.54016	+	2.54016i	0.116673	+	0.116673i
$475$	15.4169			0.707378
$476$	−11.6217	+	7.27654i	−0.532682	+	0.333520i
$477$	1.68287			0.0770533
$478$	1.56934	+	1.56934i	0.0717801	+	0.0717801i
$479$	1.30557	−	0.540785i	0.0596530	−	0.0247091i	−0.352657	−	0.935752i	$-0.614722\pi$
$479$	1.30557	−	0.540785i	0.0596530	−	0.0247091i	0.412310	+	0.911043i	$0.364722\pi$
$480$			12.2568i			0.559444i
$481$	−6.59552	−	15.9230i	−0.300730	−	0.726026i
$482$	1.55109	+	0.642482i	0.0706501	+	0.0292642i
$483$	−5.05426	+	12.2021i	−0.229977	+	0.555213i
$484$	−3.44286	+	3.44286i	−0.156494	+	0.156494i
$485$	−2.05975	+	2.05975i	−0.0935282	+	0.0935282i
$486$	−5.00272	+	12.0776i	−0.226928	+	0.547852i
$487$	−22.3667	−	9.26458i	−1.01353	−	0.419818i	−0.186789	−	0.982400i	$-0.559808\pi$
$487$	−22.3667	−	9.26458i	−1.01353	−	0.419818i	−0.826742	+	0.562582i	$0.809808\pi$
$488$	9.30653	+	22.4680i	0.421287	+	1.01708i
$489$			16.8510i			0.762028i
$490$	1.59655	−	0.661314i	0.0721250	−	0.0298751i
$491$	−10.5206	−	10.5206i	−0.474789	−	0.474789i	0.428671	−	0.903461i	$-0.358982\pi$
$491$	−10.5206	−	10.5206i	−0.474789	−	0.474789i	−0.903461	+	0.428671i	$0.858982\pi$
$492$	−0.593666			−0.0267645
$493$	34.1028	+	7.84112i	1.53591	+	0.353146i
$494$	9.71084			0.436911
$495$	−15.4054	−	15.4054i	−0.692422	−	0.692422i
$496$	0.510504	−	0.211458i	0.0229223	−	0.00949473i
$497$		−	2.81109i		−	0.126094i
$498$	−0.593744	−	1.43342i	−0.0266063	−	0.0642333i
$499$	−34.2097	−	14.1701i	−1.53144	−	0.634341i	−0.551593	−	0.834113i	$-0.685980\pi$
$499$	−34.2097	−	14.1701i	−1.53144	−	0.634341i	−0.979842	+	0.199772i	$0.935980\pi$
$500$	−0.791704	+	1.91134i	−0.0354061	+	0.0854779i
$501$	8.79618	−	8.79618i	0.392984	−	0.392984i
$502$	−17.8951	+	17.8951i	−0.798696	+	0.798696i
$503$	3.15174	−	7.60897i	0.140529	−	0.339267i	−0.837908	−	0.545811i	$-0.816222\pi$
$503$	3.15174	−	7.60897i	0.140529	−	0.339267i	0.978437	+	0.206544i	$0.0662216\pi$
$504$	18.5068	+	7.66578i	0.824360	+	0.341461i
$505$	5.40468	+	13.0481i	0.240505	+	0.580631i
$506$			16.6855i			0.741761i
$507$	1.42309	−	0.589463i	0.0632016	−	0.0261790i
$508$	1.71615	+	1.71615i	0.0761418	+	0.0761418i
$509$	−25.0232			−1.10913			−0.554566	−	0.832140i	$-0.687116\pi$
$509$	−25.0232			−1.10913			−0.554566	+	0.832140i	$0.687116\pi$
$510$	−6.55384	−	4.66597i	−0.290209	−	0.206613i
$511$	−36.4798			−1.61377
$512$	−1.05074	−	1.05074i	−0.0464366	−	0.0464366i
$513$	−9.64281	+	3.99418i	−0.425741	+	0.176348i
$514$		−	11.9464i		−	0.526933i
$515$	0.318610	+	0.769192i	0.0140396	+	0.0338947i
$516$	0.752468	+	0.311683i	0.0331256	+	0.0137211i
$517$	−2.66036	+	6.42268i	−0.117003	+	0.282469i
$518$	−7.65474	+	7.65474i	−0.336330	+	0.336330i
$519$	8.72840	−	8.72840i	0.383134	−	0.383134i
$520$	−13.8648	+	33.4727i	−0.608014	+	1.46787i
$521$	−31.2420	−	12.9408i	−1.36874	−	0.566949i	−0.427290	−	0.904115i	$-0.640532\pi$
$521$	−31.2420	−	12.9408i	−1.36874	−	0.566949i	−0.941445	+	0.337166i	$0.890532\pi$
$522$	−7.36093	−	17.7709i	−0.322179	−	0.777810i
$523$			34.8994i			1.52605i	0.646372	+	0.763023i	$0.276286\pi$
$523$			34.8994i			1.52605i	−0.646372	+	0.763023i	$0.723714\pi$
$524$	−14.8353	+	6.14499i	−0.648084	+	0.268445i
$525$	−7.27420	−	7.27420i	−0.317472	−	0.317472i
$526$	0.797923			0.0347911
$527$	3.88502	−	16.8968i	0.169234	−	0.736038i
$528$	−0.234103			−0.0101880
$529$	19.3594	+	19.3594i	0.841713	+	0.841713i
$530$	1.76628	−	0.731618i	0.0767224	−	0.0317795i
$531$		−	9.52353i		−	0.413286i
$532$	3.54897	+	8.56798i	0.153868	+	0.371469i
$533$	−2.63252	−	1.09042i	−0.114027	−	0.0472315i
$534$	−3.23215	+	7.80310i	−0.139869	+	0.337673i
$535$	44.4459	−	44.4459i	1.92156	−	1.92156i
$536$	7.21595	−	7.21595i	0.311681	−	0.311681i
$537$	4.81398	−	11.6220i	0.207738	−	0.501525i
$538$	−7.62002	−	3.15632i	−0.328523	−	0.136078i
$539$	−0.603796	−	1.45769i	−0.0260073	−	0.0627872i
$540$		−	14.6521i		−	0.630527i
$541$	0.293956	−	0.121761i	0.0126382	−	0.00523490i	−0.376355	−	0.926475i	$-0.622823\pi$
$541$	0.293956	−	0.121761i	0.0126382	−	0.00523490i	0.388994	+	0.921240i	$0.372823\pi$
$542$	−3.65812	−	3.65812i	−0.157130	−	0.157130i
$543$	−0.789906			−0.0338981
$544$	−22.7513	+	3.82819i	−0.975455	+	0.164132i
$545$	19.2433			0.824291
$546$	−4.58188	−	4.58188i	−0.196086	−	0.196086i
$547$	36.0191	−	14.9196i	1.54007	−	0.637917i	0.558581	−	0.829450i	$-0.311346\pi$
$547$	36.0191	−	14.9196i	1.54007	−	0.637917i	0.981486	+	0.191534i	$0.0613461\pi$
$548$		−	12.9704i		−	0.554068i
$549$	−8.28985	−	20.0135i	−0.353802	−	0.854154i
$550$	−12.0071	−	4.97350i	−0.511984	−	0.212071i
$551$	9.05702	−	21.8656i	0.385842	−	0.931505i
$552$	−9.67749	+	9.67749i	−0.411901	+	0.411901i
$553$	−11.6434	+	11.6434i	−0.495128	+	0.495128i
$554$	−10.8493	+	26.1925i	−0.460942	+	1.11281i
$555$	8.92217	+	3.69568i	0.378725	+	0.156873i
$556$	8.95399	+	21.6168i	0.379734	+	0.916758i
$557$			41.5942i			1.76240i	0.472739	+	0.881202i	$0.343265\pi$
$557$			41.5942i			1.76240i	−0.472739	+	0.881202i	$0.656735\pi$
$558$	−8.80489	+	3.64711i	−0.372741	+	0.154394i
$559$	2.76421	+	2.76421i	0.116914	+	0.116914i
$560$	1.17529			0.0496650
$561$	−4.26014	+	5.98381i	−0.179863	+	0.252637i
$562$	18.3648			0.774671
$563$	−12.9626	−	12.9626i	−0.546309	−	0.546309i	0.379062	−	0.925371i	$-0.376247\pi$
$563$	−12.9626	−	12.9626i	−0.546309	−	0.546309i	−0.925371	+	0.379062i	$0.876247\pi$
$564$	−1.98220	+	0.821056i	−0.0834658	+	0.0345727i
$565$		−	63.4977i		−	2.67137i
$566$	1.89226	+	4.56833i	0.0795378	+	0.192021i
$567$	−13.0034	−	5.38620i	−0.546093	−	0.226199i
$568$	1.11474	−	2.69122i	0.0467735	−	0.112921i
$569$	−8.56477	+	8.56477i	−0.359054	+	0.359054i	−0.863464	−	0.504410i	$-0.831710\pi$
$569$	−8.56477	+	8.56477i	−0.359054	+	0.359054i	0.504410	+	0.863464i	$0.331710\pi$
$570$	−3.84758	+	3.84758i	−0.161157	+	0.161157i
$571$	7.45033	−	17.9867i	0.311787	−	0.752720i	−0.687852	−	0.725851i	$-0.741446\pi$
$571$	7.45033	−	17.9867i	0.311787	−	0.752720i	0.999639	−	0.0268689i	$-0.00855367\pi$
$572$	11.4992	+	4.76311i	0.480804	+	0.199156i
$573$	2.03933	+	4.92339i	0.0851944	+	0.205678i
$574$			1.78975i			0.0747026i
$575$	−36.2528	+	15.0164i	−1.51185	+	0.626228i
$576$	9.44031	+	9.44031i	0.393346	+	0.393346i
$577$	−18.1904			−0.757276			−0.378638	−	0.925545i	$-0.623607\pi$
$577$	−18.1904			−0.757276			−0.378638	+	0.925545i	$0.623607\pi$
$578$	6.61410	−	13.6227i	0.275110	−	0.566630i
$579$	−3.35317			−0.139353
$580$	23.4932	+	23.4932i	0.975504	+	0.975504i
$581$	6.57044	−	2.72157i	0.272588	−	0.112910i
$582$		−	0.539849i		−	0.0223775i
$583$	−0.667985	−	1.61266i	−0.0276651	−	0.0667895i
$584$	−34.9244	−	14.4661i	−1.44518	−	0.598613i
$585$	12.3502	−	29.8160i	0.510617	−	1.23274i
$586$	−10.4674	+	10.4674i	−0.432404	+	0.432404i
$587$	21.8186	−	21.8186i	0.900551	−	0.900551i	−0.0949325	−	0.995484i	$-0.530264\pi$
$587$	21.8186	−	21.8186i	0.900551	−	0.900551i	0.995484	+	0.0949325i	$0.0302635\pi$
$588$	0.186347	−	0.449881i	0.00768481	−	0.0185528i
$589$	−10.8337	−	4.48746i	−0.446395	−	0.184903i
$590$	−4.14030	−	9.99557i	−0.170453	−	0.411511i
$591$			11.9253i			0.490541i
$592$	−0.535248	+	0.221707i	−0.0219985	+	0.00911209i
$593$	30.5969	+	30.5969i	1.25646	+	1.25646i	0.952770	+	0.303694i	$0.0982201\pi$
$593$	30.5969	+	30.5969i	1.25646	+	1.25646i	0.303694	+	0.952770i	$0.401780\pi$
$594$	8.79857			0.361010
$595$	21.3876	−	30.0411i	0.876806	−	1.23157i
$596$	0.648469			0.0265623
$597$	7.60372	+	7.60372i	0.311199	+	0.311199i
$598$	−22.8350	+	9.45855i	−0.933791	+	0.386789i
$599$		−	48.2164i		−	1.97007i	−0.172362	−	0.985034i	$-0.555140\pi$
$599$		−	48.2164i		−	1.97007i	0.172362	−	0.985034i	$-0.444860\pi$
$600$	−4.07944	−	9.84863i	−0.166542	−	0.402069i
$601$	8.28799	+	3.43300i	0.338074	+	0.140035i	0.545261	−	0.838267i	$-0.316431\pi$
$601$	8.28799	+	3.43300i	0.338074	+	0.140035i	−0.207187	+	0.978301i	$0.566431\pi$
$602$	0.939641	−	2.26850i	0.0382969	−	0.0924570i
$603$	−6.42764	+	6.42764i	−0.261754	+	0.261754i
$604$	0.344655	−	0.344655i	0.0140238	−	0.0140238i
$605$	5.01110	−	12.0979i	0.203730	−	0.491848i
$606$	−2.41818	−	1.00164i	−0.0982320	−	0.0406890i
$607$	12.3244	+	29.7537i	0.500231	+	1.20766i	0.949358	+	0.314196i	$0.101735\pi$
$607$	12.3244	+	29.7537i	0.500231	+	1.20766i	−0.449128	+	0.893468i	$0.648265\pi$
$608$			15.6041i			0.632829i
$609$	−14.5903	+	6.04348i	−0.591227	+	0.244894i
$610$	−17.4015	−	17.4015i	−0.704565	−	0.704565i
$611$	−10.2978			−0.416606
$612$	12.4810	−	2.10009i	0.504515	−	0.0848910i
$613$	−37.8169			−1.52741			−0.763706	−	0.645565i	$-0.776622\pi$
$613$	−37.8169			−1.52741			−0.763706	+	0.645565i	$0.776622\pi$
$614$	9.27150	+	9.27150i	0.374167	+	0.374167i
$615$	1.47508	−	0.611000i	0.0594811	−	0.0246379i
$616$		−	20.7775i		−	0.837149i
$617$	−10.0870	−	24.3521i	−0.406086	−	0.980378i	−0.986157	−	0.165812i	$-0.946975\pi$
$617$	−10.0870	−	24.3521i	−0.406086	−	0.980378i	0.580071	−	0.814566i	$-0.303025\pi$
$618$	−0.142554	−	0.0590477i	−0.00573435	−	0.00237525i
$619$	3.79981	−	9.17356i	0.152727	−	0.368717i	−0.828935	−	0.559345i	$-0.811053\pi$
$619$	3.79981	−	9.17356i	0.152727	−	0.368717i	0.981662	+	0.190629i	$0.0610526\pi$
$620$	11.6401	−	11.6401i	0.467480	−	0.467480i
$621$	18.7846	−	18.7846i	0.753799	−	0.753799i
$622$	−0.179127	+	0.432450i	−0.00718233	+	0.0173397i
$623$	−35.7674	−	14.8153i	−1.43299	−	0.593564i
$624$	−0.132706	−	0.320382i	−0.00531251	−	0.0128255i
$625$			22.0784i			0.883136i
$626$	−6.15388	+	2.54902i	−0.245959	+	0.101879i
$627$	3.51293	+	3.51293i	0.140293	+	0.140293i
$628$	10.7613			0.429424
$629$	−4.07333	+	17.7158i	−0.162414	+	0.706376i
$630$	−20.2707			−0.807606
$631$	2.38723	+	2.38723i	0.0950343	+	0.0950343i	0.753026	−	0.657991i	$-0.228594\pi$
$631$	2.38723	+	2.38723i	0.0950343	+	0.0950343i	−0.657991	+	0.753026i	$0.728594\pi$
$632$	−15.7642	+	6.52973i	−0.627065	+	0.259739i
$633$			12.4432i			0.494574i
$634$	1.01309	+	2.44583i	0.0402351	+	0.0971361i
$635$	−6.03037	−	2.49786i	−0.239308	−	0.0991247i
$636$	0.206157	−	0.497707i	0.00817466	−	0.0197354i
$637$	1.65265	−	1.65265i	0.0654804	−	0.0654804i
$638$	−14.1076	+	14.1076i	−0.558527	+	0.558527i
$639$	−0.992962	+	2.39722i	−0.0392810	+	0.0948327i
$640$	−19.5361	−	8.09212i	−0.772233	−	0.319869i
$641$	−17.7498	−	42.8518i	−0.701076	−	1.69255i	−0.721179	−	0.692748i	$-0.756400\pi$
$641$	−17.7498	−	42.8518i	−0.701076	−	1.69255i	0.0201038	−	0.999798i	$-0.493600\pi$
$642$			11.6490i			0.459751i
$643$	19.8190	−	8.20928i	0.781584	−	0.323743i	0.0440292	−	0.999030i	$-0.485981\pi$
$643$	19.8190	−	8.20928i	0.781584	−	0.323743i	0.737554	+	0.675288i	$0.235981\pi$
$644$	−16.6908	−	16.6908i	−0.657708	−	0.657708i
$645$	−2.19044			−0.0862486
$646$	−8.34368	−	5.94023i	−0.328278	−	0.233715i
$647$	20.3847			0.801406			0.400703	−	0.916208i	$-0.368766\pi$
$647$	20.3847			0.801406			0.400703	+	0.916208i	$0.368766\pi$
$648$	−10.3131	−	10.3131i	−0.405136	−	0.405136i
$649$	−9.12619	+	3.78019i	−0.358234	+	0.148386i
$650$		−	19.2516i		−	0.755111i
$651$	2.99435	+	7.22901i	0.117358	+	0.283327i
$652$	−27.8237	−	11.5249i	−1.08966	−	0.451352i
$653$	5.15037	−	12.4341i	0.201550	−	0.486584i	−0.790495	−	0.612468i	$-0.790177\pi$
$653$	5.15037	−	12.4341i	0.201550	−	0.486584i	0.992045	+	0.125884i	$0.0401768\pi$
$654$	−2.52178	+	2.52178i	−0.0986095	+	0.0986095i
$655$	30.5370	−	30.5370i	1.19318	−	1.19318i
$656$	−0.0366543	+	0.0884914i	−0.00143111	+	0.00345501i
$657$	31.1091	+	12.8858i	1.21368	+	0.502723i
$658$	2.47527	+	5.97583i	0.0964960	+	0.232962i
$659$		−	32.2707i		−	1.25709i	−0.777775	−	0.628543i	$-0.783651\pi$
$659$		−	32.2707i		−	1.25709i	0.777775	−	0.628543i	$-0.216349\pi$
$660$	−6.44335	+	2.66892i	−0.250807	+	0.103888i
$661$	−25.4436	−	25.4436i	−0.989643	−	0.989643i	0.0103039	−	0.999947i	$-0.496720\pi$
$661$	−25.4436	−	25.4436i	−0.989643	−	0.989643i	−0.999947	+	0.0103039i	$0.996720\pi$
$662$	−6.65415			−0.258621
$663$	−10.6041	−	2.43816i	−0.411829	−	0.0946903i
$664$	7.36952			0.285993
$665$	−17.6363	−	17.6363i	−0.683906	−	0.683906i
$666$	9.23166	−	3.82388i	0.357719	−	0.148172i
$667$			60.2385i			2.33244i
$668$	8.50791	+	20.5399i	0.329181	+	0.794713i
$669$	5.06152	+	2.09655i	0.195690	+	0.0810574i
$670$	−3.95185	+	9.54062i	−0.152673	+	0.368586i
$671$	−15.8880	+	15.8880i	−0.613348	+	0.613348i
$672$	7.36250	−	7.36250i	0.284015	−	0.284015i
$673$	5.14179	−	12.4134i	0.198202	−	0.478501i	−0.793263	−	0.608880i	$-0.791619\pi$
$673$	5.14179	−	12.4134i	0.198202	−	0.478501i	0.991464	+	0.130379i	$0.0416193\pi$
$674$	12.3788	+	5.12745i	0.476812	+	0.197502i
$675$	7.91843	+	19.1168i	0.304780	+	0.735805i
$676$			2.75290i			0.105881i
$677$	40.5939	−	16.8145i	1.56015	−	0.646235i	0.575034	−	0.818129i	$-0.304989\pi$
$677$	40.5939	−	16.8145i	1.56015	−	0.646235i	0.985115	+	0.171894i	$0.0549887\pi$
$678$	8.32121	+	8.32121i	0.319574	+	0.319574i
$679$	2.47453			0.0949636
$680$	32.3885	−	20.2789i	1.24204	−	0.777660i
$681$	−11.3436			−0.434688
$682$	6.98989	+	6.98989i	0.267657	+	0.267657i
$683$	−23.8151	+	9.86456i	−0.911261	+	0.377457i	−0.788539	−	0.614984i	$-0.789162\pi$
$683$	−23.8151	+	9.86456i	−0.911261	+	0.377457i	−0.122722	+	0.992441i	$0.539162\pi$
$684$		−	8.56016i		−	0.327306i
$685$	13.3491	+	32.2276i	0.510043	+	1.23135i
$686$	14.5232	+	6.01570i	0.554498	+	0.229681i
$687$	4.55351	−	10.9931i	0.173727	−	0.419415i
$688$	0.0929183	−	0.0929183i	0.00354248	−	0.00354248i
$689$	1.82834	−	1.82834i	0.0696543	−	0.0696543i
$690$	5.29993	−	12.7952i	0.201765	−	0.487104i
$691$	20.3858	+	8.44407i	0.775512	+	0.321227i	0.735103	−	0.677956i	$-0.237134\pi$
$691$	20.3858	+	8.44407i	0.775512	+	0.321227i	0.0404090	+	0.999183i	$0.487134\pi$
$692$	8.44234	+	20.3816i	0.320930	+	0.774793i
$693$			18.5077i			0.703048i
$694$	−29.2143	+	12.1010i	−1.10896	+	0.459347i
$695$	−44.4960	−	44.4960i	−1.68783	−	1.68783i
$696$	−16.3647			−0.620302
$697$	1.59487	+	2.54725i	0.0604099	+	0.0964839i
$698$	3.03532			0.114888
$699$	−2.51389	−	2.51389i	−0.0950841	−	0.0950841i
$700$	16.9859	−	7.03580i	0.642008	−	0.265928i
$701$		−	34.8257i		−	1.31535i	−0.753302	−	0.657674i	$-0.771540\pi$
$701$		−	34.8257i		−	1.31535i	0.753302	−	0.657674i	$-0.228460\pi$
$702$	4.98767	+	12.0413i	0.188247	+	0.454469i
$703$	11.3588	+	4.70497i	0.428405	+	0.177451i
$704$	5.29929	−	12.7936i	0.199724	−	0.482177i
$705$	4.08016	−	4.08016i	0.153668	−	0.153668i
$706$	1.20062	−	1.20062i	0.0451857	−	0.0451857i
$707$	4.59128	−	11.0843i	0.172673	−	0.416869i
$708$	−2.81658	−	1.16666i	−0.105853	−	0.0438459i
$709$	15.1033	+	36.4625i	0.567216	+	1.36938i	0.903893	+	0.427759i	$0.140697\pi$
$709$	15.1033	+	36.4625i	0.567216	+	1.36938i	−0.336677	+	0.941620i	$0.609303\pi$
$710$			2.94773i			0.110626i
$711$	14.0420	−	5.81639i	0.526616	−	0.218132i
$712$	−28.3672	−	28.3672i	−1.06311	−	1.06311i
$713$	29.8462			1.11775
$714$	1.13402	+	6.73960i	0.0424397	+	0.252223i
$715$	−33.4742			−1.25186
$716$	15.8973	+	15.8973i	0.594110	+	0.594110i
$717$	−1.55389	+	0.643644i	−0.0580313	+	0.0240373i
$718$			12.9250i			0.482356i
$719$	7.03334	+	16.9800i	0.262299	+	0.633247i	0.999080	−	0.0428851i	$-0.0136549\pi$
$719$	7.03334	+	16.9800i	0.262299	+	0.633247i	−0.736781	+	0.676132i	$0.763655\pi$
$720$	−1.00226	−	0.415148i	−0.0373519	−	0.0154717i
$721$	0.270659	−	0.653429i	0.0100799	−	0.0243350i
$722$	7.06948	−	7.06948i	0.263099	−	0.263099i
$723$	−0.899662	+	0.899662i	−0.0334588	+	0.0334588i
$724$	0.540242	−	1.30426i	0.0200779	−	0.0484725i
$725$	−43.3483	−	17.9555i	−1.60992	−	0.666849i
$726$	0.928703	+	2.24209i	0.0344674	+	0.0832116i
$727$			28.3954i			1.05313i	0.850136	+	0.526563i	$0.176520\pi$
$727$			28.3954i			1.05313i	−0.850136	+	0.526563i	$0.823480\pi$
$728$	28.4351	−	11.7782i	1.05387	−	0.436529i
$729$	3.82661	+	3.82661i	0.141726	+	0.141726i
$730$	38.2530			1.41581
$731$	−0.684146	−	4.06595i	−0.0253041	−	0.150385i
$732$	−6.93450			−0.256306
$733$	11.3853	+	11.3853i	0.420527	+	0.420527i	0.885385	−	0.464858i	$-0.153895\pi$
$733$	11.3853	+	11.3853i	0.420527	+	0.420527i	−0.464858	+	0.885385i	$0.653895\pi$
$734$	−15.5197	+	6.42848i	−0.572843	+	0.237280i
$735$			1.30961i			0.0483056i
$736$	−15.1987	−	36.6929i	−0.560231	−	1.35252i
$737$	8.71081	+	3.60813i	0.320867	+	0.132907i
$738$	0.632194	−	1.52625i	0.0232714	−	0.0561821i
$739$	−3.77813	+	3.77813i	−0.138981	+	0.138981i	−0.773174	−	0.634194i	$-0.781332\pi$
$739$	−3.77813	+	3.77813i	−0.138981	+	0.138981i	0.634194	+	0.773174i	$0.281332\pi$
$740$	−12.2043	+	12.2043i	−0.448640	+	0.448640i
$741$	−2.81624	+	6.79900i	−0.103457	+	0.249768i
$742$	−1.50046	−	0.621510i	−0.0550835	−	0.0228163i
$743$	−12.1247	−	29.2715i	−0.444811	−	1.07387i	−0.974240	−	0.225514i	$-0.927594\pi$
$743$	−12.1247	−	29.2715i	−0.444811	−	1.07387i	0.529429	−	0.848354i	$-0.322406\pi$
$744$			8.10818i			0.297260i
$745$	−1.61125	+	0.667403i	−0.0590318	+	0.0244518i
$746$	5.32861	+	5.32861i	0.195094	+	0.195094i
$747$	−6.56444			−0.240180
$748$	−6.96658	−	11.1267i	−0.254723	−	0.406832i
$749$	−53.3962			−1.95105
$750$	0.729140	+	0.729140i	0.0266244	+	0.0266244i
$751$	17.1645	−	7.10978i	0.626342	−	0.259439i	−0.0468559	−	0.998902i	$-0.514920\pi$
$751$	17.1645	−	7.10978i	0.626342	−	0.259439i	0.673198	+	0.739462i	$0.264920\pi$
$752$			0.346160i			0.0126231i
$753$	−7.33941	−	17.7189i	−0.267463	−	0.645713i
$754$	−27.3043	−	11.3098i	−0.994362	−	0.411878i
$755$	−0.501647	+	1.21108i	−0.0182568	+	0.0440759i
$756$	−8.80135	+	8.80135i	−0.320102	+	0.320102i
$757$	34.4969	−	34.4969i	1.25381	−	1.25381i	0.299813	−	0.953998i	$-0.403076\pi$
$757$	34.4969	−	34.4969i	1.25381	−	1.25381i	0.953998	−	0.299813i	$-0.0969243\pi$
$758$	−2.46432	+	5.94941i	−0.0895083	+	0.216092i
$759$	−11.6823	−	4.83896i	−0.424040	−	0.175643i
$760$	−9.89059	−	23.8780i	−0.358769	−	0.866146i
$761$		−	39.2276i		−	1.42200i	−0.703191	−	0.711001i	$-0.748242\pi$
$761$		−	39.2276i		−	1.42200i	0.703191	−	0.711001i	$-0.251758\pi$
$762$	1.11760	−	0.462927i	0.0404865	−	0.0167701i
$763$	−11.5592	−	11.5592i	−0.418471	−	0.418471i
$764$	−9.52407			−0.344569
$765$	−28.8502	+	18.0635i	−1.04308	+	0.653088i
$766$	−0.515742			−0.0186345
$767$	−10.3468	−	10.3468i	−0.373600	−	0.373600i
$768$	10.1659	−	4.21087i	0.366832	−	0.151947i
$769$		−	10.0719i		−	0.363203i	−0.983372	−	0.181601i	$-0.941872\pi$
$769$		−	10.0719i		−	0.363203i	0.983372	−	0.181601i	$-0.0581281\pi$
$770$	8.04611	+	19.4250i	0.289962	+	0.700029i
$771$	8.36423	+	3.46458i	0.301230	+	0.124774i
$772$	2.29335	−	5.53663i	0.0825393	−	0.199268i
$773$	5.24300	−	5.24300i	0.188578	−	0.188578i	−0.606503	−	0.795081i	$-0.707428\pi$
$773$	5.24300	−	5.24300i	0.188578	−	0.188578i	0.795081	+	0.606503i	$0.207428\pi$
$774$	−1.60260	+	1.60260i	−0.0576044	+	0.0576044i
$775$	−8.89635	+	21.4777i	−0.319566	+	0.771502i
$776$	2.36901	+	0.981278i	0.0850426	+	0.0352258i
$777$	−3.13948	−	7.57939i	−0.112628	−	0.271909i
$778$		−	28.9119i		−	1.03654i
$779$	1.87793	−	0.777862i	0.0672837	−	0.0278698i
$780$	−7.30511	−	7.30511i	−0.261565	−	0.261565i
$781$	2.69134			0.0963039
$782$	25.4060	+	5.84150i	0.908517	+	0.208892i
$783$	31.7648			1.13518
$784$	−0.0555534	−	0.0555534i	−0.00198405	−	0.00198405i
$785$	−26.7387	+	11.0755i	−0.954346	+	0.395303i
$786$			8.00358i			0.285478i
$787$	−7.55209	−	18.2324i	−0.269203	−	0.649914i	0.730243	−	0.683187i	$-0.239407\pi$
$787$	−7.55209	−	18.2324i	−0.269203	−	0.649914i	−0.999446	+	0.0332736i	$0.989407\pi$
$788$	−19.6906	−	8.15610i	−0.701447	−	0.290549i
$789$	−0.231406	+	0.558662i	−0.00823825	+	0.0198889i
$790$	12.2094	−	12.2094i	0.434390	−	0.434390i
$791$	−38.1423	+	38.1423i	−1.35618	+	1.35618i
$792$	−7.33925	+	17.7185i	−0.260789	+	0.629600i
$793$	−30.7499	−	12.7370i	−1.09196	−	0.452305i
$794$	−10.4335	−	25.1887i	−0.370271	−	0.893914i
$795$			1.44883i			0.0513848i
$796$	−17.7554	+	7.35452i	−0.629323	+	0.260674i
$797$	25.3909	+	25.3909i	0.899393	+	0.899393i	0.995382	−	0.0959893i	$-0.0306015\pi$
$797$	25.3909	+	25.3909i	0.899393	+	0.899393i	−0.0959893	+	0.995382i	$0.530601\pi$
$798$	4.62238			0.163631
$799$	8.84805	+	6.29932i	0.313021	+	0.222854i
$800$	30.9350			1.09372
$801$	25.2683	+	25.2683i	0.892811	+	0.892811i
$802$	25.5711	−	10.5919i	0.902949	−	0.374014i
$803$		−	34.9259i		−	1.23251i
$804$	1.11356	+	2.68838i	0.0392723	+	0.0948118i
$805$	58.6497	+	24.2935i	2.06713	+	0.856233i
$806$	−5.60364	+	13.5284i	−0.197380	+	0.476517i
$807$	4.41976	−	4.41976i	0.155583	−	0.155583i
$808$	8.79101	−	8.79101i	0.309267	−	0.309267i
$809$	−0.840235	+	2.02851i	−0.0295411	+	0.0713185i	−0.937962	−	0.346739i	$-0.887289\pi$
$809$	−0.840235	+	2.02851i	−0.0295411	+	0.0713185i	0.908421	+	0.418058i	$0.137289\pi$
$810$	13.6355	+	5.64801i	0.479103	+	0.198451i
$811$	−17.4264	−	42.0709i	−0.611922	−	1.47731i	−0.860886	−	0.508798i	$-0.830090\pi$
$811$	−17.4264	−	42.0709i	−0.611922	−	1.47731i	0.248964	−	0.968513i	$-0.419910\pi$
$812$		−	28.2242i		−	0.990475i
$813$	3.62211	−	1.50033i	0.127033	−	0.0526188i
$814$	−7.32868	−	7.32868i	−0.256870	−	0.256870i
$815$	80.9951			2.83713
$816$	−0.0819581	+	0.356454i	−0.00286911	+	0.0124784i
$817$	−2.78865			−0.0975624
$818$	−10.1434	−	10.1434i	−0.354656	−	0.354656i
$819$	−25.3287	+	10.4915i	−0.885056	+	0.366602i
$820$			2.85348i			0.0996480i
$821$	5.07141	+	12.2435i	0.176994	+	0.427300i	0.987333	−	0.158660i	$-0.0507174\pi$
$821$	5.07141	+	12.2435i	0.176994	+	0.427300i	−0.810340	+	0.585960i	$0.800717\pi$
$822$	−5.97271	−	2.47398i	−0.208322	−	0.0862899i
$823$	6.05310	−	14.6135i	0.210998	−	0.509394i	−0.782579	−	0.622551i	$-0.786096\pi$
$823$	6.05310	−	14.6135i	0.210998	−	0.509394i	0.993577	+	0.113157i	$0.0360963\pi$
$824$	0.518237	−	0.518237i	0.0180536	−	0.0180536i
$825$	6.96435	−	6.96435i	0.242467	−	0.242467i
$826$	−3.51719	+	8.49124i	−0.122379	+	0.295448i
$827$	25.3346	+	10.4939i	0.880971	+	0.364910i	0.776873	−	0.629657i	$-0.216805\pi$
$827$	25.3346	+	10.4939i	0.880971	+	0.364910i	0.104098	+	0.994567i	$0.466805\pi$
$828$	8.33776	+	20.1291i	0.289757	+	0.699536i
$829$		−	10.8150i		−	0.375622i	−0.982205	−	0.187811i	$-0.939861\pi$
$829$		−	10.8150i		−	0.375622i	0.982205	−	0.187811i	$-0.0601392\pi$
$830$	−6.88982	+	2.85386i	−0.239149	+	0.0990588i
$831$	−15.1922	−	15.1922i	−0.527010	−	0.527010i
$832$	20.5127			0.711150
$833$	−2.43092	+	0.409033i	−0.0842265	+	0.0141722i
$834$	11.6622			0.403828
$835$	−42.2792	−	42.2792i	−1.46313	−	1.46313i
$836$	−8.20301	+	3.39780i	−0.283707	+	0.117515i
$837$		−	15.7385i		−	0.544001i
$838$	−3.60175	−	8.69538i	−0.124420	−	0.300377i
$839$	−37.1876	−	15.4036i	−1.28386	−	0.531792i	−0.366710	−	0.930335i	$-0.619516\pi$
$839$	−37.1876	−	15.4036i	−1.28386	−	0.531792i	−0.917149	+	0.398544i	$0.869516\pi$
$840$	−6.59970	+	15.9331i	−0.227711	+	0.549744i
$841$	−30.4257	+	30.4257i	−1.04916	+	1.04916i
$842$	4.18064	−	4.18064i	0.144074	−	0.144074i
$843$	−5.32596	+	12.8580i	−0.183436	+	0.442853i
$844$	−20.5458	−	8.51034i	−0.707215	−	0.292938i
$845$	−2.83328	−	6.84014i	−0.0974678	−	0.235308i
$846$		−	5.97037i		−	0.205266i
$847$	−10.2771	+	4.25693i	−0.353127	+	0.146270i
$848$	−0.0614592	−	0.0614592i	−0.00211052	−	0.00211052i
$849$	−3.74727			−0.128606
$850$	−11.7765	+	16.5413i	−0.403929	+	0.567360i
$851$	−31.2928			−1.07270
$852$	0.587336	+	0.587336i	0.0201218	+	0.0201218i
$853$	−42.8332	+	17.7421i	−1.46658	+	0.607477i	−0.966076	−	0.258257i	$-0.916852\pi$
$853$	−42.8332	+	17.7421i	−1.46658	+	0.607477i	−0.500504	+	0.865734i	$0.666852\pi$
$854$			20.9057i			0.715378i
$855$	8.81010	+	21.2695i	0.301299	+	0.727400i
$856$	−51.1194	−	21.1743i	−1.74722	−	0.723724i
$857$	−15.9801	+	38.5795i	−0.545871	+	1.31785i	0.374653	+	0.927165i	$0.377762\pi$
$857$	−15.9801	+	38.5795i	−0.545871	+	1.31785i	−0.920525	+	0.390685i	$0.872238\pi$
$858$	4.38671	−	4.38671i	0.149760	−	0.149760i
$859$	−2.87036	+	2.87036i	−0.0979354	+	0.0979354i	−0.754377	−	0.656442i	$-0.772061\pi$
$859$	−2.87036	+	2.87036i	−0.0979354	+	0.0979354i	0.656442	+	0.754377i	$0.272061\pi$
$860$	1.49812	−	3.61677i	0.0510853	−	0.123331i
$861$	−1.25308	−	0.519045i	−0.0427050	−	0.0176890i
$862$	12.1964	+	29.4447i	0.415411	+	1.00289i
$863$		−	1.37203i		−	0.0467044i	−0.999727	−	0.0233522i	$-0.992566\pi$
$863$		−	1.37203i		−	0.0467044i	0.999727	−	0.0233522i	$-0.00743391\pi$
$864$	−19.3488	+	8.01455i	−0.658261	+	0.272661i
$865$	−41.9534	−	41.9534i	−1.42646	−	1.42646i
$866$	−3.30924			−0.112452
$867$	7.61973	+	8.58155i	0.258780	+	0.291445i
$868$	−13.9842			−0.474654
$869$	−11.1474	−	11.1474i	−0.378151	−	0.378151i
$870$	15.2995	−	6.33724i	0.518700	−	0.214853i
$871$			13.9665i			0.473238i
$872$	−6.48250	−	15.6501i	−0.219525	−	0.529980i
$873$	−2.11021	−	0.874078i	−0.0714199	−	0.0295831i
$874$	6.74733	−	16.2895i	0.228232	−	0.551000i
$875$	−3.34219	+	3.34219i	−0.112987	+	0.112987i
$876$	7.62193	−	7.62193i	0.257521	−	0.257521i
$877$	−17.2859	+	41.7318i	−0.583702	+	1.40918i	0.305732	+	0.952118i	$0.401099\pi$
$877$	−17.2859	+	41.7318i	−0.583702	+	1.40918i	−0.889434	+	0.457064i	$0.848901\pi$
$878$	−14.0775	−	5.83111i	−0.475094	−	0.196790i
$879$	−4.29306	−	10.3644i	−0.144801	−	0.349581i
$880$			1.12523i			0.0379314i
$881$	−12.0292	+	4.98264i	−0.405273	+	0.167869i	−0.576002	−	0.817449i	$-0.695388\pi$
$881$	−12.0292	+	4.98264i	−0.405273	+	0.167869i	0.170729	+	0.985318i	$0.445388\pi$
$882$	0.958154	+	0.958154i	0.0322627	+	0.0322627i
$883$	13.1068			0.441079			0.220539	−	0.975378i	$-0.429218\pi$
$883$	13.1068			0.441079			0.220539	+	0.975378i	$0.429218\pi$
$884$	11.2783	−	15.8415i	0.379330	−	0.532808i
$885$	8.19908			0.275609
$886$	19.5970	+	19.5970i	0.658373	+	0.658373i
$887$	15.4970	−	6.41905i	0.520337	−	0.215531i	−0.107028	−	0.994256i	$-0.534133\pi$
$887$	15.4970	−	6.41905i	0.520337	−	0.215531i	0.627365	+	0.778725i	$0.284133\pi$
$888$		−	8.50117i		−	0.285281i
$889$	2.12193	+	5.12280i	0.0711674	+	0.171813i
$890$	37.5060	+	15.5355i	1.25720	+	0.520750i
$891$	5.15677	−	12.4495i	0.172758	−	0.417075i
$892$	−6.92349	+	6.92349i	−0.231815	+	0.231815i
$893$	5.19444	−	5.19444i	0.173825	−	0.173825i
$894$	0.123689	−	0.298612i	0.00413679	−	0.00998709i
$895$	−55.8615	−	23.1386i	−1.86724	−	0.773438i
$896$	6.87426	+	16.5959i	0.229653	+	0.554431i
$897$		−	18.7309i		−	0.625406i
$898$	−4.69146	+	1.94326i	−0.156556	+	0.0648476i
$899$	25.2351	+	25.2351i	0.841637	+	0.841637i
$900$	−16.9704			−0.565681
$901$	−2.68935	+	0.452517i	−0.0895953	+	0.0150755i
$902$	−1.71351			−0.0570537
$903$	1.31577	+	1.31577i	0.0437862	+	0.0437862i
$904$	−51.6413	+	21.3905i	−1.71756	+	0.711438i
$905$			3.79672i			0.126207i
$906$	−0.0929698	−	0.224449i	−0.00308872	−	0.00745682i
$907$	12.2328	+	5.06698i	0.406182	+	0.168246i	0.576414	−	0.817158i	$-0.304452\pi$
$907$	12.2328	+	5.06698i	0.406182	+	0.168246i	−0.170232	+	0.985404i	$0.554452\pi$
$908$	7.75826	−	18.7301i	0.257467	−	0.621580i
$909$	−7.83064	+	7.83064i	−0.259726	+	0.259726i
$910$	−22.0230	+	22.0230i	−0.730055	+	0.730055i
$911$	−15.5035	+	37.4287i	−0.513653	+	1.24007i	0.428090	+	0.903736i	$0.359186\pi$
$911$	−15.5035	+	37.4287i	−0.513653	+	1.24007i	−0.941743	+	0.336332i	$0.890814\pi$
$912$	0.228547	+	0.0946671i	0.00756794	+	0.00313474i
$913$	2.60564	+	6.29056i	0.0862340	+	0.208187i
$914$			23.0128i			0.761195i
$915$	17.2302	−	7.13697i	0.569612	−	0.235941i
$916$	15.0371	+	15.0371i	0.496841	+	0.496841i
$917$	−36.6863			−1.21149
$918$	3.08033	−	13.3970i	0.101666	−	0.442168i
$919$	−22.8992			−0.755373			−0.377687	−	0.925933i	$-0.623280\pi$
$919$	−22.8992			−0.755373			−0.377687	+	0.925933i	$0.623280\pi$
$920$	46.5153	+	46.5153i	1.53356	+	1.53356i
$921$	−9.18022	+	3.80257i	−0.302499	+	0.125299i
$922$			37.0733i			1.22094i
$923$	1.52565	+	3.68324i	0.0502173	+	0.121235i
$924$	5.47363	+	2.26725i	0.180069	+	0.0745871i
$925$	9.32755	−	22.5187i	0.306688	−	0.740410i
$926$	−17.9590	+	17.9590i	−0.590171	+	0.590171i
$927$	−0.461622	+	0.461622i	−0.0151617	+	0.0151617i
$928$	18.1734	−	43.8745i	0.596572	−	1.44025i
$929$	11.6208	+	4.81351i	0.381268	+	0.157926i	0.565082	−	0.825035i	$-0.308845\pi$
$929$	11.6208	+	4.81351i	0.381268	+	0.157926i	−0.183814	+	0.982961i	$0.558845\pi$
$930$	−3.13990	−	7.58039i	−0.102961	−	0.248571i
$931$			1.66726i			0.0546422i
$932$	5.87017	−	2.43150i	0.192284	−	0.0796465i
$933$	−0.250830	−	0.250830i	−0.00821179	−	0.00821179i
$934$	14.1691			0.463626
$935$	28.7615	+	20.4766i	0.940600	+	0.669655i
$936$	−28.4091			−0.928580
$937$	22.2459	+	22.2459i	0.726741	+	0.726741i	0.969969	−	0.243228i	$-0.0782063\pi$
$937$	22.2459	+	22.2459i	0.726741	+	0.726741i	−0.243228	+	0.969969i	$0.578206\pi$
$938$	8.10476	−	3.35710i	0.264630	−	0.109613i
$939$		−	5.04786i		−	0.164731i
$940$	3.94644	+	9.52755i	0.128719	+	0.310754i
$941$	50.1242	+	20.7621i	1.63400	+	0.676825i	0.995672	−	0.0929380i	$-0.0296258\pi$
$941$	50.1242	+	20.7621i	1.63400	+	0.676825i	0.638329	+	0.769763i	$0.279626\pi$
$942$	2.05262	−	4.95546i	0.0668779	−	0.161458i
$943$	−3.65827	+	3.65827i	−0.119130	+	0.119130i
$944$	−0.347804	+	0.347804i	−0.0113201	+	0.0113201i
$945$	12.8104	−	30.9271i	0.416723	−	1.00606i
$946$	2.17187	+	0.899616i	0.0706134	+	0.0292490i
$947$	17.3911	+	41.9859i	0.565136	+	1.36436i	0.905612	+	0.424106i	$0.139412\pi$
$947$	17.3911	+	41.9859i	0.565136	+	1.36436i	−0.340476	+	0.940253i	$0.610588\pi$
$948$		−	4.86544i		−	0.158022i
$949$	47.7979	−	19.7985i	1.55159	−	0.642688i
$950$	9.71091	+	9.71091i	0.315063	+	0.315063i
$951$	−2.00624			−0.0650568
$952$	−31.6366	−	7.27409i	−1.02535	−	0.235754i
$953$	−60.7530			−1.96798			−0.983991	−	0.178218i	$-0.942967\pi$
$953$	−60.7530			−1.96798			−0.983991	+	0.178218i	$0.942967\pi$
$954$	1.06001	+	1.06001i	0.0343192	+	0.0343192i
$955$	23.6645	−	9.80215i	0.765765	−	0.317190i
$956$		−	3.00594i		−	0.0972190i
$957$	−5.78605	−	13.9688i	−0.187037	−	0.451546i
$958$	1.16299	+	0.481727i	0.0375746	+	0.0155639i
$959$	11.3401	−	27.3774i	0.366190	−	0.884061i
$960$	−8.12744	+	8.12744i	−0.262312	+	0.262312i
$961$	−9.41714	+	9.41714i	−0.303779	+	0.303779i
$962$	5.87524	−	14.1841i	0.189425	−	0.457313i
$963$	45.5349	+	18.8612i	1.46734	+	0.607792i
$964$	−0.870177	−	2.10079i	−0.0280265	−	0.0676620i
$965$			16.1172i			0.518830i
$966$	−10.8695	+	4.50229i	−0.349720	+	0.144859i
$967$	28.6776	+	28.6776i	0.922210	+	0.922210i	0.997185	−	0.0749754i	$-0.0238878\pi$
$967$	28.6776	+	28.6776i	0.922210	+	0.922210i	−0.0749754	+	0.997185i	$0.523888\pi$
$968$	−11.5270			−0.370493
$969$	6.57878	−	4.11906i	0.211341	−	0.132323i
$970$	−2.59481			−0.0833142
$971$	16.7079	+	16.7079i	0.536182	+	0.536182i	0.922405	−	0.386223i	$-0.126221\pi$
$971$	16.7079	+	16.7079i	0.536182	+	0.536182i	−0.386223	+	0.922405i	$0.626221\pi$
$972$	16.3579	−	6.77568i	0.524681	−	0.217330i
$973$			53.4564i			1.71373i
$974$	−8.25282	−	19.9241i	−0.264437	−	0.638408i
$975$	13.4790	+	5.58316i	0.431672	+	0.178804i
$976$	−0.428152	+	1.03365i	−0.0137048	+	0.0330863i
$977$	−35.9738	+	35.9738i	−1.15090	+	1.15090i	−0.164533	+	0.986372i	$0.552612\pi$
$977$	−35.9738	+	35.9738i	−1.15090	+	1.15090i	−0.986372	+	0.164533i	$0.947388\pi$
$978$	−10.6142	+	10.6142i	−0.339404	+	0.339404i
$979$	14.1843	−	34.2438i	0.453331	−	1.09444i
$980$	−2.16237	−	0.895684i	−0.0690745	−	0.0286116i
$981$	5.77432	+	13.9404i	0.184360	+	0.445084i
$982$		−	13.2536i		−	0.422939i
$983$	−29.6010	+	12.2612i	−0.944127	+	0.391070i	−0.801020	−	0.598637i	$-0.795709\pi$
$983$	−29.6010	+	12.2612i	−0.944127	+	0.391070i	−0.143106	+	0.989707i	$0.545709\pi$
$984$	−0.993826	−	0.993826i	−0.0316820	−	0.0316820i
$985$	57.3194			1.82635
$986$	16.5418	+	26.4199i	0.526800	+	0.841380i
$987$	−4.90180			−0.156026
$988$	−9.30012	−	9.30012i	−0.295876	−	0.295876i
$989$	6.55748	−	2.71620i	0.208516	−	0.0863701i
$990$		−	19.4073i		−	0.616804i
$991$	16.9516	+	40.9247i	0.538484	+	1.30002i	0.925781	+	0.378061i	$0.123409\pi$
$991$	16.9516	+	40.9247i	0.538484	+	1.30002i	−0.387296	+	0.921955i	$0.626591\pi$
$992$	−21.7384	−	9.00434i	−0.690195	−	0.285888i
$993$	1.92977	−	4.65887i	0.0612394	−	0.147845i
$994$	1.77066	−	1.77066i	0.0561620	−	0.0561620i
$995$	36.5476	−	36.5476i	1.15864	−	1.15864i
$996$	−0.804166	+	1.94143i	−0.0254810	+	0.0615165i
$997$	−35.4689	−	14.6917i	−1.12331	−	0.465291i	−0.257809	−	0.966196i	$-0.583001\pi$
$997$	−35.4689	−	14.6917i	−1.12331	−	0.465291i	−0.865502	+	0.500905i	$0.833001\pi$
$998$	−12.6226	−	30.4737i	−0.399562	−	0.964629i
$999$			16.5013i			0.522078i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.b.87.20	✓	116
17.9	even	8	inner	731.2.m.b.689.20	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.b.87.20	✓	116	1.1	even	1	trivial
731.2.m.b.689.20	yes	116	17.9	even	8	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.629885 + 0.629885i) q^{2} +(-0.623684 + 0.258339i) q^{3} -1.20649i q^{4} +(1.24172 + 2.99777i) q^{5} +(-0.555573 - 0.230126i) q^{6} +(1.05484 - 2.54660i) q^{7} +(2.01972 - 2.01972i) q^{8} +(-1.79908 + 1.79908i) q^{9} +O(q^{10})\)	\(q+(0.629885 + 0.629885i) q^{2} +(-0.623684 + 0.258339i) q^{3} -1.20649i q^{4} +(1.24172 + 2.99777i) q^{5} +(-0.555573 - 0.230126i) q^{6} +(1.05484 - 2.54660i) q^{7} +(2.01972 - 2.01972i) q^{8} +(-1.79908 + 1.79908i) q^{9} +(-1.10611 + 2.67039i) q^{10} +(2.43813 + 1.00991i) q^{11} +(0.311683 + 0.752468i) q^{12} +3.90919i q^{13} +(2.26850 - 0.939641i) q^{14} +(-1.54888 - 1.54888i) q^{15} +0.131406 q^{16} +(2.39130 - 3.35882i) q^{17} -2.26642 q^{18} +(-1.97187 - 1.97187i) q^{19} +(3.61677 - 1.49812i) q^{20} +1.86078i q^{21} +(0.899616 + 2.17187i) q^{22} +(6.55748 + 2.71620i) q^{23} +(-0.737897 + 1.78144i) q^{24} +(-3.90922 + 3.90922i) q^{25} +(-2.46234 + 2.46234i) q^{26} +(1.43230 - 3.45788i) q^{27} +(-3.07245 - 1.27265i) q^{28} +(3.24782 + 7.84093i) q^{29} -1.95123i q^{30} +(3.88493 - 1.60919i) q^{31} +(-3.95667 - 3.95667i) q^{32} -1.78152 q^{33} +(3.62192 - 0.609432i) q^{34} +8.94393 q^{35} +(2.17057 + 2.17057i) q^{36} +(-4.07323 + 1.68719i) q^{37} -2.48411i q^{38} +(-1.00989 - 2.43810i) q^{39} +(8.56257 + 3.54673i) q^{40} +(-0.278939 + 0.673418i) q^{41} +(-1.17208 + 1.17208i) q^{42} +(0.707107 - 0.707107i) q^{43} +(1.21844 - 2.94157i) q^{44} +(-7.62716 - 3.15927i) q^{45} +(2.41957 + 5.84136i) q^{46} +2.63427i q^{47} +(-0.0819561 + 0.0339473i) q^{48} +(-0.422760 - 0.422760i) q^{49} -4.92472 q^{50} +(-0.623700 + 2.71261i) q^{51} +4.71639 q^{52} +(-0.467704 - 0.467704i) q^{53} +(3.08025 - 1.27588i) q^{54} +8.56295i q^{55} +(-3.01295 - 7.27390i) q^{56} +(1.73924 + 0.720415i) q^{57} +(-2.89313 + 6.98464i) q^{58} +(-2.64678 + 2.64678i) q^{59} +(-1.86870 + 1.86870i) q^{60} +(-3.25823 + 7.86606i) q^{61} +(3.46066 + 1.43345i) q^{62} +(2.68380 + 6.47927i) q^{63} -5.24731i q^{64} +(-11.7188 + 4.85410i) q^{65} +(-1.12215 - 1.12215i) q^{66} +3.57275 q^{67} +(-4.05239 - 2.88507i) q^{68} -4.79150 q^{69} +(5.63365 + 5.63365i) q^{70} +(0.942201 - 0.390273i) q^{71} +7.26726i q^{72} +(-5.06462 - 12.2271i) q^{73} +(-3.62840 - 1.50293i) q^{74} +(1.42822 - 3.44802i) q^{75} +(-2.37904 + 2.37904i) q^{76} +(5.14366 - 5.14366i) q^{77} +(0.899606 - 2.17184i) q^{78} +(-5.51905 - 2.28607i) q^{79} +(0.163169 + 0.393926i) q^{80} -5.10619i q^{81} +(-0.599876 + 0.248477i) q^{82} +(1.82439 + 1.82439i) q^{83} +2.24501 q^{84} +(13.0383 + 2.99784i) q^{85} +0.890792 q^{86} +(-4.05123 - 4.05123i) q^{87} +(6.96406 - 2.88461i) q^{88} -14.0451i q^{89} +(-2.81425 - 6.79421i) q^{90} +(9.95515 + 4.12356i) q^{91} +(3.27706 - 7.91153i) q^{92} +(-2.00725 + 2.00725i) q^{93} +(-1.65929 + 1.65929i) q^{94} +(3.46271 - 8.35972i) q^{95} +(3.48987 + 1.44555i) q^{96} +(0.343547 + 0.829395i) q^{97} -0.532581i q^{98} +(-6.20328 + 2.56948i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 8 q^{6}+O(q^{10}) \) 116 * q - 8 * q^6	\( 116 q - 8 q^{6} - 8 q^{10} + 8 q^{14} + 4 q^{15} - 68 q^{16} - 4 q^{17} - 44 q^{18} + 12 q^{19} + 8 q^{20} - 16 q^{22} - 28 q^{23} - 12 q^{24} - 4 q^{25} - 8 q^{26} + 24 q^{28} + 80 q^{33} + 32 q^{34} - 112 q^{35} + 160 q^{36} - 20 q^{37} + 8 q^{39} - 112 q^{40} + 8 q^{41} + 4 q^{42} + 32 q^{44} - 52 q^{45} - 40 q^{46} + 40 q^{48} + 8 q^{49} + 100 q^{50} - 32 q^{51} - 152 q^{52} + 28 q^{53} - 36 q^{54} + 124 q^{56} - 104 q^{57} - 32 q^{58} - 36 q^{59} - 24 q^{60} + 52 q^{61} - 68 q^{62} + 20 q^{63} + 20 q^{65} - 60 q^{66} + 64 q^{67} - 128 q^{69} + 188 q^{70} + 52 q^{73} - 104 q^{74} + 36 q^{75} - 112 q^{76} + 28 q^{77} + 56 q^{78} - 108 q^{79} - 44 q^{80} + 52 q^{82} - 52 q^{83} + 120 q^{84} + 12 q^{85} - 20 q^{86} + 56 q^{87} + 36 q^{88} + 144 q^{90} - 16 q^{92} - 176 q^{93} - 8 q^{94} + 164 q^{95} - 164 q^{96} - 8 q^{97} - 24 q^{99}+O(q^{100}) \) 116 * q - 8 * q^6 - 8 * q^10 + 8 * q^14 + 4 * q^15 - 68 * q^16 - 4 * q^17 - 44 * q^18 + 12 * q^19 + 8 * q^20 - 16 * q^22 - 28 * q^23 - 12 * q^24 - 4 * q^25 - 8 * q^26 + 24 * q^28 + 80 * q^33 + 32 * q^34 - 112 * q^35 + 160 * q^36 - 20 * q^37 + 8 * q^39 - 112 * q^40 + 8 * q^41 + 4 * q^42 + 32 * q^44 - 52 * q^45 - 40 * q^46 + 40 * q^48 + 8 * q^49 + 100 * q^50 - 32 * q^51 - 152 * q^52 + 28 * q^53 - 36 * q^54 + 124 * q^56 - 104 * q^57 - 32 * q^58 - 36 * q^59 - 24 * q^60 + 52 * q^61 - 68 * q^62 + 20 * q^63 + 20 * q^65 - 60 * q^66 + 64 * q^67 - 128 * q^69 + 188 * q^70 + 52 * q^73 - 104 * q^74 + 36 * q^75 - 112 * q^76 + 28 * q^77 + 56 * q^78 - 108 * q^79 - 44 * q^80 + 52 * q^82 - 52 * q^83 + 120 * q^84 + 12 * q^85 - 20 * q^86 + 56 * q^87 + 36 * q^88 + 144 * q^90 - 16 * q^92 - 176 * q^93 - 8 * q^94 + 164 * q^95 - 164 * q^96 - 8 * q^97 - 24 * q^99

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