LMFDB - Embedded newform 177.2.e.a.85.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,2,Mod(4,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(58))

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

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

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

chi := DirichletCharacter("177.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	177.e (of order $29$, degree $28$, 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:	$1.41335211578$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$5$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			85.3
Character	$\chi$	$=$	177.85
Dual form			177.2.e.a.25.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0877061 - 0.0666724i) q^{2} +(0.468408 - 0.883512i) q^{3} +(-0.531810 + 1.91540i) q^{4} +(0.442982 - 0.419615i) q^{5} +(-0.0178236 - 0.108719i) q^{6} +(2.33019 + 2.74331i) q^{7} +(0.162618 + 0.408142i) q^{8} +(-0.561187 - 0.827689i) q^{9} +O(q^{10})$	\(q+(0.0877061 - 0.0666724i) q^{2} +(0.468408 - 0.883512i) q^{3} +(-0.531810 + 1.91540i) q^{4} +(0.442982 - 0.419615i) q^{5} +(-0.0178236 - 0.108719i) q^{6} +(2.33019 + 2.74331i) q^{7} +(0.162618 + 0.408142i) q^{8} +(-0.561187 - 0.827689i) q^{9} +(0.0108755 - 0.0663375i) q^{10} +(3.02513 - 1.82016i) q^{11} +(1.44318 + 1.36705i) q^{12} +(0.575044 - 0.848127i) q^{13} +(0.387275 + 0.0852456i) q^{14} +(-0.163238 - 0.587931i) q^{15} +(-3.36515 - 2.02475i) q^{16} +(-0.775943 + 0.913511i) q^{17} +(-0.104404 - 0.0351777i) q^{18} +(-3.75617 - 1.73779i) q^{19} +(0.568150 + 1.07165i) q^{20} +(3.51523 - 0.773760i) q^{21} +(0.143968 - 0.361332i) q^{22} +(2.81680 - 0.949089i) q^{23} +(0.436770 + 0.0475016i) q^{24} +(-0.250538 + 4.62090i) q^{25} +(-0.00611180 - 0.112725i) q^{26} +(-0.994138 + 0.108119i) q^{27} +(-6.49376 + 3.00434i) q^{28} +(-7.21499 - 5.48469i) q^{29} +(-0.0535158 - 0.0406816i) q^{30} +(-1.77855 + 0.822846i) q^{31} +(-1.30368 + 0.141784i) q^{32} +(-0.191137 - 3.52532i) q^{33} +(-0.00714894 + 0.131854i) q^{34} +(2.18337 + 0.237455i) q^{35} +(1.88380 - 0.634728i) q^{36} +(-1.02217 + 2.56546i) q^{37} +(-0.445302 + 0.0980184i) q^{38} +(-0.479975 - 0.905328i) q^{39} +(0.243299 + 0.112562i) q^{40} +(6.93080 + 2.33526i) q^{41} +(0.256718 - 0.302232i) q^{42} +(-4.73188 - 2.84708i) q^{43} +(1.87755 + 6.76233i) q^{44} +(-0.595906 - 0.131169i) q^{45} +(0.183772 - 0.271044i) q^{46} +(-7.93582 - 7.51721i) q^{47} +(-3.36515 + 2.02475i) q^{48} +(-0.963497 + 5.87707i) q^{49} +(0.286113 + 0.421985i) q^{50} +(0.443639 + 1.11345i) q^{51} +(1.31869 + 1.55248i) q^{52} +(-1.55014 - 9.45546i) q^{53} +(-0.0799834 + 0.0757643i) q^{54} +(0.576312 - 2.07569i) q^{55} +(-0.740727 + 1.39716i) q^{56} +(-3.29478 + 2.50463i) q^{57} -0.998476 q^{58} +(-4.40030 + 6.29582i) q^{59} +1.21294 q^{60} +(2.38339 - 1.81180i) q^{61} +(-0.101129 + 0.190749i) q^{62} +(0.962936 - 3.46818i) q^{63} +(5.59755 - 5.30228i) q^{64} +(-0.101152 - 0.617002i) q^{65} +(-0.251805 - 0.296448i) q^{66} +(-2.67693 - 6.71858i) q^{67} +(-1.33709 - 1.97206i) q^{68} +(0.480880 - 2.93324i) q^{69} +(0.207326 - 0.124744i) q^{70} +(-1.08168 - 1.02462i) q^{71} +(0.246555 - 0.363641i) q^{72} +(13.9795 + 3.07713i) q^{73} +(0.0813946 + 0.293157i) q^{74} +(3.96527 + 2.38582i) q^{75} +(5.32614 - 6.27042i) q^{76} +(12.0424 + 4.05755i) q^{77} +(-0.102457 - 0.0474017i) q^{78} +(0.722413 + 1.36261i) q^{79} +(-2.34032 + 0.515143i) q^{80} +(-0.370138 + 0.928977i) q^{81} +(0.763571 - 0.257277i) q^{82} +(-5.87437 - 0.638876i) q^{83} +(-0.387368 + 7.14458i) q^{84} +(0.0395939 + 0.730266i) q^{85} +(-0.604836 + 0.0657798i) q^{86} +(-8.22535 + 3.80545i) q^{87} +(1.23483 + 0.938690i) q^{88} +(13.4725 + 10.2416i) q^{89} +(-0.0610100 + 0.0282262i) q^{90} +(3.66664 - 0.398771i) q^{91} +(0.319891 + 5.90004i) q^{92} +(-0.106095 + 1.95680i) q^{93} +(-1.19721 - 0.130205i) q^{94} +(-2.39312 + 0.806336i) q^{95} +(-0.485387 + 1.21823i) q^{96} +(9.58132 - 2.10901i) q^{97} +(0.307334 + 0.579693i) q^{98} +(-3.20419 - 1.48242i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - q^{2} - 5 q^{3} - 9 q^{4} - 2 q^{5} - q^{6} - 2 q^{7} - 9 q^{8} - 5 q^{9}+O(q^{10}) $ 140 * q - q^2 - 5 * q^3 - 9 * q^4 - 2 * q^5 - q^6 - 2 * q^7 - 9 * q^8 - 5 * q^9	\( 140 q - q^{2} - 5 q^{3} - 9 q^{4} - 2 q^{5} - q^{6} - 2 q^{7} - 9 q^{8} - 5 q^{9} + 88 q^{10} - 14 q^{11} - 9 q^{12} - 12 q^{13} - q^{14} - 2 q^{15} - 41 q^{16} - 16 q^{17} - q^{18} - 10 q^{19} - 32 q^{20} + 27 q^{21} - 26 q^{22} - 22 q^{23} - 9 q^{24} + 27 q^{25} - 56 q^{26} - 5 q^{27} - 50 q^{28} - 24 q^{29} - 28 q^{30} - 24 q^{31} + 106 q^{32} - 14 q^{33} - 54 q^{34} - 70 q^{35} - 9 q^{36} - 28 q^{37} - 80 q^{38} - 12 q^{39} - 50 q^{40} - 40 q^{41} - 30 q^{42} + 4 q^{43} - 104 q^{44} - 2 q^{45} - 28 q^{46} + 31 q^{47} - 41 q^{48} - q^{49} + 39 q^{50} - 16 q^{51} + 62 q^{52} + 4 q^{53} - q^{54} + 5 q^{55} + 96 q^{56} - 10 q^{57} + 128 q^{58} - q^{59} - 32 q^{60} - 16 q^{61} + 223 q^{62} - 2 q^{63} + 97 q^{64} + 121 q^{65} - 26 q^{66} - 12 q^{67} + 10 q^{68} + 36 q^{69} - 2 q^{70} - 22 q^{71} - 9 q^{72} + 179 q^{73} - 38 q^{74} - 31 q^{75} + 112 q^{76} - 62 q^{77} - 56 q^{78} - 84 q^{79} + 204 q^{80} - 5 q^{81} - 152 q^{82} - 88 q^{83} + 95 q^{84} - 118 q^{85} - 118 q^{86} + 34 q^{87} + 18 q^{88} - 86 q^{89} - 28 q^{90} + 78 q^{91} - 174 q^{92} - 24 q^{93} - 164 q^{94} + 218 q^{95} - 39 q^{96} - 84 q^{97} + 129 q^{98} - 14 q^{99}+O(q^{100}) \) 140 * q - q^2 - 5 * q^3 - 9 * q^4 - 2 * q^5 - q^6 - 2 * q^7 - 9 * q^8 - 5 * q^9 + 88 * q^10 - 14 * q^11 - 9 * q^12 - 12 * q^13 - q^14 - 2 * q^15 - 41 * q^16 - 16 * q^17 - q^18 - 10 * q^19 - 32 * q^20 + 27 * q^21 - 26 * q^22 - 22 * q^23 - 9 * q^24 + 27 * q^25 - 56 * q^26 - 5 * q^27 - 50 * q^28 - 24 * q^29 - 28 * q^30 - 24 * q^31 + 106 * q^32 - 14 * q^33 - 54 * q^34 - 70 * q^35 - 9 * q^36 - 28 * q^37 - 80 * q^38 - 12 * q^39 - 50 * q^40 - 40 * q^41 - 30 * q^42 + 4 * q^43 - 104 * q^44 - 2 * q^45 - 28 * q^46 + 31 * q^47 - 41 * q^48 - q^49 + 39 * q^50 - 16 * q^51 + 62 * q^52 + 4 * q^53 - q^54 + 5 * q^55 + 96 * q^56 - 10 * q^57 + 128 * q^58 - q^59 - 32 * q^60 - 16 * q^61 + 223 * q^62 - 2 * q^63 + 97 * q^64 + 121 * q^65 - 26 * q^66 - 12 * q^67 + 10 * q^68 + 36 * q^69 - 2 * q^70 - 22 * q^71 - 9 * q^72 + 179 * q^73 - 38 * q^74 - 31 * q^75 + 112 * q^76 - 62 * q^77 - 56 * q^78 - 84 * q^79 + 204 * q^80 - 5 * q^81 - 152 * q^82 - 88 * q^83 + 95 * q^84 - 118 * q^85 - 118 * q^86 + 34 * q^87 + 18 * q^88 - 86 * q^89 - 28 * q^90 + 78 * q^91 - 174 * q^92 - 24 * q^93 - 164 * q^94 + 218 * q^95 - 39 * q^96 - 84 * q^97 + 129 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{23}{29}\right)$	$1$

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 $

$2$	0.0877061	−	0.0666724i	0.0620176	−	0.0471445i	−0.573706	−	0.819061i	$-0.694495\pi$
$2$	0.0877061	−	0.0666724i	0.0620176	−	0.0471445i	0.635724	+	0.771917i	$0.280702\pi$
$3$	0.468408	−	0.883512i	0.270436	−	0.510096i
$3$	0.468408	−	0.883512i	0.270436	−	0.510096i
$4$	−0.531810	+	1.91540i	−0.265905	+	0.957702i
$5$	0.442982	−	0.419615i	0.198108	−	0.187657i	−0.582215	−	0.813035i	$-0.697814\pi$
$5$	0.442982	−	0.419615i	0.198108	−	0.187657i	0.780322	+	0.625378i	$0.215055\pi$
$6$	−0.0178236	−	0.108719i	−0.00727646	−	0.0443845i
$7$	2.33019	+	2.74331i	0.880728	+	1.03687i	0.999036	+	0.0438966i	$0.0139772\pi$
$7$	2.33019	+	2.74331i	0.880728	+	1.03687i	−0.118308	+	0.992977i	$0.537747\pi$
$8$	0.162618	+	0.408142i	0.0574943	+	0.144300i
$9$	−0.561187	−	0.827689i	−0.187062	−	0.275896i
$10$	0.0108755	−	0.0663375i	0.00343913	−	0.0209777i
$11$	3.02513	−	1.82016i	0.912111	−	0.548799i	0.0195917	−	0.999808i	$-0.493763\pi$
$11$	3.02513	−	1.82016i	0.912111	−	0.548799i	0.892519	+	0.451009i	$0.148936\pi$
$12$	1.44318	+	1.36705i	0.416610	+	0.394634i
$13$	0.575044	−	0.848127i	0.159489	−	0.235228i	−0.739546	−	0.673106i	$-0.764960\pi$
$13$	0.575044	−	0.848127i	0.159489	−	0.235228i	0.899034	+	0.437878i	$0.144270\pi$
$14$	0.387275	+	0.0852456i	0.103504	+	0.0227829i
$15$	−0.163238	−	0.587931i	−0.0421479	−	0.151803i
$16$	−3.36515	−	2.02475i	−0.841288	−	0.506186i
$17$	−0.775943	+	0.913511i	−0.188194	+	0.221559i	−0.848165	−	0.529732i	$-0.822293\pi$
$17$	−0.775943	+	0.913511i	−0.188194	+	0.221559i	0.659971	+	0.751291i	$0.270568\pi$
$18$	−0.104404	−	0.0351777i	−0.0246082	−	0.00829145i
$19$	−3.75617	−	1.73779i	−0.861725	−	0.398677i	−0.0613074	−	0.998119i	$-0.519527\pi$
$19$	−3.75617	−	1.73779i	−0.861725	−	0.398677i	−0.800418	+	0.599442i	$0.795389\pi$
$20$	0.568150	+	1.07165i	0.127042	+	0.239627i
$21$	3.51523	−	0.773760i	0.767085	−	0.168848i
$22$	0.143968	−	0.361332i	0.0306940	−	0.0770362i
$23$	2.81680	−	0.949089i	0.587343	−	0.197899i	−0.00991139	−	0.999951i	$-0.503155\pi$
$23$	2.81680	−	0.949089i	0.587343	−	0.197899i	0.597254	+	0.802052i	$0.296258\pi$
$24$	0.436770	+	0.0475016i	0.0891553	+	0.00969622i
$25$	−0.250538	+	4.62090i	−0.0501076	+	0.924181i
$26$	−0.00611180	−	0.112725i	−0.00119862	−	0.0221073i
$27$	−0.994138	+	0.108119i	−0.191322	+	0.0208075i
$28$	−6.49376	+	3.00434i	−1.22721	+	0.567766i
$29$	−7.21499	−	5.48469i	−1.33979	−	1.01848i	−0.996865	−	0.0791185i	$-0.974789\pi$
$29$	−7.21499	−	5.48469i	−1.33979	−	1.01848i	−0.342924	−	0.939363i	$-0.611417\pi$
$30$	−0.0535158	−	0.0406816i	−0.00977060	−	0.00742742i
$31$	−1.77855	+	0.822846i	−0.319438	+	0.147788i	−0.573055	−	0.819517i	$-0.694242\pi$
$31$	−1.77855	+	0.822846i	−0.319438	+	0.147788i	0.253617	+	0.967305i	$0.418380\pi$
$32$	−1.30368	+	0.141784i	−0.230460	+	0.0250640i
$33$	−0.191137	−	3.52532i	−0.0332727	−	0.613679i
$34$	−0.00714894	+	0.131854i	−0.00122603	+	0.0226128i
$35$	2.18337	+	0.237455i	0.369056	+	0.0401373i
$36$	1.88380	−	0.634728i	0.313967	−	0.105788i
$37$	−1.02217	+	2.56546i	−0.168044	+	0.421758i	−0.988747	−	0.149596i	$-0.952203\pi$
$37$	−1.02217	+	2.56546i	−0.168044	+	0.421758i	0.820703	+	0.571355i	$0.193582\pi$
$38$	−0.445302	+	0.0980184i	−0.0722375	+	0.0159007i
$39$	−0.479975	−	0.905328i	−0.0768575	−	0.144969i
$40$	0.243299	+	0.112562i	0.0384690	+	0.0177977i
$41$	6.93080	+	2.33526i	1.08241	+	0.364706i	0.803313	−	0.595557i	$-0.203069\pi$
$41$	6.93080	+	2.33526i	1.08241	+	0.364706i	0.279096	+	0.960263i	$0.409965\pi$
$42$	0.256718	−	0.302232i	0.0396125	−	0.0466354i
$43$	−4.73188	−	2.84708i	−0.721604	−	0.434175i	0.106818	−	0.994279i	$-0.465934\pi$
$43$	−4.73188	−	2.84708i	−0.721604	−	0.434175i	−0.828423	+	0.560104i	$0.810761\pi$
$44$	1.87755	+	6.76233i	0.283051	+	1.01946i
$45$	−0.595906	−	0.131169i	−0.0888325	−	0.0195535i
$46$	0.183772	−	0.271044i	0.0270957	−	0.0399632i
$47$	−7.93582	−	7.51721i	−1.15756	−	1.09650i	−0.993934	−	0.109975i	$-0.964923\pi$
$47$	−7.93582	−	7.51721i	−1.15756	−	1.09650i	−0.163625	−	0.986523i	$-0.552319\pi$
$48$	−3.36515	+	2.02475i	−0.485718	+	0.292247i
$49$	−0.963497	+	5.87707i	−0.137642	+	0.839581i
$50$	0.286113	+	0.421985i	0.0404625	+	0.0596777i
$51$	0.443639	+	1.11345i	0.0621219	+	0.155914i
$52$	1.31869	+	1.55248i	0.182870	+	0.215291i
$53$	−1.55014	−	9.45546i	−0.212929	−	1.29881i	−0.849500	−	0.527589i	$-0.823096\pi$
$53$	−1.55014	−	9.45546i	−0.212929	−	1.29881i	0.636571	−	0.771218i	$-0.280352\pi$
$54$	−0.0799834	+	0.0757643i	−0.0108844	+	0.0103102i
$55$	0.576312	−	2.07569i	0.0777099	−	0.279886i
$56$	−0.740727	+	1.39716i	−0.0989838	+	0.186703i
$57$	−3.29478	+	2.50463i	−0.436405	+	0.331746i
$58$	−0.998476			−0.131106
$59$	−4.40030	+	6.29582i	−0.572870	+	0.819646i
$59$	−4.40030	+	6.29582i	−0.572870	+	0.819646i
$60$	1.21294			0.156590
$61$	2.38339	−	1.81180i	0.305161	−	0.231978i	−0.441374	−	0.897323i	$-0.645509\pi$
$61$	2.38339	−	1.81180i	0.305161	−	0.231978i	0.746536	+	0.665346i	$0.231716\pi$
$62$	−0.101129	+	0.190749i	−0.0128434	+	0.0242252i
$63$	0.962936	−	3.46818i	0.121318	−	0.436950i
$64$	5.59755	−	5.30228i	0.699694	−	0.662785i
$65$	−0.101152	−	0.617002i	−0.0125464	−	0.0765297i
$66$	−0.251805	−	0.296448i	−0.0309951	−	0.0364902i
$67$	−2.67693	−	6.71858i	−0.327039	−	0.820805i	−0.996926	−	0.0783430i	$-0.975037\pi$
$67$	−2.67693	−	6.71858i	−0.327039	−	0.820805i	0.669888	−	0.742462i	$-0.266342\pi$
$68$	−1.33709	−	1.97206i	−0.162146	−	0.239147i
$69$	0.480880	−	2.93324i	0.0578911	−	0.353120i
$70$	0.207326	−	0.124744i	0.0247802	−	0.0149098i
$71$	−1.08168	−	1.02462i	−0.128372	−	0.121600i	0.620821	−	0.783953i	$-0.286800\pi$
$71$	−1.08168	−	1.02462i	−0.128372	−	0.121600i	−0.749192	+	0.662352i	$0.769558\pi$
$72$	0.246555	−	0.363641i	0.0290568	−	0.0428555i
$73$	13.9795	+	3.07713i	1.63618	+	0.360151i	0.935501	−	0.353325i	$-0.114949\pi$
$73$	13.9795	+	3.07713i	1.63618	+	0.360151i	0.700680	+	0.713475i	$0.252880\pi$
$74$	0.0813946	+	0.293157i	0.00946193	+	0.0340788i
$75$	3.96527	+	2.38582i	0.457870	+	0.275491i
$76$	5.32614	−	6.27042i	0.610950	−	0.719266i
$77$	12.0424	+	4.05755i	1.37236	+	0.462401i
$78$	−0.102457	−	0.0474017i	−0.0116010	−	0.00536719i
$79$	0.722413	+	1.36261i	0.0812778	+	0.153306i	0.920819	−	0.389989i	$-0.127521\pi$
$79$	0.722413	+	1.36261i	0.0812778	+	0.153306i	−0.839542	+	0.543295i	$0.817176\pi$
$80$	−2.34032	+	0.515143i	−0.261655	+	0.0575947i
$81$	−0.370138	+	0.928977i	−0.0411265	+	0.103220i
$82$	0.763571	−	0.257277i	0.0843223	−	0.0284115i
$83$	−5.87437	−	0.638876i	−0.644796	−	0.0701258i	−0.220122	−	0.975472i	$-0.570646\pi$
$83$	−5.87437	−	0.638876i	−0.644796	−	0.0701258i	−0.424674	+	0.905347i	$0.639611\pi$
$84$	−0.387368	+	7.14458i	−0.0422653	+	0.779537i
$85$	0.0395939	+	0.730266i	0.00429456	+	0.0792085i
$86$	−0.604836	+	0.0657798i	−0.0652211	+	0.00709322i
$87$	−8.22535	+	3.80545i	−0.881850	+	0.407987i
$88$	1.23483	+	0.938690i	0.131633	+	0.100065i
$89$	13.4725	+	10.2416i	1.42809	+	1.08560i	0.981629	+	0.190799i	$0.0611078\pi$
$89$	13.4725	+	10.2416i	1.42809	+	1.08560i	0.446458	+	0.894805i	$0.352685\pi$
$90$	−0.0610100	+	0.0282262i	−0.00643101	+	0.00297530i
$91$	3.66664	−	0.398771i	0.384368	−	0.0418025i
$92$	0.319891	+	5.90004i	0.0333509	+	0.615122i
$93$	−0.106095	+	1.95680i	−0.0110015	+	0.202911i
$94$	−1.19721	−	0.130205i	−0.123483	−	0.0134296i
$95$	−2.39312	+	0.806336i	−0.245529	+	0.0827284i
$96$	−0.485387	+	1.21823i	−0.0495396	+	0.124335i
$97$	9.58132	−	2.10901i	0.972836	−	0.214137i	0.300008	−	0.953937i	$-0.403011\pi$
$97$	9.58132	−	2.10901i	0.972836	−	0.214137i	0.672828	+	0.739799i	$0.265080\pi$
$98$	0.307334	+	0.579693i	0.0310454	+	0.0585579i
$99$	−3.20419	−	1.48242i	−0.322033	−	0.148988i
$100$	−8.71766	−	2.93732i	−0.871766	−	0.293732i
$101$	−0.407277	+	0.479483i	−0.0405256	+	0.0477104i	−0.782051	−	0.623214i	$-0.785827\pi$
$101$	−0.407277	+	0.479483i	−0.0405256	+	0.0477104i	0.741526	+	0.670924i	$0.234102\pi$
$102$	0.113146	+	0.0680779i	0.0112032	+	0.00674072i
$103$	2.97286	+	10.7073i	0.292925	+	1.05502i	0.952789	+	0.303634i	$0.0982002\pi$
$103$	2.97286	+	10.7073i	0.292925	+	1.05502i	−0.659864	+	0.751385i	$0.729386\pi$
$104$	0.439669	+	0.0967784i	0.0431131	+	0.00948990i
$105$	1.23250	−	1.81780i	0.120280	−	0.177399i
$106$	−0.766376	−	0.725950i	−0.0744370	−	0.0705105i
$107$	−1.25426	+	0.754662i	−0.121254	+	0.0729560i	−0.574889	−	0.818232i	$-0.694955\pi$
$107$	−1.25426	+	0.754662i	−0.121254	+	0.0729560i	0.453635	+	0.891188i	$0.350127\pi$
$108$	0.321600	−	1.96168i	0.0309460	−	0.188762i
$109$	8.42733	+	12.4294i	0.807192	+	1.19052i	0.978692	+	0.205335i	$0.0658285\pi$
$109$	8.42733	+	12.4294i	0.807192	+	1.19052i	−0.171500	+	0.985184i	$0.554861\pi$
$110$	−0.0878451	−	0.220475i	−0.00837570	−	0.0210214i
$111$	1.78782	+	2.10478i	0.169692	+	0.199777i
$112$	−2.28694	−	13.9497i	−0.216095	−	1.31812i
$113$	−1.52599	+	1.44550i	−0.143553	+	0.135981i	−0.756107	−	0.654448i	$-0.772901\pi$
$113$	−1.52599	+	1.44550i	−0.143553	+	0.135981i	0.612554	+	0.790429i	$0.290142\pi$
$114$	−0.121983	+	0.439342i	−0.0114247	+	0.0411482i
$115$	0.849538	−	1.60240i	0.0792199	−	0.149425i
$116$	14.3424	−	10.9028i	1.33166	−	1.01230i
$117$	−1.02469			−0.0947329
$118$	0.0338250	+	0.845560i	0.00311384	+	0.0778401i
$119$	−4.31414			−0.395476
$120$	0.213414	−	0.162233i	0.0194819	−	0.0148098i
$121$	0.685935	−	1.29381i	0.0623578	−	0.117619i
$122$	0.0882401	−	0.317812i	0.00798889	−	0.0287734i
$123$	5.30968	−	5.02959i	0.478757	−	0.453503i
$124$	−0.630232	−	3.84425i	−0.0565965	−	0.345224i
$125$	3.80310	+	4.47736i	0.340160	+	0.400467i
$126$	−0.146777	−	0.368382i	−0.0130759	−	0.0328181i
$127$	−6.96378	−	10.2708i	−0.617936	−	0.911387i	0.381983	−	0.924170i	$-0.375241\pi$
$127$	−6.96378	−	10.2708i	−0.617936	−	0.911387i	−0.999918	+	0.0127825i	$0.995931\pi$
$128$	0.561734	−	3.42643i	0.0496507	−	0.302856i
$129$	−4.73188	+	2.84708i	−0.416618	+	0.250671i
$130$	−0.0500087	−	0.0473708i	−0.00438605	−	0.00415469i
$131$	−1.58643	+	2.33980i	−0.138607	+	0.204430i	−0.890657	−	0.454677i	$-0.849755\pi$
$131$	−1.58643	+	2.33980i	−0.138607	+	0.204430i	0.752050	+	0.659106i	$0.229065\pi$
$132$	6.85406	+	1.50869i	0.596569	+	0.131315i
$133$	−3.98529	−	14.3537i	−0.345569	−	1.24463i
$134$	−0.682727	−	0.410783i	−0.0589786	−	0.0354863i
$135$	−0.395017	+	0.465050i	−0.0339976	+	0.0400251i
$136$	−0.499024	−	0.168141i	−0.0427910	−	0.0144180i
$137$	−20.9000	−	9.66939i	−1.78561	−	0.826112i	−0.968249	−	0.249987i	$-0.919573\pi$
$137$	−20.9000	−	9.66939i	−1.78561	−	0.826112i	−0.817362	−	0.576124i	$-0.804564\pi$
$138$	−0.153390	−	0.289324i	−0.0130574	−	0.0246289i
$139$	11.3696	−	2.50265i	0.964360	−	0.212272i	0.295237	−	0.955424i	$-0.404601\pi$
$139$	11.3696	−	2.50265i	0.964360	−	0.212272i	0.669122	+	0.743152i	$0.266670\pi$
$140$	−1.61596	+	4.05575i	−0.136573	+	0.342773i
$141$	−10.3588	+	3.49027i	−0.872365	+	0.293934i
$142$	−0.163184	−	0.0177473i	−0.0136941	−	0.00148932i
$143$	0.195857	−	3.61237i	0.0163784	−	0.302081i
$144$	0.212621	+	3.92156i	0.0177184	+	0.326797i
$145$	−5.49757	+	0.597897i	−0.456548	+	0.0496526i
$146$	1.43125	−	0.662167i	0.118451	−	0.0548013i
$147$	4.74115	+	3.60413i	0.391044	+	0.297264i
$148$	−4.37029	−	3.32221i	−0.359235	−	0.273084i
$149$	−19.8372	+	9.17765i	−1.62512	+	0.751863i	−0.999598	−	0.0283406i	$-0.990978\pi$
$149$	−19.8372	+	9.17765i	−1.62512	+	0.751863i	−0.625526	+	0.780203i	$0.715116\pi$
$150$	0.506847	−	0.0551229i	0.0413839	−	0.00450077i
$151$	0.145304	+	2.67998i	0.0118247	+	0.218093i	0.998474	+	0.0552316i	$0.0175897\pi$
$151$	0.145304	+	2.67998i	0.0118247	+	0.218093i	−0.986649	+	0.162862i	$0.947928\pi$
$152$	0.0984416	−	1.81565i	0.00798466	−	0.147268i
$153$	1.19155	+	0.129589i	0.0963313	+	0.0104767i
$154$	1.32672	−	0.447023i	0.106910	−	0.0360221i
$155$	−0.442589	+	1.11081i	−0.0355496	+	0.0892227i
$156$	1.98933	−	0.437884i	0.159273	−	0.0350587i
$157$	−2.11610	−	3.99139i	−0.168883	−	0.318548i	0.784595	−	0.620008i	$-0.212871\pi$
$157$	−2.11610	−	3.99139i	−0.168883	−	0.318548i	−0.953479	+	0.301461i	$0.902526\pi$
$158$	0.154209	+	0.0713446i	0.0122682	+	0.00567587i
$159$	−9.08012	−	3.05945i	−0.720100	−	0.242630i
$160$	−0.518012	+	0.609851i	−0.0409524	+	0.0482129i
$161$	9.16731	+	5.51579i	0.722485	+	0.434705i
$162$	0.0294738	+	0.106155i	0.00231568	+	0.00834032i
$163$	−9.34031	−	2.05596i	−0.731590	−	0.161035i	−0.166473	−	0.986046i	$-0.553238\pi$
$163$	−9.34031	−	2.05596i	−0.731590	−	0.161035i	−0.565117	+	0.825011i	$0.691169\pi$
$164$	−8.15883	+	12.0334i	−0.637098	+	0.939649i
$165$	−1.56395	−	1.48145i	−0.121753	−	0.115331i
$166$	−0.557813	+	0.335625i	−0.0432947	+	0.0260496i
$167$	−0.530567	+	3.23631i	−0.0410565	+	0.250433i	−0.999378	−	0.0352576i	$-0.988775\pi$
$167$	−0.530567	+	3.23631i	−0.0410565	+	0.250433i	0.958322	+	0.285691i	$0.0922231\pi$
$168$	0.887444	+	1.30888i	0.0684678	+	0.100982i
$169$	4.42315	+	11.1013i	0.340243	+	0.853944i
$170$	0.0521612	+	0.0614089i	0.00400058	+	0.00470985i
$171$	0.669566	+	4.08417i	0.0512030	+	0.312324i
$172$	7.96976	−	7.54936i	0.607688	−	0.575633i
$173$	−3.19371	+	11.5027i	−0.242813	+	0.874534i	0.737212	+	0.675661i	$0.236142\pi$
$173$	−3.19371	+	11.5027i	−0.242813	+	0.874534i	−0.980025	+	0.198872i	$0.936272\pi$
$174$	−0.467695	+	0.882165i	−0.0354558	+	0.0668768i
$175$	−13.2604	+	10.0803i	−1.00239	+	0.761997i
$176$	−13.8654			−1.04514
$177$	3.50130	+	6.83673i	0.263174	+	0.513880i
$178$	1.86445			0.139747
$179$	15.2500	−	11.5927i	1.13984	−	0.866481i	0.147379	−	0.989080i	$-0.452916\pi$
$179$	15.2500	−	11.5927i	1.13984	−	0.866481i	0.992456	+	0.122600i	$0.0391231\pi$
$180$	0.568150	−	1.07165i	0.0423474	−	0.0798757i
$181$	3.95710	−	14.2522i	0.294129	−	1.05936i	−0.657839	−	0.753159i	$-0.728529\pi$
$181$	3.95710	−	14.2522i	0.294129	−	1.05936i	0.951968	−	0.306198i	$-0.0990570\pi$
$182$	0.294999	−	0.279438i	0.0218668	−	0.0207133i
$183$	−0.484352	−	2.95441i	−0.0358043	−	0.218397i
$184$	0.845426	+	0.995312i	0.0623256	+	0.0733754i
$185$	0.623700	+	1.56537i	0.0458553	+	0.115088i
$186$	0.121160	+	0.178697i	0.00888385	+	0.0131027i
$187$	−0.684592	+	4.17583i	−0.0500624	+	0.305367i
$188$	18.6189	−	11.2026i	1.35792	−	0.817033i
$189$	−2.61313	−	2.47529i	−0.190077	−	0.180051i
$190$	−0.156131	+	0.230276i	−0.0113269	+	0.0167060i
$191$	−19.1231	−	4.20931i	−1.38370	−	0.304575i	−0.540123	−	0.841586i	$-0.681622\pi$
$191$	−19.1231	−	4.20931i	−1.38370	−	0.304575i	−0.843575	+	0.537011i	$0.819553\pi$
$192$	−2.06269	−	7.42913i	−0.148862	−	0.536152i
$193$	14.0361	+	8.44527i	1.01034	+	0.607904i	0.921596	−	0.388151i	$-0.126886\pi$
$193$	14.0361	+	8.44527i	1.01034	+	0.607904i	0.0887477	+	0.996054i	$0.471714\pi$
$194$	0.699727	−	0.823783i	0.0502375	−	0.0591441i
$195$	−0.592509	−	0.199640i	−0.0424305	−	0.0142965i
$196$	−10.7446	−	4.97097i	−0.767469	−	0.355069i
$197$	3.95454	+	7.45905i	0.281749	+	0.531435i	0.983482	−	0.181005i	$-0.0579349\pi$
$197$	3.95454	+	7.45905i	0.281749	+	0.531435i	−0.701733	+	0.712440i	$0.747590\pi$
$198$	−0.379863	+	0.0836142i	−0.0269957	+	0.00594220i
$199$	−8.40846	+	21.1036i	−0.596060	+	1.49600i	0.252875	+	0.967499i	$0.418624\pi$
$199$	−8.40846	+	21.1036i	−0.596060	+	1.49600i	−0.848935	+	0.528498i	$0.822755\pi$
$200$	−1.92672	+	0.649189i	−0.136240	+	0.0459046i
$201$	−7.18984	−	0.781943i	−0.507133	−	0.0551540i
$202$	−0.00375234	+	0.0692077i	−0.000264013	+	0.00486944i
$203$	−1.76607	−	32.5733i	−0.123954	−	2.28620i
$204$	−2.36864	+	0.257605i	−0.165838	+	0.0180360i
$205$	4.05013	−	1.87379i	0.282873	−	0.130871i
$206$	0.974618	+	0.740886i	0.0679049	+	0.0516199i
$207$	−2.36630	−	1.79881i	−0.164469	−	0.125026i
$208$	−3.65235	+	1.68976i	−0.253245	+	0.117164i
$209$	−14.5260	+	1.57979i	−1.00478	+	0.109277i
$210$	−0.0130995	−	0.241606i	−0.000903952	−	0.0166724i
$211$	0.245052	−	4.51972i	0.0168701	−	0.311150i	−0.977904	−	0.209053i	$-0.932962\pi$
$211$	0.245052	−	4.51972i	0.0168701	−	0.311150i	0.994774	−	0.102097i	$-0.0325553\pi$
$212$	18.9354	+	2.05935i	1.30049	+	0.141437i
$213$	−1.41194	+	0.475736i	−0.0967442	+	0.0325969i
$214$	−0.0596909	+	0.149813i	−0.00408039	+	0.0102410i
$215$	−3.29081	+	0.724362i	−0.224431	+	0.0494011i
$216$	−0.205793	−	0.388167i	−0.0140024	−	0.0264114i
$217$	−6.40169	−	2.96174i	−0.434575	−	0.201056i
$218$	1.56783	+	0.528262i	0.106187	+	0.0357784i
$219$	9.26681	−	10.9097i	0.626193	−	0.737212i
$220$	3.66929	+	2.20774i	0.247384	+	0.148846i
$221$	0.328571	+	1.18341i	0.0221021	+	0.0796046i
$222$	0.297133	+	0.0654040i	0.0199423	+	0.00438963i
$223$	−0.937385	+	1.38254i	−0.0627719	+	0.0925817i	−0.857779	−	0.514018i	$-0.828156\pi$
$223$	−0.937385	+	1.38254i	−0.0627719	+	0.0925817i	0.795008	+	0.606600i	$0.207467\pi$
$224$	−3.42677	−	3.24601i	−0.228961	−	0.216883i
$225$	3.96527	−	2.38582i	0.264351	−	0.159055i
$226$	−0.0374640	+	0.228520i	−0.00249207	+	0.0152009i
$227$	10.6230	+	15.6677i	0.705071	+	1.03990i	0.996523	+	0.0833160i	$0.0265511\pi$
$227$	10.6230	+	15.6677i	0.705071	+	1.03990i	−0.291453	+	0.956585i	$0.594139\pi$
$228$	−3.04518	−	7.64283i	−0.201672	−	0.506159i
$229$	16.4079	+	19.3168i	1.08426	+	1.27649i	0.958704	+	0.284406i	$0.0917964\pi$
$229$	16.4079	+	19.3168i	1.08426	+	1.27649i	0.125559	+	0.992086i	$0.459928\pi$
$230$	−0.0323262	−	0.197181i	−0.00213152	−	0.0130017i
$231$	9.22565	−	8.73900i	0.607003	−	0.574984i
$232$	1.06524	−	3.83665i	0.0699364	−	0.251888i
$233$	1.50328	−	2.83550i	0.0984834	−	0.185759i	−0.829375	−	0.558693i	$-0.811303\pi$
$233$	1.50328	−	2.83550i	0.0984834	−	0.185759i	0.927858	+	0.372933i	$0.121648\pi$
$234$	−0.0898718	+	0.0683187i	−0.00587510	+	0.00446614i
$235$	−6.66976			−0.435087
$236$	−9.71893	−	11.7765i	−0.632648	−	0.766587i
$237$	1.54227			0.100181
$238$	−0.378376	+	0.287634i	−0.0245265	+	0.0186445i
$239$	9.17670	−	17.3091i	0.593591	−	1.11963i	−0.386725	−	0.922195i	$-0.626394\pi$
$239$	9.17670	−	17.3091i	0.593591	−	1.11963i	0.980316	−	0.197436i	$-0.0632616\pi$
$240$	−0.641089	+	2.30899i	−0.0413821	+	0.149045i
$241$	−10.0323	+	9.50309i	−0.646236	+	0.612148i	−0.938950	−	0.344052i	$-0.888200\pi$
$241$	−10.0323	+	9.50309i	−0.646236	+	0.612148i	0.292714	+	0.956200i	$0.405442\pi$
$242$	−0.0261008	−	0.159208i	−0.00167783	−	0.0102343i
$243$	0.647386	+	0.762162i	0.0415298	+	0.0488927i
$244$	2.20283	+	5.52868i	0.141022	+	0.353938i
$245$	2.03929	+	3.00773i	0.130286	+	0.192157i
$246$	0.130356	−	0.795135i	0.00831118	−	0.0506959i
$247$	−3.63383	+	2.18640i	−0.231215	+	0.139118i
$248$	−0.625063	−	0.592091i	−0.0396916	−	0.0375978i
$249$	−3.31606	+	4.89082i	−0.210147	+	0.309943i
$250$	0.632071	+	0.139129i	0.0399757	+	0.00879932i
$251$	−0.618401	−	2.22728i	−0.0390331	−	0.140585i	0.941466	−	0.337108i	$-0.109449\pi$
$251$	−0.618401	−	2.22728i	−0.0390331	−	0.140585i	−0.980499	+	0.196523i	$0.937035\pi$
$252$	6.13087	+	3.68882i	0.386209	+	0.232374i
$253$	6.79368	−	7.99814i	0.427115	−	0.502839i
$254$	−1.29555	−	0.436520i	−0.0812898	−	0.0273897i
$255$	0.663745	+	0.307081i	0.0415653	+	0.0192302i
$256$	7.04384	+	13.2861i	0.440240	+	0.830380i
$257$	14.8244	−	3.26310i	0.924722	−	0.203547i	0.273008	−	0.962012i	$-0.411981\pi$
$257$	14.8244	−	3.26310i	0.924722	−	0.203547i	0.651714	+	0.758465i	$0.274050\pi$
$258$	−0.225193	+	0.565191i	−0.0140199	+	0.0351873i
$259$	−9.41969	+	3.17386i	−0.585311	+	0.197214i
$260$	1.23560	+	0.134380i	0.0766288	+	0.00833389i
$261$	−0.490661	+	9.04970i	−0.0303711	+	0.560163i
$262$	0.0168612	+	0.310986i	0.00104169	+	0.0192128i
$263$	25.8939	−	2.81613i	1.59669	−	0.173650i	0.733915	−	0.679242i	$-0.237691\pi$
$263$	25.8939	−	2.81613i	1.59669	−	0.173650i	0.862773	+	0.505591i	$0.168726\pi$
$264$	1.40775	−	0.651293i	0.0866408	−	0.0400843i
$265$	−4.65434	−	3.53814i	−0.285914	−	0.217346i
$266$	−1.30653	−	0.993200i	−0.0801086	−	0.0608970i
$267$	15.3592	−	7.10592i	0.939968	−	0.434875i
$268$	14.2924	−	1.55439i	0.873049	−	0.0949498i
$269$	1.41192	+	26.0413i	0.0860860	+	1.58776i	0.648700	+	0.761044i	$0.275313\pi$
$269$	1.41192	+	26.0413i	0.0860860	+	1.58776i	−0.562614	+	0.826720i	$0.690204\pi$
$270$	−0.00363938	+	0.0671244i	−0.000221486	+	0.00408506i
$271$	12.3384	+	1.34188i	0.749504	+	0.0815135i	0.474895	−	0.880042i	$-0.342486\pi$
$271$	12.3384	+	1.34188i	0.749504	+	0.0815135i	0.274609	+	0.961556i	$0.411451\pi$
$272$	4.46079	−	1.50302i	0.270475	−	0.0911338i
$273$	1.36516	−	3.42630i	0.0826235	−	0.207369i
$274$	−2.47774	+	0.545392i	−0.149686	+	0.0329484i
$275$	7.65287	+	14.4349i	0.461486	+	0.870454i
$276$	5.36260	+	2.48100i	0.322790	+	0.149339i
$277$	−18.5738	−	6.25823i	−1.11599	−	0.376020i	−0.299914	−	0.953966i	$-0.596958\pi$
$277$	−18.5738	−	6.25823i	−1.11599	−	0.376020i	−0.816075	+	0.577946i	$0.803854\pi$
$278$	0.830328	−	0.977538i	0.0497998	−	0.0586288i
$279$	1.67916	+	1.01032i	0.100529	+	0.0604862i
$280$	0.258140	+	0.929737i	0.0154268	+	0.0555624i
$281$	−7.43561	−	1.63670i	−0.443571	−	0.0976375i	−0.0124319	−	0.999923i	$-0.503957\pi$
$281$	−7.43561	−	1.63670i	−0.443571	−	0.0976375i	−0.431140	+	0.902285i	$0.641888\pi$
$282$	−0.675821	+	0.996761i	−0.0402446	+	0.0593563i
$283$	−8.29610	−	7.85848i	−0.493152	−	0.467138i	0.400244	−	0.916409i	$-0.368925\pi$
$283$	−8.29610	−	7.85848i	−0.493152	−	0.467138i	−0.893396	+	0.449270i	$0.851684\pi$
$284$	2.53782	−	1.52695i	0.150592	−	0.0906080i
$285$	−0.408550	+	2.49205i	−0.0242004	+	0.147616i
$286$	−0.223667	−	0.329885i	−0.0132257	−	0.0195065i
$287$	9.74373	+	24.4549i	0.575154	+	1.44353i
$288$	0.848960	+	0.999474i	0.0500255	+	0.0588945i
$289$	2.51788	+	15.3584i	0.148111	+	0.903435i
$290$	−0.442307	+	0.418975i	−0.0259732	+	0.0246031i
$291$	2.62464	−	9.45309i	0.153859	−	0.554150i
$292$	−13.3284	+	25.1400i	−0.779986	+	1.47121i
$293$	24.0432	−	18.2772i	1.40462	−	1.06776i	0.417343	−	0.908749i	$-0.362961\pi$
$293$	24.0432	−	18.2772i	1.40462	−	1.06776i	0.987276	−	0.159015i	$-0.0508317\pi$
$294$	0.656124			0.0382659
$295$	0.692568	+	4.63537i	0.0403229	+	0.269881i
$296$	−1.21329			−0.0705212
$297$	−2.81060	+	2.13656i	−0.163088	+	0.123976i
$298$	−1.12794	+	2.12753i	−0.0653400	+	0.123244i
$299$	0.814835	−	2.93477i	0.0471231	−	0.169722i
$300$	−6.67859	+	6.32629i	−0.385588	+	0.365249i
$301$	−3.21575	−	19.6152i	−0.185353	−	1.13060i
$302$	0.191425	+	0.225363i	0.0110153	+	0.0129682i
$303$	0.232857	+	0.584428i	0.0133773	+	0.0335745i
$304$	9.12152	+	13.4532i	0.523155	+	0.771596i
$305$	0.295538	−	1.80270i	0.0169224	−	0.103222i
$306$	0.113146	−	0.0680779i	0.00646815	−	0.00389175i
$307$	−21.2593	−	20.1378i	−1.21333	−	1.14933i	−0.984411	−	0.175882i	$-0.943722\pi$
$307$	−21.2593	−	20.1378i	−1.21333	−	1.14933i	−0.228919	−	0.973445i	$-0.573519\pi$
$308$	−14.1761	+	20.9082i	−0.807759	+	1.19136i
$309$	10.8525	+	2.38882i	0.617379	+	0.135895i
$310$	0.0352429	+	0.126934i	0.00200166	+	0.00720934i
$311$	−15.0579	−	9.06003i	−0.853855	−	0.513747i	0.0200758	−	0.999798i	$-0.493609\pi$
$311$	−15.0579	−	9.06003i	−0.853855	−	0.513747i	−0.873930	+	0.486051i	$0.838437\pi$
$312$	0.291449	−	0.343121i	0.0165001	−	0.0194254i
$313$	1.68097	+	0.566384i	0.0950139	+	0.0320139i	0.366407	−	0.930455i	$-0.380588\pi$
$313$	1.68097	+	0.566384i	0.0950139	+	0.0320139i	−0.271393	+	0.962469i	$0.587484\pi$
$314$	−0.451710	−	0.208984i	−0.0254915	−	0.0117936i
$315$	−1.02874	−	1.94040i	−0.0579628	−	0.109329i
$316$	−2.99414	+	0.659061i	−0.168434	+	0.0370751i
$317$	1.00637	−	2.52580i	0.0565234	−	0.141863i	−0.898003	−	0.439989i	$-0.854982\pi$
$317$	1.00637	−	2.52580i	0.0565234	−	0.141863i	0.954527	+	0.298126i	$0.0963616\pi$
$318$	−1.00036	+	0.337061i	−0.0560975	+	0.0189015i
$319$	−31.8093	−	3.45947i	−1.78098	−	0.193693i
$320$	0.254698	−	4.69763i	0.0142381	−	0.262605i
$321$	0.0792480	+	1.46164i	0.00442319	+	0.0815809i
$322$	1.17178	−	0.127439i	0.0653007	−	0.00710188i
$323$	4.50207	−	2.08288i	0.250502	−	0.115894i
$324$	−1.58252	−	1.20300i	−0.0879180	−	0.0668335i
$325$	3.77504	+	2.86971i	0.209402	+	0.159183i
$326$	−0.956278	+	0.442421i	−0.0529633	+	0.0245034i
$327$	14.9289	−	1.62362i	0.825573	−	0.0897864i
$328$	0.173960	+	3.20850i	0.00960534	+	0.177160i
$329$	2.13008	−	39.2869i	0.117435	−	2.16596i
$330$	−0.235939	−	0.0256599i	−0.0129880	−	0.00141253i
$331$	3.60783	−	1.21562i	0.198304	−	0.0668165i	−0.218397	−	0.975860i	$-0.570083\pi$
$331$	3.60783	−	1.21562i	0.198304	−	0.0668165i	0.416701	+	0.909044i	$0.363186\pi$
$332$	4.34775	−	10.9120i	0.238614	−	0.598876i
$333$	2.69703	−	0.593661i	0.147796	−	0.0325324i
$334$	0.169239	+	0.319219i	0.00926034	+	0.0174669i
$335$	−4.00505	−	1.85293i	−0.218819	−	0.101237i
$336$	−13.3959	−	4.51362i	−0.730809	−	0.246238i
$337$	23.2166	−	27.3327i	1.26469	−	1.48891i	0.469002	−	0.883197i	$-0.344614\pi$
$337$	23.2166	−	27.3327i	1.26469	−	1.48891i	0.795687	−	0.605709i	$-0.207110\pi$
$338$	1.12809	+	0.678747i	0.0613598	+	0.0369190i
$339$	0.562326	+	2.02531i	0.0305413	+	0.110000i
$340$	−1.41981	−	0.312524i	−0.0770001	−	0.0169490i
$341$	−3.88264	+	5.72647i	−0.210257	+	0.310106i
$342$	0.331026	+	0.313565i	0.0178999	+	0.0169556i
$343$	3.22132	−	1.93820i	0.173935	−	0.104653i
$344$	0.392519	−	2.39426i	0.0211632	−	0.129090i
$345$	−1.01781	−	1.50115i	−0.0547969	−	0.0808195i
$346$	0.486805	+	1.22179i	0.0261708	+	0.0656837i
$347$	11.0729	+	13.0360i	0.594425	+	0.699812i	0.974307	−	0.225223i	$-0.0723112\pi$
$347$	11.0729	+	13.0360i	0.594425	+	0.699812i	−0.379882	+	0.925035i	$0.624035\pi$
$348$	−2.91466	−	17.7787i	−0.156242	−	0.953036i
$349$	5.10275	−	4.83358i	0.273144	−	0.258736i	−0.538850	−	0.842402i	$-0.681141\pi$
$349$	5.10275	−	4.83358i	0.273144	−	0.258736i	0.811994	+	0.583666i	$0.198382\pi$
$350$	−0.490939	+	1.76820i	−0.0262418	+	0.0945144i
$351$	−0.479975	+	0.905328i	−0.0256192	+	0.0483228i
$352$	−3.68573	+	2.80182i	−0.196450	+	0.149337i
$353$	−26.9522			−1.43452			−0.717259	−	0.696806i	$-0.754604\pi$
$353$	−26.9522			−1.43452			−0.717259	+	0.696806i	$0.754604\pi$
$354$	0.762907	+	0.366183i	0.0405480	+	0.0194624i
$355$	−0.909112			−0.0482507
$356$	−26.7816	+	20.3588i	−1.41942	+	1.07902i
$357$	−2.02078	+	3.81159i	−0.106951	+	0.201731i
$358$	0.564600	−	2.03350i	0.0298400	−	0.107474i
$359$	−9.34279	+	8.84996i	−0.493094	+	0.467083i	−0.893377	−	0.449309i	$-0.851670\pi$
$359$	−9.34279	+	8.84996i	−0.493094	+	0.467083i	0.400283	+	0.916392i	$0.368912\pi$
$360$	−0.0433699	−	0.264545i	−0.00228579	−	0.0139427i
$361$	−1.21141	−	1.42619i	−0.0637587	−	0.0750625i
$362$	−0.603166	−	1.51383i	−0.0317017	−	0.0795653i
$363$	−0.821800	−	1.21206i	−0.0431333	−	0.0636169i
$364$	−1.18614	+	7.23516i	−0.0621709	+	0.379226i
$365$	7.48389	−	4.50291i	0.391725	−	0.235693i
$366$	−0.239458	−	0.226827i	−0.0125167	−	0.0118564i
$367$	−15.2967	+	22.5610i	−0.798483	+	1.17767i	0.182428	+	0.983219i	$0.441604\pi$
$367$	−15.2967	+	22.5610i	−0.798483	+	1.17767i	−0.980911	+	0.194456i	$0.937706\pi$
$368$	−11.4006	−	2.50947i	−0.594298	−	0.130815i
$369$	−1.95661	−	7.04707i	−0.101857	−	0.366856i
$370$	0.159069	+	0.0957088i	0.00826962	+	0.00497566i
$371$	22.3271	−	26.2855i	1.15917	−	1.36468i
$372$	−3.69164	−	1.24386i	−0.191403	−	0.0644911i
$373$	6.97633	+	3.22759i	0.361221	+	0.167118i	0.592101	−	0.805864i	$-0.298299\pi$
$373$	6.97633	+	3.22759i	0.361221	+	0.167118i	−0.230881	+	0.972982i	$0.574161\pi$
$374$	0.218370	+	0.411889i	0.0112916	+	0.0212983i
$375$	5.73720	−	1.26285i	0.296268	−	0.0652135i
$376$	1.77758	−	4.46138i	0.0916714	−	0.230078i
$377$	−8.80065	+	2.96528i	−0.453257	+	0.152720i
$378$	−0.394221	−	0.0428741i	−0.0202766	−	0.00220521i
$379$	−0.788724	+	14.5472i	−0.0405140	+	0.747237i	0.905744	+	0.423825i	$0.139313\pi$
$379$	−0.788724	+	14.5472i	−0.0405140	+	0.747237i	−0.946258	+	0.323412i	$0.895170\pi$
$380$	−0.271776	−	5.01261i	−0.0139418	−	0.257142i
$381$	−12.3363	+	1.34165i	−0.632007	+	0.0687349i
$382$	−1.95786	+	0.905800i	−0.100173	+	0.0463448i
$383$	−13.8101	−	10.4982i	−0.705663	−	0.536431i	0.189660	−	0.981850i	$-0.439262\pi$
$383$	−13.8101	−	10.4982i	−0.705663	−	0.536431i	−0.895322	+	0.445419i	$0.853055\pi$
$384$	−2.76417	−	2.10127i	−0.141058	−	0.107230i
$385$	7.03717	−	3.25574i	0.358647	−	0.165928i
$386$	1.79412	−	0.195122i	0.0913184	−	0.00993147i
$387$	0.298975	+	5.51426i	0.0151977	+	0.280306i
$388$	−1.05583	+	19.4737i	−0.0536018	+	0.988627i
$389$	−30.5482	−	3.32232i	−1.54886	−	0.168448i	−0.706634	−	0.707579i	$-0.749787\pi$
$389$	−30.5482	−	3.32232i	−1.54886	−	0.168448i	−0.842222	+	0.539131i	$0.818753\pi$
$390$	−0.0652771	+	0.0219944i	−0.00330544	+	0.00111373i
$391$	−1.31867	+	3.30961i	−0.0666880	+	0.167374i
$392$	−2.55536	+	0.562477i	−0.129065	+	0.0284094i
$393$	1.32415	+	2.49761i	0.0667945	+	0.125988i
$394$	0.844150	+	0.390545i	0.0425277	+	0.0196754i
$395$	0.891789	+	0.300479i	0.0448708	+	0.0151187i
$396$	4.54345	−	5.34896i	0.228317	−	0.268795i
$397$	7.93304	+	4.77315i	0.398148	+	0.239557i	0.700521	−	0.713632i	$-0.252951\pi$
$397$	7.93304	+	4.77315i	0.398148	+	0.239557i	−0.302373	+	0.953190i	$0.597779\pi$
$398$	0.669558	+	2.41153i	0.0335619	+	0.120879i
$399$	−14.5484	−	3.20235i	−0.728333	−	0.160318i
$400$	10.1993	−	15.0428i	0.509963	−	0.752139i
$401$	22.5525	+	21.3629i	1.12622	+	1.06681i	0.997170	+	0.0751738i	$0.0239512\pi$
$401$	22.5525	+	21.3629i	1.12622	+	1.06681i	0.129049	+	0.991638i	$0.458807\pi$
$402$	−0.682727	+	0.410783i	−0.0340513	+	0.0204880i
$403$	−0.324869	+	1.98161i	−0.0161829	+	0.0987111i
$404$	−0.701811	−	1.03509i	−0.0349164	−	0.0514979i
$405$	0.225848	+	0.566835i	0.0112225	+	0.0281663i
$406$	−2.32664	−	2.73913i	−0.115469	−	0.135941i
$407$	1.57734	+	9.62135i	0.0781859	+	0.476913i
$408$	−0.382302	+	0.362135i	−0.0189268	+	0.0179284i
$409$	4.86633	−	17.5269i	0.240624	−	0.866651i	−0.740302	−	0.672274i	$-0.765318\pi$
$409$	4.86633	−	17.5269i	0.240624	−	0.866651i	0.980927	−	0.194377i	$-0.0622685\pi$
$410$	0.230291	−	0.434375i	0.0113733	−	0.0214522i
$411$	−18.3328	+	13.9362i	−0.904289	+	0.687423i
$412$	−22.0898			−1.08828
$413$	−27.5249	+	2.59908i	−1.35441	+	0.127892i
$414$	−0.327470			−0.0160943
$415$	−2.87032	+	2.18196i	−0.140899	+	0.107108i
$416$	−0.629423	+	1.18722i	−0.0308600	+	0.0582081i
$417$	3.11451	−	11.2175i	0.152518	−	0.549322i
$418$	−1.16869	+	1.10704i	−0.0571624	+	0.0541471i
$419$	−1.34207	−	8.18626i	−0.0655643	−	0.399925i	−0.999137	−	0.0415366i	$-0.986775\pi$
$419$	−1.34207	−	8.18626i	−0.0655643	−	0.399925i	0.933573	−	0.358388i	$-0.116674\pi$
$420$	2.82637	+	3.32746i	0.137913	+	0.162364i
$421$	−0.593519	−	1.48962i	−0.0289264	−	0.0725997i	0.913804	−	0.406155i	$-0.133131\pi$
$421$	−0.593519	−	1.48962i	−0.0289264	−	0.0725997i	−0.942730	+	0.333556i	$0.891751\pi$
$422$	−0.279848	−	0.412745i	−0.0136228	−	0.0200921i
$423$	−1.76843	+	10.7870i	−0.0859841	+	0.524480i
$424$	3.60708	−	2.17031i	0.175176	−	0.105400i
$425$	−4.02684	−	3.81443i	−0.195330	−	0.185027i
$426$	−0.0921168	+	0.135862i	−0.00446307	+	0.00658254i
$427$	10.5241	+	2.31652i	0.509296	+	0.112104i
$428$	−0.778457	−	2.80375i	−0.0376282	−	0.135524i
$429$	−3.09983	−	1.86510i	−0.149661	−	0.0900481i
$430$	−0.240329	+	0.282937i	−0.0115897	+	0.0136444i
$431$	7.22039	+	2.43283i	0.347794	+	0.117185i	0.487776	−	0.872969i	$-0.337808\pi$
$431$	7.22039	+	2.43283i	0.347794	+	0.117185i	−0.139983	+	0.990154i	$0.544705\pi$
$432$	3.56434	+	1.64904i	0.171489	+	0.0793395i
$433$	2.32069	+	4.37729i	0.111525	+	0.210359i	0.932992	−	0.359898i	$-0.117188\pi$
$433$	2.32069	+	4.37729i	0.111525	+	0.210359i	−0.821466	+	0.570257i	$0.806844\pi$
$434$	−0.758933	+	0.167054i	−0.0364299	+	0.00801884i
$435$	−2.04686	+	5.13723i	−0.0981394	+	0.246311i
$436$	−28.2890	+	9.53169i	−1.35480	+	0.456485i
$437$	−12.2297	−	1.33006i	−0.585026	−	0.0636254i
$438$	0.0853773	−	1.57469i	0.00407948	−	0.0752417i
$439$	−1.11657	−	20.5939i	−0.0532908	−	0.982892i	−0.895869	−	0.444318i	$-0.853446\pi$
$439$	−1.11657	−	20.5939i	−0.0532908	−	0.982892i	0.842578	−	0.538574i	$-0.181037\pi$
$440$	0.940893	−	0.102328i	0.0448553	−	0.00487831i
$441$	5.40509	−	2.50066i	0.257385	−	0.119079i
$442$	0.107718	+	0.0818853i	0.00512364	+	0.00389489i
$443$	25.9804	+	19.7498i	1.23437	+	0.938341i	0.999433	−	0.0336699i	$-0.0107195\pi$
$443$	25.9804	+	19.7498i	1.23437	+	0.938341i	0.234934	+	0.972011i	$0.424513\pi$
$444$	−4.98229	+	2.30505i	−0.236449	+	0.109393i
$445$	10.2656	−	1.11645i	0.486637	−	0.0529249i
$446$	0.00996290	+	0.183755i	0.000471757	+	0.00870104i
$447$	−1.18333	+	21.8253i	−0.0559697	+	1.03230i
$448$	27.5891	+	3.00050i	1.30346	+	0.141760i
$449$	36.0636	−	12.1513i	1.70195	−	0.573453i	0.710470	−	0.703727i	$-0.248482\pi$
$449$	36.0636	−	12.1513i	1.70195	−	0.573453i	0.991478	+	0.130274i	$0.0415857\pi$
$450$	0.188710	−	0.473625i	0.00889586	−	0.0223269i
$451$	25.2171	−	5.55071i	1.18743	−	0.261373i
$452$	−1.95717	−	3.69162i	−0.0920576	−	0.173639i
$453$	2.43585	+	1.12695i	0.114446	+	0.0529485i
$454$	1.97630	+	0.665893i	0.0927524	+	0.0312519i
$455$	1.45692	−	1.71522i	0.0683016	−	0.0804109i
$456$	−1.55804	−	0.937439i	−0.0729617	−	0.0438996i
$457$	−9.13864	−	32.9144i	−0.427488	−	1.53967i	−0.793210	−	0.608948i	$-0.791592\pi$
$457$	−9.13864	−	32.9144i	−0.427488	−	1.53967i	0.365723	−	0.930724i	$-0.380822\pi$
$458$	2.72697	+	0.600251i	0.127423	+	0.0280479i
$459$	0.672626	−	0.992050i	0.0313955	−	0.0463049i
$460$	2.61745	+	2.47938i	0.122039	+	0.115602i
$461$	−7.48377	+	4.50283i	−0.348554	+	0.209718i	−0.679055	−	0.734088i	$-0.737610\pi$
$461$	−7.48377	+	4.50283i	−0.348554	+	0.209718i	0.330501	+	0.943806i	$0.392782\pi$
$462$	0.226495	−	1.38156i	0.0105375	−	0.0642760i
$463$	−11.2644	−	16.6137i	−0.523499	−	0.772103i	0.470394	−	0.882457i	$-0.344112\pi$
$463$	−11.2644	−	16.6137i	−0.523499	−	0.772103i	−0.993892	+	0.110354i	$0.964802\pi$
$464$	13.1744	+	33.0653i	0.611608	+	1.53502i
$465$	0.774105	+	0.911347i	0.0358983	+	0.0422627i
$466$	−0.0572022	−	0.348918i	−0.00264984	−	0.0161633i
$467$	−6.30194	+	5.96951i	−0.291619	+	0.276236i	−0.819496	−	0.573085i	$-0.805747\pi$
$467$	−6.30194	+	5.96951i	−0.291619	+	0.276236i	0.527877	+	0.849321i	$0.322988\pi$
$468$	0.544941	−	1.96270i	0.0251899	−	0.0907259i
$469$	12.1934	−	22.9992i	0.563039	−	1.06200i
$470$	−0.584979	+	0.444689i	−0.0269831	+	0.0205120i
$471$	−4.51764			−0.208162
$472$	−3.28516	−	0.772127i	−0.151212	−	0.0355400i
$473$	−19.4967			−0.896458
$474$	0.135267	−	0.102827i	0.00621300	−	0.00472300i
$475$	8.97123	−	16.9215i	0.411628	−	0.776413i
$476$	2.29430	−	8.26332i	0.105159	−	0.378748i
$477$	−6.95626	+	6.58932i	−0.318505	+	0.301704i
$478$	−0.349187	−	2.12994i	−0.0159714	−	0.0974214i
$479$	−6.83750	−	8.04973i	−0.312413	−	0.367802i	0.583436	−	0.812159i	$-0.301708\pi$
$479$	−6.83750	−	8.04973i	−0.312413	−	0.367802i	−0.895850	+	0.444358i	$0.853432\pi$
$480$	0.296169	+	0.743329i	0.0135182	+	0.0339282i
$481$	1.58804	+	2.34218i	0.0724083	+	0.106794i
$482$	−0.246299	+	1.50236i	−0.0112186	+	0.0684304i
$483$	9.16731	−	5.51579i	0.417127	−	0.250977i
$484$	2.11339	+	2.00190i	0.0960630	+	0.0909957i
$485$	3.35938	−	4.95472i	0.152542	−	0.224982i
$486$	0.107595	+	0.0236834i	0.00488060	+	0.00107430i
$487$	−8.08231	−	29.1098i	−0.366244	−	1.31909i	−0.885566	−	0.464514i	$-0.846229\pi$
$487$	−8.08231	−	29.1098i	−0.366244	−	1.31909i	0.519322	−	0.854579i	$-0.326185\pi$
$488$	1.12705	+	0.678126i	0.0510194	+	0.0306973i
$489$	−6.19154	+	7.28925i	−0.279991	+	0.329631i
$490$	0.379391	+	0.127832i	0.0171392	+	0.00577485i
$491$	17.1177	+	7.91950i	0.772512	+	0.357402i	0.766220	−	0.642578i	$-0.222135\pi$
$491$	17.1177	+	7.91950i	0.772512	+	0.357402i	0.00629199	+	0.999980i	$0.497997\pi$
$492$	6.80997	+	12.8450i	0.307017	+	0.579096i
$493$	10.6087	−	2.33516i	0.477794	−	0.105170i
$494$	−0.172936	+	0.434037i	−0.00778077	+	0.0195283i
$495$	−2.04144	+	0.687842i	−0.0917560	+	0.0309162i
$496$	7.65116	+	0.832114i	0.343547	+	0.0373630i
$497$	0.290337	−	5.35495i	0.0130234	−	0.240202i
$498$	0.0352444	+	0.650044i	0.00157934	+	0.0291292i
$499$	1.85049	−	0.201252i	0.0828391	−	0.00900930i	−0.0666056	−	0.997779i	$-0.521217\pi$
$499$	1.85049	−	0.201252i	0.0828391	−	0.00900930i	0.149445	+	0.988770i	$0.452251\pi$
$500$	−10.5985	+	4.90338i	−0.473978	+	0.219286i
$501$	2.61080	+	1.98468i	0.116642	+	0.0886689i
$502$	−0.202736	−	0.154116i	−0.00904854	−	0.00687852i
$503$	−23.9343	+	11.0732i	−1.06718	+	0.493729i	−0.873243	−	0.487286i	$-0.837987\pi$
$503$	−23.9343	+	11.0732i	−1.06718	+	0.493729i	−0.193935	+	0.981014i	$0.562125\pi$
$504$	1.57210	−	0.170976i	0.0700269	−	0.00761588i
$505$	0.0207820	+	0.383302i	0.000924788	+	0.0170567i
$506$	0.0625917	−	1.15444i	0.00278254	−	0.0513210i
$507$	11.8800	+	1.29202i	0.527607	+	0.0573807i
$508$	23.3762	−	7.87635i	1.03715	−	0.349456i
$509$	−10.7651	+	27.0184i	−0.477155	+	1.19757i	0.471673	+	0.881774i	$0.343650\pi$
$509$	−10.7651	+	27.0184i	−0.477155	+	1.19757i	−0.948828	+	0.315795i	$0.897729\pi$
$510$	0.0786883	−	0.0173206i	0.00348438	−	0.000766969i
$511$	24.1334	+	45.5205i	1.06760	+	2.01371i
$512$	7.80611	+	3.61149i	0.344985	+	0.159607i
$513$	3.92204	+	1.32149i	0.173162	+	0.0583452i
$514$	1.08263	−	1.27457i	0.0477529	−	0.0562191i
$515$	5.80986	+	3.49568i	0.256013	+	0.154038i
$516$	−2.93684	−	10.5776i	−0.129287	−	0.465651i
$517$	−37.6894	−	8.29607i	−1.65758	−	0.364861i
$518$	−0.614555	+	0.906401i	−0.0270020	+	0.0398250i
$519$	8.66681	+	8.20964i	0.380431	+	0.360363i
$520$	0.235375	−	0.141620i	0.0103219	−	0.00621047i
$521$	−0.187351	+	1.14279i	−0.00820797	+	0.0500664i	−0.990613	−	0.136697i	$-0.956351\pi$
$521$	−0.187351	+	1.14279i	−0.00820797	+	0.0500664i	0.982405	+	0.186763i	$0.0597997\pi$
$522$	0.560332	+	0.826428i	0.0245251	+	0.0361717i
$523$	5.16239	+	12.9566i	0.225736	+	0.566554i	0.997601	−	0.0692330i	$-0.0220552\pi$
$523$	5.16239	+	12.9566i	0.225736	+	0.566554i	−0.771865	+	0.635786i	$0.780676\pi$
$524$	−3.63799	−	4.28298i	−0.158926	−	0.187103i
$525$	2.69477	+	16.4374i	0.117609	+	0.717386i
$526$	2.08330	−	1.97340i	0.0908360	−	0.0860445i
$527$	0.628377	−	2.26321i	0.0273725	−	0.0985869i
$528$	−6.49467	+	12.2502i	−0.282644	+	0.533123i
$529$	−11.2766	+	8.57222i	−0.490286	+	0.372705i
$530$	−0.644110			−0.0279783
$531$	7.68037	+	0.108943i	0.333300	+	0.00472773i
$532$	29.6126			1.28387
$533$	5.96611	−	4.53532i	0.258421	−	0.196447i
$534$	0.873326	−	1.64727i	0.0377925	−	0.0712842i
$535$	−0.238946	+	0.860607i	−0.0103306	+	0.0372073i
$536$	2.30681	−	2.18513i	0.0996392	−	0.0943833i
$537$	−3.09910	−	18.9037i	−0.133736	−	0.815753i
$538$	1.86007	+	2.18984i	0.0801932	+	0.0944107i
$539$	7.78251	+	19.5326i	0.335216	+	0.841330i
$540$	−0.680685	−	1.00394i	−0.0292920	−	0.0432025i
$541$	5.76288	−	35.1520i	0.247765	−	1.51130i	−0.510797	−	0.859702i	$-0.670649\pi$
$541$	5.76288	−	35.1520i	0.247765	−	1.51130i	0.758562	−	0.651601i	$-0.225902\pi$
$542$	1.17162	−	0.704940i	0.0503254	−	0.0302798i
$543$	−10.7384	−	10.1720i	−0.460831	−	0.436522i
$544$	0.882060	−	1.30094i	0.0378180	−	0.0557774i
$545$	8.94871	+	1.96976i	0.383321	+	0.0843753i
$546$	−0.108707	−	0.391527i	−0.00465222	−	0.0167558i
$547$	−16.8736	−	10.1525i	−0.721465	−	0.434091i	0.106908	−	0.994269i	$-0.465905\pi$
$547$	−16.8736	−	10.1525i	−0.721465	−	0.434091i	−0.828372	+	0.560178i	$0.810733\pi$
$548$	29.6356	−	34.8898i	1.26597	−	1.49042i
$549$	−2.83713	−	0.955942i	−0.121086	−	0.0407986i
$550$	1.63361	+	0.755789i	0.0696574	+	0.0322269i
$551$	17.5695	+	33.1396i	0.748486	+	1.41179i
$552$	1.27538	−	0.280731i	0.0542836	−	0.0119487i
$553$	−2.05472	+	5.15695i	−0.0873754	+	0.219296i
$554$	−2.04628	+	0.689473i	−0.0869382	+	0.0292929i
$555$	1.67517	+	0.182186i	0.0711070	+	0.00773335i
$556$	−1.25290	+	23.1084i	−0.0531348	+	0.980014i
$557$	−1.07774	−	19.8778i	−0.0456655	−	0.842251i	−0.928218	−	0.372037i	$-0.878659\pi$
$557$	−1.07774	−	19.8778i	−0.0456655	−	0.842251i	0.882552	−	0.470214i	$-0.155823\pi$
$558$	0.214633	−	0.0233428i	0.00908614	−	0.000988177i
$559$	−5.13572	+	2.37604i	−0.217218	+	0.100496i
$560$	−6.86657	−	5.21983i	−0.290166	−	0.220578i
$561$	3.36873	+	2.56084i	0.142228	+	0.108119i
$562$	−0.761271	+	0.352202i	−0.0321123	+	0.0148567i
$563$	0.0619912	−	0.00674195i	0.00261262	−	0.000284139i	−0.106813	−	0.994279i	$-0.534064\pi$
$563$	0.0619912	−	0.00674195i	0.00261262	−	0.000284139i	0.109425	+	0.993995i	$0.465099\pi$
$564$	−1.17640	−	21.6974i	−0.0495353	−	0.913624i
$565$	−0.0694352	+	1.28066i	−0.00292116	+	0.0538776i
$566$	−1.25156	−	0.136116i	−0.0526071	−	0.00572136i
$567$	−3.41096	+	1.14929i	−0.143247	+	0.0482655i
$568$	0.242290	−	0.608102i	0.0101663	−	0.0255154i
$569$	−7.46458	+	1.64308i	−0.312932	+	0.0688814i	−0.368659	−	0.929565i	$-0.620183\pi$
$569$	−7.46458	+	1.64308i	−0.312932	+	0.0688814i	0.0557279	+	0.998446i	$0.482252\pi$
$570$	0.130318	+	0.245807i	0.00545844	+	0.0102957i
$571$	43.2404	+	20.0051i	1.80956	+	0.837189i	0.937722	+	0.347385i	$0.112930\pi$
$571$	43.2404	+	20.0051i	1.80956	+	0.837189i	0.871833	+	0.489804i	$0.162932\pi$
$572$	6.81499	+	2.29624i	0.284949	+	0.0960105i
$573$	−12.6764	+	14.9238i	−0.529564	+	0.623451i
$574$	2.48505	+	1.49521i	0.103724	+	0.0624087i
$575$	3.67994	+	13.2539i	0.153464	+	0.552727i
$576$	−7.52991	−	1.65746i	−0.313746	−	0.0690608i
$577$	−15.2449	+	22.4846i	−0.634655	+	0.936046i	0.365332	+	0.930877i	$0.380956\pi$
$577$	−15.2449	+	22.4846i	−0.634655	+	0.936046i	−0.999987	+	0.00516878i	$0.998355\pi$
$578$	1.24481	+	1.17915i	0.0517774	+	0.0490462i
$579$	14.0361	−	8.44527i	0.583322	−	0.350973i
$580$	1.77845	−	10.8480i	0.0738459	−	0.450440i
$581$	−11.9357	−	17.6039i	−0.495178	−	0.730333i
$582$	−0.400064	−	1.00408i	−0.0165832	−	0.0416206i
$583$	−21.8998	−	25.7825i	−0.906999	−	1.06780i
$584$	1.01743	+	6.20603i	0.0421014	+	0.256807i
$585$	−0.453920	+	0.429976i	−0.0187673	+	0.0177773i
$586$	0.890152	−	3.20604i	0.0367718	−	0.132440i
$587$	11.5787	−	21.8397i	0.477903	−	0.901420i	−0.520953	−	0.853586i	$-0.674423\pi$
$587$	11.5787	−	21.8397i	0.477903	−	0.901420i	0.998855	−	0.0478346i	$-0.0152320\pi$
$588$	−9.42476	+	7.16452i	−0.388670	+	0.295460i
$589$	8.11049			0.334187
$590$	0.369794	+	0.360375i	0.0152242	+	0.0148364i
$591$	8.44250			0.347278
$592$	8.63416	−	6.56352i	0.354862	−	0.269759i
$593$	3.96723	−	7.48300i	0.162915	−	0.307290i	−0.788592	−	0.614916i	$-0.789190\pi$
$593$	3.96723	−	7.48300i	0.162915	−	0.307290i	0.951507	+	0.307626i	$0.0995347\pi$
$594$	−0.104057	+	0.374779i	−0.00426951	+	0.0153774i
$595$	−1.91108	+	1.81028i	−0.0783468	+	0.0742141i
$596$	−7.02932	−	42.8770i	−0.287932	−	1.75631i
$597$	14.7067	+	17.3141i	0.601906	+	0.708619i
$598$	−0.124202	−	0.311724i	−0.00507901	−	0.0127473i
$599$	6.62004	+	9.76383i	0.270488	+	0.398939i	0.938538	−	0.345177i	$-0.112181\pi$
$599$	6.62004	+	9.76383i	0.270488	+	0.398939i	−0.668050	+	0.744116i	$0.732871\pi$
$600$	−0.328928	+	2.00637i	−0.0134284	+	0.0819097i
$601$	38.4690	−	23.1460i	1.56918	−	0.944145i	0.577363	−	0.816488i	$-0.304082\pi$
$601$	38.4690	−	23.1460i	1.56918	−	0.944145i	0.991818	−	0.127658i	$-0.0407459\pi$
$602$	−1.58984	−	1.50597i	−0.0647969	−	0.0613788i
$603$	−4.05864	+	5.98605i	−0.165281	+	0.243771i
$604$	−5.21052	−	1.14692i	−0.212013	−	0.0466676i
$605$	−0.239045	−	0.860964i	−0.00971858	−	0.0350032i
$606$	0.0593883	+	0.0357327i	0.00241248	+	0.00145154i
$607$	−13.3720	+	15.7427i	−0.542751	+	0.638976i	−0.963343	−	0.268274i	$-0.913547\pi$
$607$	−13.3720	+	15.7427i	−0.542751	+	0.638976i	0.420591	+	0.907250i	$0.361823\pi$
$608$	5.14323	+	1.73296i	0.208586	+	0.0702807i
$609$	−29.6062	−	13.6973i	−1.19970	−	0.555041i
$610$	−0.0942699	−	0.177812i	−0.00381688	−	0.00719940i
$611$	−10.9390	+	2.40786i	−0.442545	+	0.0974114i
$612$	−0.881894	+	2.21339i	−0.0356485	+	0.0894709i
$613$	−30.9970	+	10.4441i	−1.25196	+	0.421833i	−0.865702	−	0.500559i	$-0.833128\pi$
$613$	−30.9970	+	10.4441i	−1.25196	+	0.421833i	−0.386254	+	0.922392i	$0.626231\pi$
$614$	−3.20721	−	0.348805i	−0.129432	−	0.0140766i
$615$	0.241599	−	4.45604i	0.00974223	−	0.179685i
$616$	0.302259	+	5.57483i	0.0121783	+	0.224616i
$617$	−15.4501	+	1.68030i	−0.621997	+	0.0676463i	−0.413691	−	0.910417i	$-0.635761\pi$
$617$	−15.4501	+	1.68030i	−0.621997	+	0.0676463i	−0.208306	+	0.978064i	$0.566795\pi$
$618$	1.11110	−	0.514050i	0.0446950	−	0.0206781i
$619$	13.6885	+	10.4058i	0.550189	+	0.418243i	0.842989	−	0.537931i	$-0.180794\pi$
$619$	13.6885	+	10.4058i	0.550189	+	0.418243i	−0.292800	+	0.956174i	$0.594587\pi$
$620$	−1.89228	−	1.43848i	−0.0759960	−	0.0577706i
$621$	−2.69767	+	1.24807i	−0.108254	+	0.0500835i
$622$	−1.92472	+	0.209326i	−0.0771743	+	0.00839322i
$623$	3.29779	+	60.8241i	0.132123	+	2.43687i
$624$	−0.217871	+	4.01840i	−0.00872182	+	0.160865i
$625$	−19.4393	−	2.11416i	−0.777574	−	0.0845662i
$626$	0.185193	−	0.0623989i	0.00740181	−	0.00249396i
$627$	−5.40832	+	13.5739i	−0.215988	+	0.542088i
$628$	8.77049	−	1.93053i	0.349981	−	0.0770366i
$629$	−1.55043	−	2.92441i	−0.0618195	−	0.116604i
$630$	−0.219598	−	0.101597i	−0.00874899	−	0.00404771i
$631$	6.28192	+	2.11663i	0.250079	+	0.0842616i	0.441550	−	0.897237i	$-0.354429\pi$
$631$	6.28192	+	2.11663i	0.250079	+	0.0842616i	−0.191470	+	0.981498i	$0.561326\pi$
$632$	−0.438662	+	0.516433i	−0.0174490	+	0.0205426i
$633$	−3.87844	−	2.33358i	−0.154154	−	0.0927515i
$634$	−0.0801364	−	0.288625i	−0.00318262	−	0.0114628i
$635$	−7.39461	−	1.62768i	−0.293446	−	0.0645924i
$636$	10.6890	−	15.7651i	0.423845	−	0.625125i
$637$	4.43045	+	4.19674i	0.175541	+	0.166281i
$638$	−3.02052	+	1.81739i	−0.119584	+	0.0719510i
$639$	−0.241044	+	1.47030i	−0.00953554	+	0.0581642i
$640$	−1.18894	−	1.75356i	−0.0469970	−	0.0693154i
$641$	0.829442	+	2.08174i	0.0327610	+	0.0822239i	0.944447	−	0.328664i	$-0.106598\pi$
$641$	0.829442	+	2.08174i	0.0327610	+	0.0822239i	−0.911686	+	0.410887i	$0.865219\pi$
$642$	0.104402	+	0.122911i	0.00412041	+	0.00485092i
$643$	−4.93577	−	30.1069i	−0.194648	−	1.18730i	−0.885617	−	0.464416i	$-0.846264\pi$
$643$	−4.93577	−	30.1069i	−0.194648	−	1.18730i	0.690969	−	0.722884i	$-0.257184\pi$
$644$	−15.4402	+	14.6258i	−0.608430	+	0.576336i
$645$	−0.901461	+	3.24677i	−0.0354950	+	0.127841i
$646$	0.255988	−	0.482845i	0.0100717	−	0.0189973i
$647$	−6.69078	+	5.08620i	−0.263042	+	0.199959i	−0.728379	−	0.685174i	$-0.759726\pi$
$647$	−6.69078	+	5.08620i	−0.263042	+	0.199959i	0.465337	+	0.885133i	$0.345933\pi$
$648$	−0.439345			−0.0172591
$649$	−1.85206	+	27.0549i	−0.0726999	+	1.06200i
$650$	0.522425			0.0204912
$651$	−5.61533	+	4.26866i	−0.220082	+	0.167302i
$652$	8.90526	−	16.7971i	0.348757	−	0.657825i
$653$	−12.1427	+	43.7341i	−0.475181	+	1.71145i	0.205314	+	0.978696i	$0.434179\pi$
$653$	−12.1427	+	43.7341i	−0.475181	+	1.71145i	−0.680495	+	0.732753i	$0.738235\pi$
$654$	1.20111	−	1.13775i	0.0469671	−	0.0444896i
$655$	0.279058	+	1.70218i	0.0109037	+	0.0665096i
$656$	−18.5949	−	21.8916i	−0.726009	−	0.854724i
$657$	−5.29823	−	13.2976i	−0.206704	−	0.518787i
$658$	−2.43254	−	3.58772i	−0.0948301	−	0.139864i
$659$	6.85355	−	41.8048i	0.266976	−	1.62848i	−0.424039	−	0.905644i	$-0.639388\pi$
$659$	6.85355	−	41.8048i	0.266976	−	1.62848i	0.691015	−	0.722840i	$-0.257164\pi$
$660$	3.66929	−	2.20774i	0.142827	−	0.0859362i
$661$	−4.41461	−	4.18174i	−0.171709	−	0.162651i	0.597020	−	0.802227i	$-0.296351\pi$
$661$	−4.41461	−	4.18174i	−0.171709	−	0.162651i	−0.768728	+	0.639576i	$0.779110\pi$
$662$	0.235380	−	0.347160i	0.00914832	−	0.0134928i
$663$	1.19946	+	0.264021i	0.0465832	+	0.0102537i
$664$	−0.694529	−	2.50147i	−0.0269529	−	0.0970757i
$665$	−7.78845	−	4.68616i	−0.302023	−	0.181721i
$666$	0.196965	−	0.231885i	0.00763224	−	0.00898537i
$667$	−25.5286	−	8.60159i	−0.988472	−	0.333055i
$668$	−5.91669	−	2.73735i	−0.228924	−	0.105911i
$669$	0.782411	+	1.47578i	0.0302498	+	0.0570571i
$670$	−0.474807	+	0.104513i	−0.0183434	+	0.00403768i
$671$	3.91228	−	9.81908i	0.151032	−	0.379061i
$672$	−4.47302	+	1.50714i	−0.172551	+	0.0581390i
$673$	0.282560	+	0.0307302i	0.0108919	+	0.00118456i	0.113563	−	0.993531i	$-0.463774\pi$
$673$	0.282560	+	0.0307302i	0.0108919	+	0.00118456i	−0.102671	+	0.994715i	$0.532739\pi$
$674$	0.213900	−	3.94515i	0.00823911	−	0.151961i
$675$	−0.250538	−	4.62090i	−0.00964322	−	0.177859i
$676$	−23.6157	+	2.56836i	−0.908297	+	0.0987832i
$677$	13.0029	−	6.01577i	0.499741	−	0.231205i	−0.153791	−	0.988103i	$-0.549148\pi$
$677$	13.0029	−	6.01577i	0.499741	−	0.231205i	0.653533	+	0.756898i	$0.273286\pi$
$678$	0.184352	+	0.140141i	0.00707999	+	0.00538207i
$679$	28.1119	+	21.3701i	1.07884	+	0.820111i
$680$	−0.291613	+	0.134915i	−0.0111829	+	0.00517374i
$681$	18.8185	−	2.04663i	0.721126	−	0.0784271i
$682$	0.0412663	+	0.761111i	0.00158017	+	0.0291445i
$683$	0.450692	−	8.31253i	0.0172453	−	0.318070i	−0.977165	−	0.212483i	$-0.931845\pi$
$683$	0.450692	−	8.31253i	0.0172453	−	0.318070i	0.994410	−	0.105587i	$-0.0336722\pi$
$684$	−8.17892	−	0.889511i	−0.312729	−	0.0340113i
$685$	−13.3158	+	4.48660i	−0.508769	+	0.171424i
$686$	0.153305	−	0.384766i	0.00585320	−	0.0146904i
$687$	24.7522	−	5.44838i	0.944357	−	0.207869i
$688$	10.1589	+	19.1617i	0.387304	+	0.730533i
$689$	−8.91083	−	4.12259i	−0.339476	−	0.157058i
$690$	−0.189354	−	0.0638007i	−0.00720857	−	0.00242885i
$691$	−13.2679	+	15.6202i	−0.504735	+	0.594219i	−0.954234	−	0.299061i	$-0.903327\pi$
$691$	−13.2679	+	15.6202i	−0.504735	+	0.594219i	0.449499	+	0.893281i	$0.351602\pi$
$692$	−20.3339	−	12.2345i	−0.772978	−	0.465085i
$693$	−3.39964	−	12.2444i	−0.129142	−	0.465126i
$694$	1.84031	+	0.405082i	0.0698571	+	0.0153767i
$695$	3.98640	−	5.87949i	0.151213	−	0.223022i
$696$	−2.89076	−	2.73827i	−0.109574	−	0.103794i
$697$	−7.51119	+	4.51933i	−0.284507	+	0.171182i
$698$	0.125276	−	0.764147i	0.00474175	−	0.0289234i
$699$	−1.80104	−	2.65634i	−0.0681217	−	0.100472i
$700$	−12.2558	−	30.7598i	−0.463226	−	1.16261i
$701$	15.7331	+	18.5225i	0.594233	+	0.699585i	0.974269	−	0.225387i	$-0.0723645\pi$
$701$	15.7331	+	18.5225i	0.594233	+	0.699585i	−0.380037	+	0.924971i	$0.624089\pi$
$702$	0.0182637	+	0.111404i	0.000689320	+	0.00420467i
$703$	8.29768	−	7.85998i	0.312953	−	0.296445i
$704$	7.28231	−	26.2285i	0.274463	−	0.988525i
$705$	−3.12417	+	5.89282i	−0.117663	+	0.221936i
$706$	−2.36387	+	1.79697i	−0.0889653	+	0.0676297i
$707$	−2.26440			−0.0851617
$708$	−14.9571	+	3.07057i	−0.562124	+	0.115399i
$709$	−17.3979			−0.653392			−0.326696	−	0.945129i	$-0.605935\pi$
$709$	−17.3979			−0.653392			−0.326696	+	0.945129i	$0.605935\pi$
$710$	−0.0797347	+	0.0606127i	−0.00299239	+	0.00227475i
$711$	0.722413	−	1.36261i	0.0270926	−	0.0511020i
$712$	−1.98912	+	7.16417i	−0.0745455	+	0.268489i
$713$	−4.22887	+	4.00580i	−0.158372	+	0.150018i
$714$	0.0768935	+	0.469030i	0.00287767	+	0.0175530i
$715$	−1.42904	−	1.68240i	−0.0534431	−	0.0629181i
$716$	14.0947	+	35.3750i	0.526743	+	1.32202i
$717$	−10.9943	−	16.2154i	−0.410591	−	0.605577i
$718$	−0.229371	+	1.39910i	−0.00856005	+	0.0522140i
$719$	−21.9137	+	13.1851i	−0.817244	+	0.491720i	−0.861776	−	0.507288i	$-0.830648\pi$
$719$	−21.9137	+	13.1851i	−0.817244	+	0.491720i	0.0445320	+	0.999008i	$0.485820\pi$
$720$	1.73973	+	1.64796i	0.0648360	+	0.0614159i
$721$	−22.4461	+	33.1055i	−0.835935	+	1.23291i
$722$	−0.201336	−	0.0443174i	−0.00749294	−	0.00164932i
$723$	3.69688	+	13.3150i	0.137489	+	0.495189i
$724$	25.1943	+	15.1589i	0.936338	+	0.563376i
$725$	27.1519	−	31.9656i	1.00839	−	1.18717i
$726$	−0.152888	−	0.0515140i	−0.00567421	−	0.00191186i
$727$	−36.2949	−	16.7918i	−1.34611	−	0.622775i	−0.391370	−	0.920233i	$-0.627999\pi$
$727$	−36.2949	−	16.7918i	−1.34611	−	0.622775i	−0.954735	+	0.297459i	$0.903861\pi$
$728$	0.759018	+	1.43166i	0.0281311	+	0.0530608i
$729$	0.976621	−	0.214970i	0.0361711	−	0.00796187i
$730$	0.356163	−	0.893902i	0.0131822	−	0.0330848i
$731$	6.27250	−	2.11345i	0.231997	−	0.0781688i
$732$	5.91648	+	0.643456i	0.218679	+	0.0237828i
$733$	0.729710	−	13.4587i	0.0269524	−	0.497109i	−0.953628	−	0.300989i	$-0.902683\pi$
$733$	0.729710	−	13.4587i	0.0269524	−	0.497109i	0.980580	−	0.196119i	$-0.0628340\pi$
$734$	0.162580	+	2.99861i	0.00600093	+	0.110681i
$735$	3.61259	−	0.392893i	0.133252	−	0.0144921i
$736$	−3.53763	+	1.63668i	−0.130399	+	0.0603289i
$737$	−20.3270	−	15.4521i	−0.748753	−	0.569187i
$738$	−0.641451	−	0.487619i	−0.0236121	−	0.0179495i
$739$	35.2121	−	16.2908i	1.29530	−	0.599268i	0.353495	−	0.935436i	$-0.384993\pi$
$739$	35.2121	−	16.2908i	1.29530	−	0.599268i	0.941802	+	0.336168i	$0.109131\pi$
$740$	−3.33001	+	0.362160i	−0.122413	+	0.0133133i
$741$	0.229597	+	4.23467i	0.00843445	+	0.155564i
$742$	0.205705	−	3.79400i	0.00755167	−	0.139282i
$743$	−15.7856	−	1.71679i	−0.579118	−	0.0629829i	−0.186128	−	0.982526i	$-0.559594\pi$
$743$	−15.7856	−	1.71679i	−0.579118	−	0.0629829i	−0.392990	+	0.919543i	$0.628559\pi$
$744$	−0.815905	+	0.274910i	−0.0299125	+	0.0100787i
$745$	−4.93643	+	12.3895i	−0.180857	+	0.453916i
$746$	0.827058	−	0.182049i	0.0302807	−	0.00666529i
$747$	2.76783	+	5.22068i	0.101270	+	0.191015i
$748$	−7.63433	−	3.53202i	−0.279139	−	0.129143i
$749$	−4.99293	−	1.68231i	−0.182438	−	0.0614704i
$750$	0.418990	−	0.493273i	0.0152994	−	0.0180118i
$751$	−26.9594	−	16.2209i	−0.983763	−	0.591910i	−0.0697363	−	0.997565i	$-0.522216\pi$
$751$	−26.9594	−	16.2209i	−0.983763	−	0.591910i	−0.914026	+	0.405655i	$0.867043\pi$
$752$	11.4848	+	41.3646i	0.418809	+	1.50841i
$753$	−2.25749	−	0.496912i	−0.0822676	−	0.0181085i
$754$	−0.574168	+	0.846834i	−0.0209100	+	0.0308399i
$755$	1.18893	+	1.12621i	0.0432694	+	0.0409870i
$756$	6.13087	−	3.68882i	0.222978	−	0.134161i
$757$	4.15817	−	25.3637i	0.151131	−	0.921860i	−0.797000	−	0.603980i	$-0.793581\pi$
$757$	4.15817	−	25.3637i	0.151131	−	0.921860i	0.948131	−	0.317880i	$-0.102971\pi$
$758$	0.900718	+	1.32846i	0.0327156	+	0.0482518i
$759$	−3.88424	−	9.74870i	−0.140989	−	0.353855i
$760$	−0.718265	−	0.845607i	−0.0260542	−	0.0306734i
$761$	−2.96677	−	18.0965i	−0.107545	−	0.655998i	−0.984495	−	0.175415i	$-0.943873\pi$
$761$	−2.96677	−	18.0965i	−0.107545	−	0.655998i	0.876949	−	0.480583i	$-0.159575\pi$
$762$	−0.992515	+	0.940161i	−0.0359550	+	0.0340584i
$763$	−14.4604	+	52.0816i	−0.523501	+	1.88548i
$764$	18.2324	−	34.3899i	0.659624	−	1.24418i
$765$	0.582214	−	0.442587i	0.0210500	−	0.0160018i
$766$	−1.91117			−0.0690532
$767$	2.80929	+	7.35239i	0.101438	+	0.265479i
$768$	15.0378			0.542630
$769$	−28.5913	+	21.7345i	−1.03103	+	0.783767i	−0.976668	−	0.214755i	$-0.931105\pi$
$769$	−28.5913	+	21.7345i	−1.03103	+	0.783767i	−0.0543593	+	0.998521i	$0.517312\pi$
$770$	0.400134	−	0.754733i	0.0144198	−	0.0271987i
$771$	4.06089	−	14.6260i	0.146250	−	0.526743i
$772$	−23.6407	+	22.3936i	−0.850846	+	0.805964i
$773$	−1.44114	−	8.79054i	−0.0518340	−	0.316174i	0.948165	−	0.317779i	$-0.102937\pi$
$773$	−1.44114	−	8.79054i	−0.0518340	−	0.316174i	−0.999999	+	0.00160574i	$0.999489\pi$
$774$	0.393871	+	0.463701i	0.0141574	+	0.0166674i
$775$	−3.35670	−	8.42468i	−0.120576	−	0.302623i
$776$	2.41887	+	3.56757i	0.0868325	+	0.128068i
$777$	−1.60812	+	9.80908i	−0.0576909	+	0.351899i
$778$	−2.90077	+	1.74534i	−0.103998	+	0.0625733i
$779$	−21.9751	−	20.8159i	−0.787340	−	0.745808i
$780$	0.697493	−	1.02873i	0.0249743	−	0.0368343i
$781$	−5.13720	−	1.13078i	−0.183824	−	0.0404626i
$782$	0.105005	+	0.378192i	0.00375495	+	0.0135241i
$783$	7.76569	+	4.67246i	0.277523	+	0.166980i
$784$	15.1419	−	17.8264i	0.540782	−	0.636657i
$785$	−2.61224	−	0.880166i	−0.0932349	−	0.0314145i
$786$	0.282658	+	0.130771i	0.0100821	+	0.00466446i
$787$	23.1410	+	43.6485i	0.824887	+	1.55590i	0.831234	+	0.555922i	$0.187635\pi$
$787$	23.1410	+	43.6485i	0.824887	+	1.55590i	−0.00634706	+	0.999980i	$0.502020\pi$
$788$	−16.3902	+	3.60775i	−0.583875	+	0.128521i
$789$	9.64084	−	24.1967i	0.343223	−	0.861425i
$790$	0.0982490	−	0.0331039i	0.00349554	−	0.00117779i
$791$	−7.52129	−	0.817989i	−0.267426	−	0.0290844i
$792$	0.0839752	−	1.54883i	0.00298393	−	0.0550353i
$793$	−0.166086	−	3.06328i	−0.00589789	−	0.108780i
$794$	1.01401	−	0.110281i	0.0359860	−	0.00391371i
$795$	−5.30612	+	2.45487i	−0.188189	+	0.0870653i
$796$	−35.9503	−	27.3287i	−1.27422	−	0.968640i
$797$	20.2810	+	15.4172i	0.718389	+	0.546105i	0.899267	−	0.437401i	$-0.144101\pi$
$797$	20.2810	+	15.4172i	0.718389	+	0.546105i	−0.180878	+	0.983506i	$0.557894\pi$
$798$	−1.48949	+	0.689114i	−0.0527275	+	0.0243944i
$799$	13.0248	−	1.41653i	0.460784	−	0.0501133i
$800$	−0.328547	−	6.05970i	−0.0116159	−	0.214243i
$801$	0.916211	−	16.8985i	0.0323727	−	0.597080i
$802$	3.40231	+	0.370024i	0.120140	+	0.0130660i
$803$	47.8908	−	16.1363i	1.69003	−	0.569437i
$804$	5.32136	−	13.3556i	0.187670	−	0.471016i
$805$	6.37546	−	1.40335i	0.224706	−	0.0494614i
$806$	0.103626	+	0.195459i	0.00365007	+	0.00688476i
$807$	23.6691	+	10.9505i	0.833192	+	0.385476i
$808$	−0.261928	−	0.0882538i	−0.00921459	−	0.00310476i
$809$	2.96604	−	3.49189i	0.104280	−	0.122768i	−0.707546	−	0.706667i	$-0.750198\pi$
$809$	2.96604	−	3.49189i	0.104280	−	0.122768i	0.811826	+	0.583899i	$0.198474\pi$
$810$	0.0576005	+	0.0346571i	0.00202388	+	0.00121773i
$811$	6.22823	+	22.4321i	0.218703	+	0.787697i	0.988733	+	0.149689i	$0.0478273\pi$
$811$	6.22823	+	22.4321i	0.218703	+	0.787697i	−0.770030	+	0.638007i	$0.779759\pi$
$812$	63.3303	+	13.9401i	2.22246	+	0.489200i
$813$	6.96498	−	10.2726i	0.244273	−	0.360275i
$814$	0.779821	+	0.738686i	0.0273327	+	0.0258909i
$815$	−5.00030	+	3.00858i	−0.175153	+	0.105386i
$816$	0.761540	−	4.64519i	0.0266592	−	0.162614i
$817$	12.8261	+	18.9171i	0.448729	+	0.661826i
$818$	−0.741757	−	1.86167i	−0.0259349	−	0.0650917i
$819$	−2.38773	−	2.81105i	−0.0834339	−	0.0982260i
$820$	1.43517	+	8.75414i	0.0501182	+	0.305708i
$821$	10.6238	−	10.0634i	0.370772	−	0.351214i	−0.479515	−	0.877534i	$-0.659187\pi$
$821$	10.6238	−	10.0634i	0.370772	−	0.351214i	0.850286	+	0.526320i	$0.176429\pi$
$822$	−0.678735	+	2.44458i	−0.0236736	+	0.0852646i
$823$	−22.6931	+	42.8038i	−0.791033	+	1.49205i	0.0778146	+	0.996968i	$0.475206\pi$
$823$	−22.6931	+	42.8038i	−0.791033	+	1.49205i	−0.868848	+	0.495079i	$0.835139\pi$
$824$	−3.88664	+	2.95455i	−0.135398	+	0.102927i
$825$	16.3380			0.568817
$826$	−2.24082	+	2.06311i	−0.0779679	+	0.0717847i
$827$	−23.4204			−0.814408			−0.407204	−	0.913337i	$-0.633496\pi$
$827$	−23.4204			−0.814408			−0.407204	+	0.913337i	$0.633496\pi$
$828$	4.70388	−	3.57580i	0.163471	−	0.124268i
$829$	6.90978	−	13.0332i	0.239986	−	0.452663i	−0.734037	−	0.679109i	$-0.762366\pi$
$829$	6.90978	−	13.0332i	0.239986	−	0.452663i	0.974024	+	0.226447i	$0.0727110\pi$
$830$	−0.106268	+	0.382743i	−0.00368861	+	0.0132852i
$831$	−14.2293	+	13.4787i	−0.493610	+	0.467572i
$832$	−1.27817	−	7.79648i	−0.0443125	−	0.270294i
$833$	−4.62115	−	5.44044i	−0.160113	−	0.188500i
$834$	−0.474734	−	1.19149i	−0.0164387	−	0.0412580i
$835$	1.12297	+	1.65626i	0.0388621	+	0.0573173i
$836$	4.69910	−	28.6633i	0.162522	−	0.991340i
$837$	1.67916	−	1.01032i	0.0580403	−	0.0349217i
$838$	−0.663505	−	0.628505i	−0.0229204	−	0.0217114i
$839$	32.1068	−	47.3540i	1.10845	−	1.63484i	0.424251	−	0.905545i	$-0.360537\pi$
$839$	32.1068	−	47.3540i	1.10845	−	1.63484i	0.684198	−	0.729296i	$-0.260152\pi$
$840$	0.942349	+	0.207427i	0.0325141	+	0.00715690i
$841$	14.2159	+	51.2010i	0.490203	+	1.76555i
$842$	−0.151372	−	0.0910774i	−0.00521662	−	0.00313874i
$843$	−4.92895	+	5.80281i	−0.169762	+	0.199859i
$844$	8.52677	+	2.87300i	0.293503	+	0.0988928i
$845$	6.61764	+	3.06165i	0.227654	+	0.105324i
$846$	0.564090	+	1.06399i	0.0193938	+	0.0365806i
$847$	5.14768	−	1.13309i	0.176876	−	0.0389335i
$848$	−13.9284	+	34.9577i	−0.478304	+	1.20045i
$849$	−10.8290	+	3.64872i	−0.371651	+	0.125224i
$850$	−0.607495	−	0.0660691i	−0.0208369	−	0.00226615i
$851$	−0.444401	+	8.19650i	−0.0152339	+	0.280972i
$852$	−0.160347	−	2.95743i	−0.00549340	−	0.101320i
$853$	35.4838	−	3.85909i	1.21494	−	0.132133i	0.521885	−	0.853016i	$-0.325229\pi$
$853$	35.4838	−	3.85909i	1.21494	−	0.132133i	0.693057	+	0.720883i	$0.256264\pi$
$854$	1.07747	−	0.498492i	0.0368704	−	0.0170581i
$855$	2.01038	+	1.52825i	0.0687537	+	0.0522652i
$856$	−0.511975	−	0.389193i	−0.0174989	−	0.0133023i
$857$	11.8539	−	5.48419i	0.404921	−	0.187336i	−0.206848	−	0.978373i	$-0.566320\pi$
$857$	11.8539	−	5.48419i	0.404921	−	0.187336i	0.611769	+	0.791037i	$0.290458\pi$
$858$	−0.396225	+	0.0430920i	−0.0135269	+	0.00147114i
$859$	−0.754266	−	13.9116i	−0.0257352	−	0.474658i	−0.982787	−	0.184742i	$-0.940855\pi$
$859$	−0.754266	−	13.9116i	−0.0257352	−	0.474658i	0.957052	−	0.289917i	$-0.0936276\pi$
$860$	0.362638	−	6.68846i	0.0123658	−	0.228075i
$861$	26.1703	+	2.84619i	0.891880	+	0.0969978i
$862$	0.795474	−	0.268027i	0.0270940	−	0.00912902i
$863$	−12.2968	+	30.8625i	−0.418586	+	1.05057i	0.556913	+	0.830571i	$0.311986\pi$
$863$	−12.2968	+	30.8625i	−0.418586	+	1.05057i	−0.975500	+	0.220002i	$0.929394\pi$
$864$	1.28071	−	0.281905i	0.0435705	−	0.00959060i
$865$	3.41195	+	6.43561i	0.116010	+	0.218817i
$866$	0.495383	+	0.229189i	0.0168338	+	0.00778814i
$867$	14.7487	+	4.96942i	0.500893	+	0.168770i
$868$	9.07740	−	10.6867i	0.308107	−	0.362732i
$869$	4.66557	+	2.80718i	0.158269	+	0.0952271i
$870$	0.162989	+	0.587035i	0.00552586	+	0.0199024i
$871$	−7.23756	−	1.59311i	−0.245235	−	0.0539804i
$872$	−3.70251	+	5.46079i	−0.125383	+	0.184926i
$873$	−7.12252	−	6.74680i	−0.241061	−	0.228345i
$874$	−1.16130	+	0.698729i	−0.0392815	+	0.0236349i
$875$	−3.42083	+	20.8662i	−0.115645	+	0.705405i
$876$	15.9684	+	23.5516i	0.539522	+	0.795735i
$877$	−9.90460	−	24.8587i	−0.334455	−	0.839418i	−0.995987	−	0.0895009i	$-0.971473\pi$
$877$	−9.90460	−	24.8587i	−0.334455	−	0.839418i	0.661532	−	0.749917i	$-0.269907\pi$
$878$	−1.47097	−	1.73176i	−0.0496429	−	0.0584442i
$879$	−4.88606	−	29.8036i	−0.164803	−	1.00525i
$880$	−6.14212	+	5.81812i	−0.207051	+	0.196129i
$881$	−9.51711	+	34.2775i	−0.320640	+	1.15484i	0.611052	+	0.791590i	$0.290746\pi$
$881$	−9.51711	+	34.2775i	−0.320640	+	1.15484i	−0.931692	+	0.363249i	$0.881667\pi$
$882$	0.307334	−	0.579693i	0.0103485	−	0.0195193i
$883$	−26.3781	+	20.0521i	−0.887695	+	0.674808i	−0.946236	−	0.323477i	$-0.895148\pi$
$883$	−26.3781	+	20.0521i	−0.887695	+	0.674808i	0.0585409	+	0.998285i	$0.481355\pi$
$884$	−2.44144			−0.0821145
$885$	4.41981	+	1.55935i	0.148570	+	0.0524171i
$886$	3.59541			0.120790
$887$	18.3169	−	13.9241i	0.615021	−	0.467527i	−0.250692	−	0.968067i	$-0.580658\pi$
$887$	18.3169	−	13.9241i	0.615021	−	0.467527i	0.865713	+	0.500540i	$0.166865\pi$
$888$	−0.568317	+	1.07196i	−0.0190715	+	0.0359726i
$889$	11.9491	−	43.0367i	0.400760	−	1.44341i
$890$	0.825920	−	0.782353i	0.0276849	−	0.0262245i
$891$	0.571171	+	3.48399i	0.0191349	+	0.116718i
$892$	−2.14961	−	2.53072i	−0.0719743	−	0.0847347i
$893$	16.7450	+	42.0268i	0.560350	+	1.40637i
$894$	1.35136	+	1.99310i	0.0451962	+	0.0666594i
$895$	1.89098	−	11.5345i	0.0632085	−	0.385555i
$896$	10.7087	−	6.44321i	0.357752	−	0.215252i
$897$	−2.21123	−	2.09459i	−0.0738308	−	0.0699362i
$898$	2.35285	−	3.47019i	0.0785155	−	0.115802i
$899$	17.3453	+	3.81799i	0.578498	+	0.127337i
$900$	2.46105	+	8.86390i	0.0820350	+	0.295463i
$901$	9.84049	+	5.92083i	0.327834	+	0.197251i
$902$	1.84162	−	2.16812i	0.0613191	−	0.0721904i
$903$	−18.8366	−	6.34678i	−0.626842	−	0.211208i
$904$	−0.838121	−	0.387756i	−0.0278755	−	0.0128966i
$905$	−4.22751	−	7.97392i	−0.140527	−	0.265062i
$906$	0.288775	−	0.0635643i	0.00959392	−	0.00211178i
$907$	16.7785	−	42.1110i	0.557122	−	1.39827i	−0.333163	−	0.942869i	$-0.608116\pi$
$907$	16.7785	−	42.1110i	0.557122	−	1.39827i	0.890286	−	0.455402i	$-0.150505\pi$
$908$	−35.6594	+	12.0150i	−1.18340	+	0.398733i
$909$	0.625422	+	0.0680187i	0.0207439	+	0.00225604i
$910$	0.0134230	−	0.247572i	0.000444967	−	0.00820694i
$911$	1.79330	+	33.0754i	0.0594146	+	1.09584i	0.864485	+	0.502658i	$0.167645\pi$
$911$	1.79330	+	33.0754i	0.0594146	+	1.09584i	−0.805071	+	0.593179i	$0.797873\pi$
$912$	16.1587	−	1.75736i	0.535068	−	0.0581921i
$913$	−18.9336	+	8.75961i	−0.626610	+	0.289901i
$914$	−2.99600	−	2.27750i	−0.0990988	−	0.0753330i
$915$	−1.45427	−	1.10551i	−0.0480768	−	0.0365471i
$916$	−45.7254	+	21.1548i	−1.51081	+	0.698975i
$917$	−10.1155	+	1.10012i	−0.334042	+	0.0363293i
$918$	−0.00714894	−	0.131854i	−0.000235950	−	0.00435184i
$919$	−0.232181	+	4.28233i	−0.00765895	+	0.141261i	0.992203	+	0.124634i	$0.0397756\pi$
$919$	−0.232181	+	4.28233i	−0.00765895	+	0.141261i	−0.999862	+	0.0166272i	$0.994707\pi$
$920$	0.792156	+	0.0861522i	0.0261166	+	0.00284035i
$921$	−27.7501	+	9.35008i	−0.914395	+	0.308096i
$922$	−0.356157	+	0.893887i	−0.0117294	+	0.0294386i
$923$	−1.49102	+	0.328199i	−0.0490777	+	0.0108028i
$924$	11.8324	+	22.3183i	0.389259	+	0.734220i
$925$	−11.5986	−	5.36610i	−0.381361	−	0.176436i
$926$	−2.09563	−	0.706099i	−0.0688666	−	0.0232038i
$927$	7.19397	−	8.46939i	0.236281	−	0.278171i
$928$	10.1837	+	6.12731i	0.334295	+	0.201139i
$929$	2.13358	+	7.68447i	0.0700006	+	0.252119i	0.990269	−	0.139169i	$-0.0444432\pi$
$929$	2.13358	+	7.68447i	0.0700006	+	0.252119i	−0.920268	+	0.391289i	$0.872029\pi$
$930$	0.128655	+	0.0283192i	0.00421878	+	0.000928623i
$931$	13.8322	−	20.4009i	0.453331	−	0.668614i
$932$	4.63166	+	4.38734i	0.151715	+	0.143712i
$933$	−15.0579	+	9.06003i	−0.492973	+	0.296612i
$934$	−0.154716	+	0.943728i	−0.00506247	+	0.0308797i
$935$	1.44898	+	2.13708i	0.0473866	+	0.0698901i
$936$	−0.166634	−	0.418220i	−0.00544660	−	0.0136699i
$937$	21.9708	+	25.8660i	0.717754	+	0.845006i	0.993213	−	0.116307i	$-0.0371057\pi$
$937$	21.9708	+	25.8660i	0.717754	+	0.845006i	−0.275459	+	0.961313i	$0.588830\pi$
$938$	−0.463977	−	2.83013i	−0.0151494	−	0.0924071i
$939$	1.28779	−	1.21986i	0.0420253	−	0.0398085i
$940$	3.54704	−	12.7753i	0.115692	−	0.416684i
$941$	16.5182	−	31.1566i	0.538478	−	1.01568i	−0.453736	−	0.891136i	$-0.649909\pi$
$941$	16.5182	−	31.1566i	0.538478	−	1.01568i	0.992214	−	0.124541i	$-0.0397460\pi$
$942$	−0.396224	+	0.301202i	−0.0129097	+	0.00981369i
$943$	21.7390			0.707920
$944$	27.5551	−	12.2769i	0.896843	−	0.399580i
$945$	−2.19624			−0.0714437
$946$	−1.70998	+	1.29989i	−0.0555961	+	0.0422631i
$947$	5.27947	−	9.95814i	0.171560	−	0.323596i	−0.782791	−	0.622285i	$-0.786204\pi$
$947$	5.27947	−	9.95814i	0.171560	−	0.323596i	0.954351	+	0.298689i	$0.0965493\pi$
$948$	−0.820194	+	2.95407i	−0.0266387	+	0.0959438i
$949$	10.6486	−	10.0869i	0.345670	−	0.327436i
$950$	−0.341368	−	2.08225i	−0.0110755	−	0.0675573i
$951$	−1.76018	−	2.07225i	−0.0570779	−	0.0671972i
$952$	−0.701558	−	1.76078i	−0.0227376	−	0.0570671i
$953$	−9.39431	−	13.8556i	−0.304312	−	0.448826i	0.644530	−	0.764579i	$-0.277053\pi$
$953$	−9.39431	−	13.8556i	−0.304312	−	0.448826i	−0.948841	+	0.315753i	$0.897743\pi$
$954$	−0.170780	+	1.04171i	−0.00552922	+	0.0337267i
$955$	−10.2375	+	6.15968i	−0.331277	+	0.199323i
$956$	28.2736	+	26.7822i	0.914435	+	0.866199i
$957$	−17.9562	+	26.4834i	−0.580442	+	0.856088i
$958$	−1.13639	−	0.250137i	−0.0367149	−	0.00808157i
$959$	−22.1749	−	79.8668i	−0.716065	−	2.57903i
$960$	−4.03111	−	2.42544i	−0.130103	−	0.0782807i
$961$	−17.5828	+	20.7001i	−0.567187	+	0.667744i
$962$	0.295440	+	0.0995452i	0.00952535	+	0.00320947i
$963$	1.32850	+	0.614629i	0.0428103	+	0.0198062i
$964$	−12.8670	−	24.2697i	−0.414418	−	0.781675i
$965$	9.76152	−	2.14867i	0.314234	−	0.0691682i
$966$	0.436278	−	1.09498i	0.0140370	−	0.0352302i
$967$	13.8683	−	4.67277i	0.445974	−	0.150266i	−0.0873489	−	0.996178i	$-0.527840\pi$
$967$	13.8683	−	4.67277i	0.445974	−	0.150266i	0.533323	+	0.845912i	$0.320943\pi$
$968$	0.639604	+	0.0695611i	0.0205576	+	0.00223578i
$969$	0.268558	−	4.95327i	0.00862734	−	0.159122i
$970$	−0.0357048	−	0.658537i	−0.00114641	−	0.0211443i
$971$	10.7399	−	1.16804i	0.344660	−	0.0374841i	0.0658480	−	0.997830i	$-0.479025\pi$
$971$	10.7399	−	1.16804i	0.344660	−	0.0374841i	0.278812	+	0.960346i	$0.410059\pi$
$972$	−1.80414	+	0.834682i	−0.0578677	+	0.0267724i
$973$	33.3589	+	25.3588i	1.06944	+	0.812966i
$974$	−2.64969	−	2.01424i	−0.0849016	−	0.0645405i
$975$	4.30369	−	1.99110i	0.137828	−	0.0637661i
$976$	−11.6889	+	1.27124i	−0.374153	+	0.0406915i
$977$	−0.321443	−	5.92867i	−0.0102839	−	0.189675i	−0.999161	−	0.0409433i	$-0.986964\pi$
$977$	−0.321443	−	5.92867i	−0.0102839	−	0.189675i	0.988878	−	0.148732i	$-0.0475191\pi$
$978$	−0.0570441	+	1.05212i	−0.00182407	+	0.0336430i
$979$	59.3975	+	6.45987i	1.89835	+	0.206458i
$980$	−6.84554	+	2.30653i	−0.218673	+	0.0736795i
$981$	5.55836	−	13.9504i	0.177465	−	0.445403i
$982$	2.02934	−	0.446692i	0.0647589	−	0.0142545i
$983$	−14.1703	−	26.7281i	−0.451963	−	0.852493i	−0.999873	−	0.0159555i	$-0.994921\pi$
$983$	−14.1703	−	26.7281i	−0.451963	−	0.852493i	0.547909	−	0.836538i	$-0.315424\pi$
$984$	2.91624	+	1.34919i	0.0929662	+	0.0430108i
$985$	4.88172	+	1.64484i	0.155544	+	0.0524090i
$986$	0.774760	−	0.912118i	0.0246734	−	0.0290478i
$987$	−33.7127	−	20.2843i	−1.07309	−	0.645656i
$988$	−2.25534	−	8.12301i	−0.0717520	−	0.258427i
$989$	−16.0309	−	3.52866i	−0.509752	−	0.112205i
$990$	−0.133187	+	0.196436i	−0.00423296	+	0.00624314i
$991$	9.65975	+	9.15020i	0.306852	+	0.290666i	0.825593	−	0.564266i	$-0.190841\pi$
$991$	9.65975	+	9.15020i	0.306852	+	0.290666i	−0.518741	+	0.854931i	$0.673599\pi$
$992$	2.20200	−	1.32490i	0.0699134	−	0.0420655i
$993$	0.615924	−	3.75697i	0.0195458	−	0.119224i
$994$	−0.331563	−	0.489019i	−0.0105165	−	0.0155107i
$995$	5.13060	+	12.8768i	0.162651	+	0.408223i
$996$	−7.60439	−	8.95258i	−0.240954	−	0.283673i
$997$	−1.81909	−	11.0959i	−0.0576111	−	0.351412i	−0.999864	−	0.0165091i	$-0.994745\pi$
$997$	−1.81909	−	11.0959i	−0.0576111	−	0.351412i	0.942253	−	0.334903i	$-0.108704\pi$
$998$	0.148881	−	0.141027i	0.00471274	−	0.00446414i
$999$	0.738805	−	2.66093i	0.0233747	−	0.0841882i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.2.e.a.85.3	yes	140
3.2	odd	2		531.2.i.c.262.3		140
59.25	even	29	inner	177.2.e.a.25.3	✓	140
177.143	odd	58		531.2.i.c.379.3		140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.e.a.25.3	✓	140	59.25	even	29	inner
177.2.e.a.85.3	yes	140	1.1	even	1	trivial
531.2.i.c.262.3		140	3.2	odd	2
531.2.i.c.379.3		140	177.143	odd	58

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	177.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0877061 - 0.0666724i) q^{2} +(0.468408 - 0.883512i) q^{3} +(-0.531810 + 1.91540i) q^{4} +(0.442982 - 0.419615i) q^{5} +(-0.0178236 - 0.108719i) q^{6} +(2.33019 + 2.74331i) q^{7} +(0.162618 + 0.408142i) q^{8} +(-0.561187 - 0.827689i) q^{9} +O(q^{10})\)	\(q+(0.0877061 - 0.0666724i) q^{2} +(0.468408 - 0.883512i) q^{3} +(-0.531810 + 1.91540i) q^{4} +(0.442982 - 0.419615i) q^{5} +(-0.0178236 - 0.108719i) q^{6} +(2.33019 + 2.74331i) q^{7} +(0.162618 + 0.408142i) q^{8} +(-0.561187 - 0.827689i) q^{9} +(0.0108755 - 0.0663375i) q^{10} +(3.02513 - 1.82016i) q^{11} +(1.44318 + 1.36705i) q^{12} +(0.575044 - 0.848127i) q^{13} +(0.387275 + 0.0852456i) q^{14} +(-0.163238 - 0.587931i) q^{15} +(-3.36515 - 2.02475i) q^{16} +(-0.775943 + 0.913511i) q^{17} +(-0.104404 - 0.0351777i) q^{18} +(-3.75617 - 1.73779i) q^{19} +(0.568150 + 1.07165i) q^{20} +(3.51523 - 0.773760i) q^{21} +(0.143968 - 0.361332i) q^{22} +(2.81680 - 0.949089i) q^{23} +(0.436770 + 0.0475016i) q^{24} +(-0.250538 + 4.62090i) q^{25} +(-0.00611180 - 0.112725i) q^{26} +(-0.994138 + 0.108119i) q^{27} +(-6.49376 + 3.00434i) q^{28} +(-7.21499 - 5.48469i) q^{29} +(-0.0535158 - 0.0406816i) q^{30} +(-1.77855 + 0.822846i) q^{31} +(-1.30368 + 0.141784i) q^{32} +(-0.191137 - 3.52532i) q^{33} +(-0.00714894 + 0.131854i) q^{34} +(2.18337 + 0.237455i) q^{35} +(1.88380 - 0.634728i) q^{36} +(-1.02217 + 2.56546i) q^{37} +(-0.445302 + 0.0980184i) q^{38} +(-0.479975 - 0.905328i) q^{39} +(0.243299 + 0.112562i) q^{40} +(6.93080 + 2.33526i) q^{41} +(0.256718 - 0.302232i) q^{42} +(-4.73188 - 2.84708i) q^{43} +(1.87755 + 6.76233i) q^{44} +(-0.595906 - 0.131169i) q^{45} +(0.183772 - 0.271044i) q^{46} +(-7.93582 - 7.51721i) q^{47} +(-3.36515 + 2.02475i) q^{48} +(-0.963497 + 5.87707i) q^{49} +(0.286113 + 0.421985i) q^{50} +(0.443639 + 1.11345i) q^{51} +(1.31869 + 1.55248i) q^{52} +(-1.55014 - 9.45546i) q^{53} +(-0.0799834 + 0.0757643i) q^{54} +(0.576312 - 2.07569i) q^{55} +(-0.740727 + 1.39716i) q^{56} +(-3.29478 + 2.50463i) q^{57} -0.998476 q^{58} +(-4.40030 + 6.29582i) q^{59} +1.21294 q^{60} +(2.38339 - 1.81180i) q^{61} +(-0.101129 + 0.190749i) q^{62} +(0.962936 - 3.46818i) q^{63} +(5.59755 - 5.30228i) q^{64} +(-0.101152 - 0.617002i) q^{65} +(-0.251805 - 0.296448i) q^{66} +(-2.67693 - 6.71858i) q^{67} +(-1.33709 - 1.97206i) q^{68} +(0.480880 - 2.93324i) q^{69} +(0.207326 - 0.124744i) q^{70} +(-1.08168 - 1.02462i) q^{71} +(0.246555 - 0.363641i) q^{72} +(13.9795 + 3.07713i) q^{73} +(0.0813946 + 0.293157i) q^{74} +(3.96527 + 2.38582i) q^{75} +(5.32614 - 6.27042i) q^{76} +(12.0424 + 4.05755i) q^{77} +(-0.102457 - 0.0474017i) q^{78} +(0.722413 + 1.36261i) q^{79} +(-2.34032 + 0.515143i) q^{80} +(-0.370138 + 0.928977i) q^{81} +(0.763571 - 0.257277i) q^{82} +(-5.87437 - 0.638876i) q^{83} +(-0.387368 + 7.14458i) q^{84} +(0.0395939 + 0.730266i) q^{85} +(-0.604836 + 0.0657798i) q^{86} +(-8.22535 + 3.80545i) q^{87} +(1.23483 + 0.938690i) q^{88} +(13.4725 + 10.2416i) q^{89} +(-0.0610100 + 0.0282262i) q^{90} +(3.66664 - 0.398771i) q^{91} +(0.319891 + 5.90004i) q^{92} +(-0.106095 + 1.95680i) q^{93} +(-1.19721 - 0.130205i) q^{94} +(-2.39312 + 0.806336i) q^{95} +(-0.485387 + 1.21823i) q^{96} +(9.58132 - 2.10901i) q^{97} +(0.307334 + 0.579693i) q^{98} +(-3.20419 - 1.48242i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - q^{2} - 5 q^{3} - 9 q^{4} - 2 q^{5} - q^{6} - 2 q^{7} - 9 q^{8} - 5 q^{9}+O(q^{10}) \) 140 * q - q^2 - 5 * q^3 - 9 * q^4 - 2 * q^5 - q^6 - 2 * q^7 - 9 * q^8 - 5 * q^9	\( 140 q - q^{2} - 5 q^{3} - 9 q^{4} - 2 q^{5} - q^{6} - 2 q^{7} - 9 q^{8} - 5 q^{9} + 88 q^{10} - 14 q^{11} - 9 q^{12} - 12 q^{13} - q^{14} - 2 q^{15} - 41 q^{16} - 16 q^{17} - q^{18} - 10 q^{19} - 32 q^{20} + 27 q^{21} - 26 q^{22} - 22 q^{23} - 9 q^{24} + 27 q^{25} - 56 q^{26} - 5 q^{27} - 50 q^{28} - 24 q^{29} - 28 q^{30} - 24 q^{31} + 106 q^{32} - 14 q^{33} - 54 q^{34} - 70 q^{35} - 9 q^{36} - 28 q^{37} - 80 q^{38} - 12 q^{39} - 50 q^{40} - 40 q^{41} - 30 q^{42} + 4 q^{43} - 104 q^{44} - 2 q^{45} - 28 q^{46} + 31 q^{47} - 41 q^{48} - q^{49} + 39 q^{50} - 16 q^{51} + 62 q^{52} + 4 q^{53} - q^{54} + 5 q^{55} + 96 q^{56} - 10 q^{57} + 128 q^{58} - q^{59} - 32 q^{60} - 16 q^{61} + 223 q^{62} - 2 q^{63} + 97 q^{64} + 121 q^{65} - 26 q^{66} - 12 q^{67} + 10 q^{68} + 36 q^{69} - 2 q^{70} - 22 q^{71} - 9 q^{72} + 179 q^{73} - 38 q^{74} - 31 q^{75} + 112 q^{76} - 62 q^{77} - 56 q^{78} - 84 q^{79} + 204 q^{80} - 5 q^{81} - 152 q^{82} - 88 q^{83} + 95 q^{84} - 118 q^{85} - 118 q^{86} + 34 q^{87} + 18 q^{88} - 86 q^{89} - 28 q^{90} + 78 q^{91} - 174 q^{92} - 24 q^{93} - 164 q^{94} + 218 q^{95} - 39 q^{96} - 84 q^{97} + 129 q^{98} - 14 q^{99}+O(q^{100}) \) 140 * q - q^2 - 5 * q^3 - 9 * q^4 - 2 * q^5 - q^6 - 2 * q^7 - 9 * q^8 - 5 * q^9 + 88 * q^10 - 14 * q^11 - 9 * q^12 - 12 * q^13 - q^14 - 2 * q^15 - 41 * q^16 - 16 * q^17 - q^18 - 10 * q^19 - 32 * q^20 + 27 * q^21 - 26 * q^22 - 22 * q^23 - 9 * q^24 + 27 * q^25 - 56 * q^26 - 5 * q^27 - 50 * q^28 - 24 * q^29 - 28 * q^30 - 24 * q^31 + 106 * q^32 - 14 * q^33 - 54 * q^34 - 70 * q^35 - 9 * q^36 - 28 * q^37 - 80 * q^38 - 12 * q^39 - 50 * q^40 - 40 * q^41 - 30 * q^42 + 4 * q^43 - 104 * q^44 - 2 * q^45 - 28 * q^46 + 31 * q^47 - 41 * q^48 - q^49 + 39 * q^50 - 16 * q^51 + 62 * q^52 + 4 * q^53 - q^54 + 5 * q^55 + 96 * q^56 - 10 * q^57 + 128 * q^58 - q^59 - 32 * q^60 - 16 * q^61 + 223 * q^62 - 2 * q^63 + 97 * q^64 + 121 * q^65 - 26 * q^66 - 12 * q^67 + 10 * q^68 + 36 * q^69 - 2 * q^70 - 22 * q^71 - 9 * q^72 + 179 * q^73 - 38 * q^74 - 31 * q^75 + 112 * q^76 - 62 * q^77 - 56 * q^78 - 84 * q^79 + 204 * q^80 - 5 * q^81 - 152 * q^82 - 88 * q^83 + 95 * q^84 - 118 * q^85 - 118 * q^86 + 34 * q^87 + 18 * q^88 - 86 * q^89 - 28 * q^90 + 78 * q^91 - 174 * q^92 - 24 * q^93 - 164 * q^94 + 218 * q^95 - 39 * q^96 - 84 * q^97 + 129 * q^98 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more